Edit Profile Golub, Gene Howard Compute Distance To: Compute Author ID: golub.gene-h Published as: Golub, G.; Golub, G. H.; Golub, Gene; Golub, Gene H. External Links: MGP · Wikidata · dblp · GND · MacTutor Documents Indexed: 265 Publications since 1961, including 22 Books Biographic References: 5 Publications all top 5 Co-Authors 19 single-authored 10 Van Loan, Charles Francis 9 Boley, Daniel L. 8 Bai, Zhongzhi 8 Concus, Paul 7 Gander, Walter 7 Meurant, Gérard A. 7 Milanfar, Peyman 7 O’Leary, Dianne P. 6 Calvetti, Daniela 6 Elhay, Sylvan 6 Elman, Howard C. 6 Reichel, Lothar 5 Chan, Tony Fan-Cheong 5 Chu, Moody T. 5 Kautsky, Jaroslav 5 Law, Kincho H. 5 Plemmons, Robert James 5 Van Dooren, Paul M. 5 von Matt, Urs 5 Zha, Hongyuan 4 Arbenz, Peter 4 Bartels, Richard Harold 4 Benzi, Michele 4 Greif, Chen 4 Ortega, James M. 4 Van Barel, Marc 4 Vandebril, Raf 4 Varah, James M. 4 Zhang, Tong 3 Bai, Zhaojun 3 Bertaccini, Daniele 3 Chandrasekaran, Shivkumar 3 Fischer, Bernd 3 Funderlic, Robert E. 3 Gu, Ming 3 Hansen, Per Christian 3 LeVeque, Randall J. 3 Luk, Franklin T. 3 Nash, Stephen G. 3 Ng, Michael Kwok-Po 3 Overton, Michael L. 3 Saunders, Michael A. 3 Sayed, Ali H. 3 Serra-Capizzano, Stefano 3 Strebel, Rolf 3 Van der Vorst, Henk Albertus 3 Wathen, Andrew John 3 Wilkinson, James Hardy 3 Ye, Qiang 2 Berry, Michael W. 2 Björck, Åke 2 Buzbee, Billy L. 2 Chang, Xiaowen 2 Cuyt, Annie A. M. 2 Dahlquist, Germund 2 de Boor, Carl 2 De Moor, Bart L. R. 2 Elad, Michael 2 Fierro, Ricardo D. 2 Fischer, Dennis 2 Gutknecht, Martin H. 2 Hald, Ole Hansen 2 Kågström, Bo 2 Lee, Chris P. 2 Leiva, Carlos 2 Li, Chi-Kwong 2 Liao, Li-Zhi 2 Mastronardi, Nicola 2 Mulet, Pep 2 Nguyen, Nhat Linh 2 Pereyra, Victor D. 2 Ram, Yitshak M. 2 Seneta, Eugene 2 Sølna, Knut 2 Tang, Wei-Pai 2 Underwood, Richard 2 Varga, Richard Steven 2 Verdonk, Brigitte M. 2 Widlund, Olof B. 2 Wu, Xiaonan 2 Yuan, Jin Yun 2 Zenios, Stefanos A. 2 Zhang, Zhenyue 1 Andersson, Lars-Erik 1 Baglama, James 1 Beckermann, Bernhard 1 Botchev, Mike A. 1 Boutry, Gregory 1 Brent, Richard Peirce 1 Businger, P. A. 1 Carey, Cheryl M. M. 1 Cecilio, W. A. G. 1 Chan, Raymond Hon-Fu 1 Chu, Delin 1 Cline, Alan K. 1 Comon, Pierre 1 Cottle, Richard W. 1 Cuminato, José Alberto 1 Dorr, Fred W. 1 Drexler, Michael ...and 96 more Co-Authors all top 5 Serials 28 SIAM Journal on Matrix Analysis and Applications 16 BIT 15 Numerische Mathematik 15 Linear Algebra and its Applications 14 SIAM Journal on Scientific Computing 13 Mathematics of Computation 11 Numerical Algorithms 8 SIAM Journal on Numerical Analysis 5 Journal of Computational and Applied Mathematics 5 SIAM Review 4 SIAM Journal on Scientific and Statistical Computing 3 Systems & Control Letters 3 Communications of the ACM 3 Numerical Linear Algebra with Applications 2 Bulletin of the Australian Mathematical Society 2 IMA Journal of Numerical Analysis 2 Inverse Problems 2 Calcolo 2 Journal of Econometrics 2 Bulletin of the Belgian Mathematical Society - Simon Stevin 2 IEEE Transactions on Image Processing 2 Internet Mathematics 2 Acta Numerica 2 Johns Hopkins Series in the Mathematical Sciences 1 The American Statistician 1 Computers & Mathematics with Applications 1 Computer Methods in Applied Mechanics and Engineering 1 International Journal for Numerical Methods in Fluids 1 Journal of Computational Physics 1 Journal of Mathematical Analysis and Applications 1 Rocky Mountain Journal of Mathematics 1 ZAMP. Zeitschrift für angewandte Mathematik und Physik 1 ACM Transactions on Mathematical Software 1 Aplikace Matematiky 1 Applied Mathematics and Optimization 1 Computing 1 IEEE Transactions on Automatic Control 1 IEEE Transactions on Computers 1 International Journal for Numerical Methods in Engineering 1 Journal of the American Statistical Association 1 Technometrics 1 SIAM Journal on Algebraic and Discrete Methods 1 Applied Numerical Mathematics 1 IEEE Transactions on Signal Processing 1 IEEE Transactions on Circuits and Systems. II: Analog and Digital Signal Processing 1 Journal of Statistical Computation and Simulation 1 Mitteilungen der Mathematischen Gesellschaft in Hamburg 1 ETNA. Electronic Transactions on Numerical Analysis 1 Annals of Numerical Mathematics 1 Journal of the Society for Industrial & Applied Mathematics 1 BIT. Nordisk Tidskrift for Informationsbehandling 1 Berliner Studienreihe zur Mathematik 1 The IMA Volumes in Mathematics and its Applications 1 ISNM. International Series of Numerical Mathematics 1 MAA Studies in Mathematics 1 NATO ASI Series. Series F. Computer and Systems Sciences 1 Texts and Readings in Mathematics 1 Annals of Mathematical Statistics 1 Journal of the Society for Industrial and Applied Mathematics. Series B, Numerical Analysis 1 Numerical Mathematics and Scientific Computation 1 Princeton Series in Applied Mathematics all top 5 Fields 215 Numerical analysis (65-XX) 54 Linear and multilinear algebra; matrix theory (15-XX) 26 Partial differential equations (35-XX) 20 Statistics (62-XX) 18 Computer science (68-XX) 11 History and biography (01-XX) 10 General and overarching topics; collections (00-XX) 9 Operations research, mathematical programming (90-XX) 8 Approximations and expansions (41-XX) 6 Fluid mechanics (76-XX) 5 Special functions (33-XX) 5 Ordinary differential equations (34-XX) 5 Probability theory and stochastic processes (60-XX) 5 Systems theory; control (93-XX) 4 Integral transforms, operational calculus (44-XX) 4 Geophysics (86-XX) 3 Information and communication theory, circuits (94-XX) 2 Harmonic analysis on Euclidean spaces (42-XX) 2 Mechanics of deformable solids (74-XX) 1 Functions of a complex variable (30-XX) 1 Differential geometry (53-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH 234 Publications have been cited 16,313 times in 11,495 Documents Cited by ▼ Year ▼ Matrix computations. 3rd ed. Zbl 0865.65009Golub, Gene; Van Loan, Charles F. 3,151 1996 Matrix computations. 2nd ed. Zbl 0733.65016Golub, Gene H.; Van Loan, Charles F. 1,489 1989 Matrix computations. Zbl 0559.65011Golub, Gene H.; Van Loan, Charles F. 931 1983 Numerical solution of saddle point problems. Zbl 1115.65034Benzi, Michele; Golub, Gene H.; Liesen, Jörg 757 2005 Matrix computations. 4th ed. Zbl 1268.65037Golub, Gene H.; Van Loan, Charles F. 668 2013 Hermitian and skew-Hermitian splitting methods for non-Hermitian positive definite linear systems. Zbl 1036.65032Bai, Zhong-Zhi; Golub, Gene H.; Ng, Michael K. 511 2003 Generalized cross-validation as a method for choosing a good ridge parameter. Zbl 0461.62059Golub, Gene H.; Heath, Michael; Wahba, Grace 336 1979 Calculation of Gauss quadrature rules. Zbl 0179.21901Golub, Gene H.; Welsch, John H. 303 1969 Preconditioned Hermitian and skew-Hermitian splitting methods for non-Hemitian positive semidefinite linear systems. Zbl 1056.65025Bai, Zhongzhi; Golub, Gene H.; Pan, Jianyu 302 2004 Accelerated Hermitian and skew-Hermitian splitting iteration methods for saddle-point problems. Zbl 1134.65022Bai, Zhongzhi; Golub, Gene H. 228 2007 A Hessenberg-Schur method for the problem AX+XB=C. Zbl 0421.65022Golub, Gene H.; Nash, S.; Van Loan, Charles F. 222 1979 Matrix computations. 3rd ed. Zbl 1118.65316Golub, Gene; Van Loan, Charles F. 221 2007 Calculating the singular values and pseudo-inverse of a matrix. Zbl 0194.18201Golub, G.; Kahan, W. 216 1965 A preconditioner for generalized saddle point problems. Zbl 1082.65034Benzi, Michele; Golub, Gene H. 212 2004 Inexact and preconditioned Uzawa algorithms for saddle point problems. Zbl 0815.65041Elman, Howard C.; Golub, Gene H. 209 1994 On direct methods for solving Poisson’s equations. Zbl 0217.52902Buzbee, B. L.; Golub, G. H.; Nielson, C. W. 188 1970 A note on preconditioning for indefinite linear systems. Zbl 0959.65063Murphy, Malcolm F.; Golub, Gene H.; Wathen, Andrew J. 182 2000 Block triangular and skew-Hermitian splitting methods for positive-definite linear systems. Zbl 1079.65028Bai, Zhong-Zhi; Golub, Gene H.; Lu, Lin-Zhang; Yin, Jun-Feng 180 2005 A nonlinear primal-dual method for total variation-based image restoration. Zbl 0929.68118Chan, Tony F.; Golub, Gene H.; Mulet, Pep 167 1999 Some modified matrix eigenvalue problems. Zbl 0254.65027Golub, Gene H. 161 1973 The differentiation of pseudo-inverses and nonlinear least squares problems whose variables separate. Zbl 0258.65045Golub, G. H.; Pereyra, V. 159 1973 An analysis of the total least squares problem. Zbl 0468.65011Golub, Gene H.; Van Loan, Charles F. 153 1980 Singular value decomposition and least squares solutions. Zbl 0181.17602Golub, G. H.; Reinsch, C. 146 1970 SOR-like methods for augmented systems. Zbl 0991.65036Golub, Gene H.; Wu, X.; Yuan, Jin-Yun 140 2001 Symmetric tensors and symmetric tensor rank. Zbl 1181.15014Comon, Pierre; Golub, Gene; Lim, Lek-Heng; Mourrain, Bernard 126 2008 Convergence properties of preconditioned Hermitian and skew-Hermitian splitting methods for non-Hermitian positive semidefinite matrices. Zbl 1114.65034Bai, Zhong-Zhi; Golub, Gene H.; Li, Chi-Kwong 126 2007 Chebyshev semi-iterative methods, successive overrelaxation iterative methods, and second order Richardson iterative methods. I, II. Zbl 0099.10903Golub, Gene H.; Varga, Richard S. 121 1961 Numerical methods for solving linear least squares problems. Zbl 0142.11502Golub, G. 120 1965 Rank-one approximation to high order tensors. Zbl 1001.65036Zhang, Tong; Golub, Gene H. 117 2001 Optimal parameter in Hermitian and skew-Hermitian splitting method for certain two-by-two block matrices. Zbl 1116.65039Bai, Zhong-Zhi; Golub, Gene H.; Li, Chi-Kwong 114 2006 Methods for modifying matrix factorizations. Zbl 0289.65021Gill, P. E.; Golub, G. H.; Murray, W.; Saunders, M. A. 114 1974 On inexact Hermitian and skew-Hermitian splitting methods for non-Hermitian positive definite linear systems. Zbl 1135.65016Bai, Zhong-Zhi; Golub, Gene H.; Ng, Michael K. 111 2008 On successive-overrelaxation acceleration of the Hermitian and skew-Hermitian splitting iterations. Zbl 1199.65097Bai, Zhong-Zhi; Golub, Gene H.; Ng, Michael K. 103 2007 Block preconditioning for the conjugate gradient method. Zbl 0556.65022Concus, P.; Golub, G. H.; Meurant, G. 95 1985 Numerical methods for computing angles between linear subspaces. Zbl 0282.65031Björck, Åke; Golub, Gene H. 94 1973 Handbook series linear algebra. Linear least squares solutions by Householder transformations. Zbl 0142.11503Businger, P.; Golub, G. H. 93 1965 A survey of matrix inverse eigenvalue problems. Zbl 0633.65036Boley, Daniel; Golub, Gene H. 87 1987 Inverse eigenvalue problems: theory, algorithms, and applications. Zbl 1075.65058Chu, Moody T.; Golub, Gene H. 80 2005 Separable nonlinear least squares: The variable projection method and its applications. Zbl 1022.65014Golub, Gene; Pereyra, Victor 80 2003 Matrices, moments and quadrature with applications. Zbl 1217.65056Golub, Gene H.; Meurant, Gérard 79 2010 The direct solution of the discrete Poisson equation on irregular regions. Zbl 0231.65083Buzbee, B. L.; Dorr, F. W.; George, J. A.; Golub, G. H. 79 1971 Numerical solution of nonlinear elliptic partial differential equations by a generalized conjugate gradient method. Zbl 0385.65048Concus, P.; Golub, G. H.; O’Leary, D. P. 77 1978 Structured inverse eigenvalue problems. Zbl 1105.65326Chu, Moody T.; Golub, Gene H. 75 2002 Tikhonov regularization and total least squares. Zbl 0945.65042Golub, Gene H.; Hansen, Per Christian; O’Leary, Dianne P. 69 1999 The numerically stable reconstruction of a Jacobi matrix from spectral data. Zbl 0388.15010de Boor, C.; Golub, G. H. 68 1978 On solving block-structured indefinite linear systems. Zbl 1036.65033Golub, Gene H.; Greif, Chen 67 2003 Matrices, moments and quadrature. Zbl 0795.65019Golub, G. H.; Meurant, Gerard 65 1994 Iterative solution of linear systems. Zbl 0762.65019Freund, Roland W.; Golub, Gene H.; Nachtigal, Noël M. 63 1992 Ill-conditioned eigensystems and the computation of the Jordan canonical form. Zbl 0341.65027Golub, G. H.; Wilkinson, J. H. 62 1976 Least-squares fitting of circles and ellipses. Zbl 0817.65008Gander, Walter; Golub, Gene H.; Strebel, Rolf 58 1994 Optimization of the Hermitian and skew-Hermitian splitting iteration for saddle-point problems. Zbl 1052.65015Benzi, Michele; Gander, Martin J.; Golub, Gene H. 53 2003 A generalized conjugate gradient method for the numerical solution of elliptic partial differential equations. Zbl 0344.65047Concus, Paul; Golub, Gene H.; O’Leary, Dianne P. 51 1976 An iteration for indefinite systems and its application to the Navier-Stokes equations. Zbl 0912.76053Golub, Gene H.; Wathen, Andrew J. 50 1998 Scientific computing. An introduction with parallel computing. Zbl 0790.65001Golub, Gene; Ortega, James M. 50 1993 The Block Lanczos method for computing eigenvalues. Zbl 0407.68040Golub, G. H.; Underwood, R. 47 1977 Quadratically constrained least squares and quadratic problems. Zbl 0745.65029Golub, Gene H.; von Matt, Urs 46 1991 Adaptive methods for the computation of PageRank. Zbl 1091.68044Kamvar, Sepandar; Haveliwala, Taher; Golub, Gene 45 2004 The simplex method of linear programming using LU decomposition. Zbl 0181.19104Bartels, R. H.; Golub, G. H. 45 1969 Some large-scale matrix computation problems. Zbl 0870.65035Bai, Zhaojun; Fahey, Mark; Golub, Gene 41 1996 Scientific computing and differential equations: an introduction to numerical methods. Rev. ed. Zbl 0749.65041Golub, Gene H.; Ortega, James M. 41 1992 A generalized conjugate gradient method for nonsymmetric systems of linear equations. Zbl 0344.65020Concus, Paul; Golub, Gene H. 41 1976 Preconditioned HSS methods for the solution of non-Hermitian positive definite linear systems and applications to the discrete convection-diffusion equation. Zbl 1068.65041Bertaccini, Daniele; Golub, Gene H.; Serra Capizzano, Stefano; Tablino Possio, Cristina 40 2005 Matrices, moments and quadrature. II: How to compute the norm of the error iterative methods. Zbl 0888.65050Golub, G. H.; Meurant, G. 40 1997 Some history of the conjugate gradient and Lanczos algorithms: 1948-1976. Zbl 0673.65017Golub, Gene H.; O’Leary, Dianne P. 40 1989 An inverse free preconditioned Krylov subspace method for symmetric generalized eigenvalue problems. Zbl 1016.65017Golub, Gene H.; Ye, Qiang 39 2002 A stable numerical method for inverting shape from moments. Zbl 0956.65030Golub, Gene H.; Milanfar, Peyman; Varah, James 39 2000 Calculation of Gauss quadratures with multiple free and fixed knots. Zbl 0525.65010Golub, G. H.; Kautsky, J. 38 1983 An Arnoldi-type algorithm for computing Page Rank. Zbl 1105.65034Golub, G. H.; Greif, C. 37 2006 Estimation of the \(L\)-curve via Lanczos bidiagonalization. Zbl 0945.65044Calvetti, D.; Golub, G. H.; Reichel, L. 37 1999 A generalization of the Eckart-Young-Mirsky matrix approximation theorem. Zbl 0623.15020Golub, G. H.; Hoffman, Alan; Stewart, G. W. 36 1987 A block Lanczos method for computing the singular values and corresponding singular vectors of a matrix. Zbl 0466.65022Golub, Gene H.; Luk, Franklin T.; Overton, Michael L. 36 1981 A constrained eigenvalue problem. Zbl 0666.15006Gander, Walter; Golub, Gene H.; von Matt, Urs 35 1989 Inexact preconditioned conjugate gradient method with inner-outer iteration. Zbl 0955.65022Golub, Gene H.; Ye, Qiang 34 2000 Bounds for the entries of matrix functions with applications to preconditioning. Zbl 0934.65054Benzi, Michele; Golub, Gene H. 34 1999 Adaptively preconditioned GMRES algorithms. Zbl 0954.65026Baglama, J.; Calvetti, D.; Golub, G. H.; Reichel, L. 34 1999 Iterative methods for cyclically reduced non-self-adjoint linear systems. Zbl 0699.65021Elman, Howard C.; Golub, Gene H. 33 1990 Imposing curvature restrictions on flexible functional forms. Zbl 0573.62098Gallant, A. Ronald; Golub, Gene H. 33 1984 On the calculation of Jacobi matrices. Zbl 0512.65030Kautsky, J.; Golub, G. H. 33 1983 On the solution of large, structured linear complementarity problems: the block partitioned case. Zbl 0391.90087Cottle, Richard W.; Golub, Gene H.; Sacher, Richard S. 33 1978 Use of fast direct methods for the efficient numerical solution of nonseparable elliptic equations. Zbl 0245.65043Concus, Paul; Golub, Gene H. 33 1973 Computation of Gauss-Kronrod quadrature rules. Zbl 0947.65022Calvetti, D.; Golub, G. H.; Gragg, W. B.; Reichel, L. 32 2000 First international symposium on domain decomposition methods for partial differential equations (Proceedings, Paris, France, January 7-9, 1987). Zbl 0649.00019Glowinski, Roland (ed.); Golub, Gene (ed.); Meurant, Gérard A. (ed.); Périaux, Jacques (ed.) 32 1988 Matrix computations. Paperback ed., 4th printing. Zbl 0592.65011Golub, Gene H.; Van Loan, Charles F. 32 1985 Note on the iterative refinement of least squares solution. Zbl 0156.16106Golub, G. H.; Wilkinson, J. H. 31 1966 Eigenvalue computation in the 20th century. Zbl 0965.65057Golub, Gene H.; van der Vorst, Henk A. 30 2000 The convergence of inexact Chebyshev and Richardson iterative methods for solving linear systems. Zbl 0661.65033Golub, Gene H.; Overton, Michael L. 29 1988 Generalized cross-validation for large scale problems. Zbl 0878.65032Golub, Gene H.; von Matt, Urs 28 1997 On Fourier-Toeplitz methods for separable elliptic problems. Zbl 0277.65065Fischer, D.; Golub, G.; Hald, O.; Leiva, C.; Widlund, O. 28 1974 A rank-one reduction formula and its applications to matrix factorizations. Zbl 0844.65033Chu, Moody T.; Funderlic, Robert E.; Golub, Gene H. 27 1995 Perturbation analysis of the canonical correlations of matrix pairs. Zbl 0811.15011Golub, Gene H.; Zha, Hongyuan 27 1994 The restricted singular value decomposition: Properties and applications. Zbl 0738.15006De Moor, Bart L. R.; Golub, Gene H. 27 1991 A class of nonsymmetric preconditioners for saddle point problems. Zbl 1104.65038Botchev, Mike A.; Golub, Gene H. 25 2006 Using the QR factorization and group inversion to compute, differentiate, and estimate the sensitivity of stationary probabilities for Markov chains. Zbl 0594.60072Golub, Gene H.; Meyer, Carl D. jun. 25 1986 A bibliography on semiseparable matrices. Zbl 1168.15312Vandebril, R.; Van Barel, M.; Golub, G.; Mastronardi, N. 24 2005 Estimates in quadratic formulas. Zbl 0822.65022Golub, Gene H.; Strakoš, Zdeněk 24 1994 Symmetric-triangular decomposition and its applications. II: Preconditioners for indefinite systems. Zbl 1151.65027Wu, Xiaonan; Golub, Gene H.; Cuminato, José A.; Yuan, Jin Yun 23 2008 On the spectral decomposition of Hermitian matrices modified by low rank perturbations with applications. Zbl 0646.65033Arbenz, Peter; Golub, Gene H. 23 1988 Inexact inverse iteration for generalized eigenvalue problems. Zbl 0984.65032Golub, Gene H.; Ye, Qiang 22 2000 Regularization by truncated total least squares. Zbl 0891.65040Fierro, R. D.; Golub, G. H.; Hansen, P. C.; O’Leary, D. P. 22 1997 Numerical techniques in mathematical programming. Zbl 0228.90030Bartels, R. H.; Golub, G. H.; Saunders, M. A. 22 1970 Matrix computations. 4th ed. Zbl 1268.65037Golub, Gene H.; Van Loan, Charles F. 668 2013 Matrices, moments and quadrature with applications. Zbl 1217.65056Golub, Gene H.; Meurant, Gérard 79 2010 Solving ellipsoid-constrained integer least squares problems. Zbl 1195.65049Chang, Xiao-Wen; Golub, Gene H. 2 2010 The QR algorithm: 50 years later its genesis by John Francis and Vera Kublanovskaya and subsequent developments. Zbl 1169.65032Golub, Gene; Uhlig, Frank 5 2009 A quasi-separable approach to solve the symmetric definite tridiagonal generalized eigenvalue problem. Zbl 1186.65046Vandebril, Raf; Golub, Gene; van Barel, Marc 1 2009 Symmetric tensors and symmetric tensor rank. Zbl 1181.15014Comon, Pierre; Golub, Gene; Lim, Lek-Heng; Mourrain, Bernard 126 2008 On inexact Hermitian and skew-Hermitian splitting methods for non-Hermitian positive definite linear systems. Zbl 1135.65016Bai, Zhong-Zhi; Golub, Gene H.; Ng, Michael K. 111 2008 Symmetric-triangular decomposition and its applications. II: Preconditioners for indefinite systems. Zbl 1151.65027Wu, Xiaonan; Golub, Gene H.; Cuminato, José A.; Yuan, Jin Yun 23 2008 Continuous methods for symmetric generalized eigenvalue problems. Zbl 1140.65029Gao, Xing-Bao; Golub, Gene H.; Liao, Li-Zhi 8 2008 Approximation of the scattering amplitude and linear systems. Zbl 1188.65032Golub, Gene H.; Stoll, Martin; Wathen, Andy 5 2008 Towards a backward perturbation analysis for data least squares problems. Zbl 1176.65047Chang, X.-W.; Golub, G. H.; Paige, C. C. 2 2008 Accelerated Hermitian and skew-Hermitian splitting iteration methods for saddle-point problems. Zbl 1134.65022Bai, Zhongzhi; Golub, Gene H. 228 2007 Matrix computations. 3rd ed. Zbl 1118.65316Golub, Gene; Van Loan, Charles F. 221 2007 Convergence properties of preconditioned Hermitian and skew-Hermitian splitting methods for non-Hermitian positive semidefinite matrices. Zbl 1114.65034Bai, Zhong-Zhi; Golub, Gene H.; Li, Chi-Kwong 126 2007 On successive-overrelaxation acceleration of the Hermitian and skew-Hermitian splitting iterations. Zbl 1199.65097Bai, Zhong-Zhi; Golub, Gene H.; Ng, Michael K. 103 2007 On the numerical condition of a generalized Hankel eigenvalue problem. Zbl 1121.65036Beckermann, B.; Golub, G. H.; Labahn, G. 11 2007 Spectral analysis of a preconditioned iterative method for the convection-diffusion equation. Zbl 1140.65024Bertaccini, Daniele; Golub, Gene H.; Serra-Capizzano, Stefano 10 2007 A hybrid approach combining Chebyshev filter and conjugate gradient for solving linear systems with multiple right-hand sides. Zbl 1151.65319Golub, Gene H.; Ruiz, Daniel; Touhami, Ahmed 6 2007 A two-stage algorithm for computing PageRank and multistage generalizations. Zbl 1221.68041Lee, Chris P.; Golub, Gene H.; Zenios, Stefanos A. 2 2007 A two-stage algorithm for computing pagerank and multistage generalizations. Zbl 1206.68050Lee, Chris P.; Golub, Gene H.; Zenios, Stefanos A. 2 2007 Milestones in matrix computation. The selected works of Gene H. Golub. With commentaries by Anne Greenbaum, Åke Björk, Nicholas Higham, Walter Gautschi and G. W. Stewart. Edited by Raymond H. Chan, Chen Greif, and Dianne P. O’Leary. Zbl 1121.65031Golub, Gene H. 2 2007 Optimal parameter in Hermitian and skew-Hermitian splitting method for certain two-by-two block matrices. Zbl 1116.65039Bai, Zhong-Zhi; Golub, Gene H.; Li, Chi-Kwong 114 2006 An Arnoldi-type algorithm for computing Page Rank. Zbl 1105.65034Golub, G. H.; Greif, C. 37 2006 A class of nonsymmetric preconditioners for saddle point problems. Zbl 1104.65038Botchev, Mike A.; Golub, Gene H. 25 2006 An algebraic analysis of a block diagonal preconditioner for saddle point systems. Zbl 1105.65048Golub, Gene H.; Greif, Chen; Varah, James M. 13 2006 Continuous methods for extreme and interior eigenvalue problems. Zbl 1092.65029Golub, Gene H.; Liao, Li-Zhi 12 2006 On a generalized eigenvalue problem for nonsquare pencils. Zbl 1128.15004Chu, Delin; Golub, Gene H. 7 2006 Some observations on local least squares. Zbl 1103.65041Bartels, R. H.; Golub, G. H.; Samavati, F. F. 1 2006 Numerical solution of saddle point problems. Zbl 1115.65034Benzi, Michele; Golub, Gene H.; Liesen, Jörg 757 2005 Block triangular and skew-Hermitian splitting methods for positive-definite linear systems. Zbl 1079.65028Bai, Zhong-Zhi; Golub, Gene H.; Lu, Lin-Zhang; Yin, Jun-Feng 180 2005 Inverse eigenvalue problems: theory, algorithms, and applications. Zbl 1075.65058Chu, Moody T.; Golub, Gene H. 80 2005 Preconditioned HSS methods for the solution of non-Hermitian positive definite linear systems and applications to the discrete convection-diffusion equation. Zbl 1068.65041Bertaccini, Daniele; Golub, Gene H.; Serra Capizzano, Stefano; Tablino Possio, Cristina 40 2005 A bibliography on semiseparable matrices. Zbl 1168.15312Vandebril, R.; Van Barel, M.; Golub, G.; Mastronardi, N. 24 2005 The generalized eigenvalue problem for nonsquare pencils using a minimal perturbation approach. Zbl 1100.65035Boutry, Gregory; Elad, Michael; Golub, Gene H.; Milanfar, Peyman 10 2005 Multidimensional integral inversion, with applications in shape reconstruction. Zbl 1099.65128Cuyt, Annie; Golub, Gene; Milanfar, Peyman; Verdonk, Brigitte 8 2005 How to deduce a proper eigenvalue cluster from a proper singular value cluster in the nonnormal case. Zbl 1088.65031Serra-Capizzano, Stefano; Bertaccini, Daniele; Golub, Gene H. 7 2005 A bibliography on semiseparable matrices. Zbl 1168.15306Van Barel, Marc; Vandebril, Raf; Golub, G.; Mastronardi, Nicola 4 2005 A subspace approximation method for the quadratic eigenvalue problem. Zbl 1079.65039Holz, U. B.; Golub, G. H.; Law, K. H. 3 2005 Preconditioned Hermitian and skew-Hermitian splitting methods for non-Hemitian positive semidefinite linear systems. Zbl 1056.65025Bai, Zhongzhi; Golub, Gene H.; Pan, Jianyu 302 2004 A preconditioner for generalized saddle point problems. Zbl 1082.65034Benzi, Michele; Golub, Gene H. 212 2004 Adaptive methods for the computation of PageRank. Zbl 1091.68044Kamvar, Sepandar; Haveliwala, Taher; Golub, Gene 45 2004 Regularized total least squares based on quadratic eigenvalue problem solvers. Zbl 1079.65048Sima, Diana M.; Van Huffel, Sabine; Golub, Gene H. 17 2004 Shape from moments – an estimation theory perspective. Zbl 1369.62145Elad, Michael; Milanfar, Peyman; Golub, Gene H. 12 2004 Semi-conjugate direction methods for real positive definite systems. Zbl 1052.65026Yuan, J. Y.; Golub, G. H.; Plemmons, R. J.; Cecilio, W. A. G. 8 2004 Hermitian and skew-Hermitian splitting methods for non-Hermitian positive definite linear systems. Zbl 1036.65032Bai, Zhong-Zhi; Golub, Gene H.; Ng, Michael K. 511 2003 Separable nonlinear least squares: The variable projection method and its applications. Zbl 1022.65014Golub, Gene; Pereyra, Victor 80 2003 On solving block-structured indefinite linear systems. Zbl 1036.65033Golub, Gene H.; Greif, Chen 67 2003 Optimization of the Hermitian and skew-Hermitian splitting iteration for saddle-point problems. Zbl 1052.65015Benzi, Michele; Gander, Martin J.; Golub, Gene H. 53 2003 Scaling by binormalization. Zbl 1050.65049Livne, Oren E.; Golub, Gene H. 5 2003 The spectrum of a modified linear pencil. Zbl 1054.65033Elhay, S.; Golub, G. H.; Ram, Y. M. 2 2003 Structured inverse eigenvalue problems. Zbl 1105.65326Chu, Moody T.; Golub, Gene H. 75 2002 An inverse free preconditioned Krylov subspace method for symmetric generalized eigenvalue problems. Zbl 1016.65017Golub, Gene H.; Ye, Qiang 39 2002 Symmetric-triangular decomposition and its applications. I: Theorems and algorithms. Zbl 1017.65020Golub, Gene H.; Yuan, Jin-Yun 13 2002 Block orderings for tensor-product grids in two and three dimensions. Zbl 1002.65041Golub, Gene H.; Greif, Chen; Varah, James M. 4 2002 SOR-like methods for augmented systems. Zbl 0991.65036Golub, Gene H.; Wu, X.; Yuan, Jin-Yun 140 2001 Rank-one approximation to high order tensors. Zbl 1001.65036Zhang, Tong; Golub, Gene H. 117 2001 From numerical analysis to computational science. Zbl 1047.65504Engquist, Björn; Golub, Gene 16 2001 Efficient generalized cross-validation with applications to parametric image restoration and resolution enhancement. Zbl 1037.68784Nguyen, Nhat; Milanfar, Peyman; Golub, Gene 13 2001 A computationally efficient superresolution image reconstruction algorithm. Zbl 1040.68567Nguyen, Nhat; Milanfar, Peyman; Golub, Gene 11 2001 A parallel balance scheme for banded linear systems. Zbl 1055.65044Golub, Gene H.; Sameh, Ahmed H.; Sarin, Vivek 5 2001 A note on preconditioning for indefinite linear systems. Zbl 0959.65063Murphy, Malcolm F.; Golub, Gene H.; Wathen, Andrew J. 182 2000 A stable numerical method for inverting shape from moments. Zbl 0956.65030Golub, Gene H.; Milanfar, Peyman; Varah, James 39 2000 Inexact preconditioned conjugate gradient method with inner-outer iteration. Zbl 0955.65022Golub, Gene H.; Ye, Qiang 34 2000 Computation of Gauss-Kronrod quadrature rules. Zbl 0947.65022Calvetti, D.; Golub, G. H.; Gragg, W. B.; Reichel, L. 32 2000 Eigenvalue computation in the 20th century. Zbl 0965.65057Golub, Gene H.; van der Vorst, Henk A. 30 2000 Inexact inverse iteration for generalized eigenvalue problems. Zbl 0984.65032Golub, Gene H.; Ye, Qiang 22 2000 On the preconditioning of matrices with skew-symmetric splittings. Zbl 0983.65041Golub, Gene H.; Vanderstraeten, Denis 21 2000 Large sparse symmetric eigenvalue problems with homogeneous linear constraints: The Lanczos process with inner-outer iterations. Zbl 0948.65033Golub, Gene H.; Zhang, Zhenyue; Zha, Hongyuan 13 2000 Computing the SVD of a general matrix product/quotient. Zbl 0969.65032Golub, Gene; Sølna, Knut; Van Dooren, Paul 8 2000 A nonlinear primal-dual method for total variation-based image restoration. Zbl 0929.68118Chan, Tony F.; Golub, Gene H.; Mulet, Pep 167 1999 Tikhonov regularization and total least squares. Zbl 0945.65042Golub, Gene H.; Hansen, Per Christian; O’Leary, Dianne P. 69 1999 Estimation of the \(L\)-curve via Lanczos bidiagonalization. Zbl 0945.65044Calvetti, D.; Golub, G. H.; Reichel, L. 37 1999 Bounds for the entries of matrix functions with applications to preconditioning. Zbl 0934.65054Benzi, Michele; Golub, Gene H. 34 1999 Adaptively preconditioned GMRES algorithms. Zbl 0954.65026Baglama, J.; Calvetti, D.; Golub, G. H.; Reichel, L. 34 1999 On some eigenvector-eigenvalue relations. Zbl 0929.15008Elhay, S.; Gladwell, G. M. L.; Golub, G. H.; Ram, Y. M. 9 1999 An efficient algorithm for a bounded errors-in-variables model. Zbl 0957.65070Chandrasekaran, S.; Golub, G. H.; Gu, M.; Sayed, A. H. 8 1999 Subspace iterative methods for eigenvalue problems. Zbl 0932.65044Zhang, T.; Golub, G. H.; Law, K. H. 2 1999 A computable error bound for matrix functionals. Zbl 0937.65054Calvetti, D.; Golub, G. H.; Reichel, L. 1 1999 An iteration for indefinite systems and its application to the Navier-Stokes equations. Zbl 0912.76053Golub, Gene H.; Wathen, Andrew J. 50 1998 Tikhonov regularization for large scale problems. Zbl 0927.65058Golub, Gene H.; von Matt, Urs 20 1998 Solution of biharmonic equations with application to radar imaging. Zbl 0933.65128Andersson, Lars-Erik; Elfving, Tommy; Golub, Gene H. 14 1998 Parameter estimation in the presence of bounded data uncertainties. Zbl 0914.65147Chandrasekaran, S.; Golub, G. H.; Gu, M.; Sayed, A. H. 14 1998 Rank modifications of semidefinite matrices associated with a secant update formula. Zbl 0922.65031Chu, Moody T.; Funderlic, R. E.; Golub, Gene H. 9 1998 A fast Poisson solver for the finite difference solution of the incompressible Navier-Stokes equations. Zbl 0957.76053Golub, Gene H.; Huang, Lan Chieh; Simon, Horst; Tang, Wei-Pai 9 1998 On the homotopy method for perturbed symmetric generalized eigenvalue problems. Zbl 0917.65035Zhang, T.; Law, K. H.; Golub, G. H. 7 1998 Inner and outer iterations for the Chebyshev algorithm. Zbl 0911.65024Giladi, Eldar; Golub, Gene H.; Keller, Joseph B. 6 1998 Cyclic reduction – history and applications. Zbl 0921.65023Gander, Walter; Golub, Gene H. 4 1998 Scientific computing, WSC ’97. Proceedings of the workshop held in Hong Kong, March 10–12, 1997. Zbl 0910.00057Golub, Gene H. (ed.); Shui-Hong, Lui (ed.); Luk, Franklin T. (ed.); Plemmons, Robert James (ed.) 2 1998 Eigenvalue perturbation and generalized Krylov subspace method. Zbl 0931.65039Zhang, T.; Golub, G. H.; Law, K. H. 1 1998 Efficient solution of the Jacobian system in Newton’s method close to a root. Zbl 0921.65039Drexler, Michael; Golub, Gene H. 1 1998 Matrices, moments and quadrature. II: How to compute the norm of the error iterative methods. Zbl 0888.65050Golub, G. H.; Meurant, G. 40 1997 Generalized cross-validation for large scale problems. Zbl 0878.65032Golub, Gene H.; von Matt, Urs 28 1997 Regularization by truncated total least squares. Zbl 0891.65040Fierro, R. D.; Golub, G. H.; Hansen, P. C.; O’Leary, D. P. 22 1997 Bounds for the trace of the inverse and the determinant of symmetric positive definite matrices. Zbl 0883.15013Bai, Zhaojun; Golub, Gene H. 13 1997 Closer to the solution: Iterative linear solvers. Zbl 0881.65025Golub, Gene H.; van der Vorst, Henk A. 11 1997 On a variational formulation of the generalized singular value decomposition. Zbl 0891.65038Chu, Moody T.; Funderlic, Robert. E.; Golub, Gene H. 10 1997 150 years old and still alive: Eigenproblems. Zbl 0881.65026van der Vorst, Henk A.; Golub, Gene H. 10 1997 Efficient algorithms for least squares type problems with bounded uncertainties. Zbl 0892.62038Chandrasekaran, Shivkumar; Golub, Gene H.; Gu, Ming; Sayed, Ali H. 4 1997 Matrix computations. 3rd ed. Zbl 0865.65009Golub, Gene; Van Loan, Charles F. 3,151 1996 Some large-scale matrix computation problems. Zbl 0870.65035Bai, Zhaojun; Fahey, Mark; Golub, Gene 41 1996 ...and 134 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 14,492 Authors 110 Reichel, Lothar 98 Wei, Yimin 71 Bai, Zhongzhi 69 Huang, Ting-Zhu 69 Jódar Sanchez, Lucas Antonio 65 Pan, Victor Yakovlevich 64 Golub, Gene Howard 61 Ma, Changfeng 57 Zhang, Guofeng 47 Benner, Peter 42 Evans, David John 41 Serra-Capizzano, Stefano 38 Van Barel, Marc 37 Ng, Michael Kwok-Po 37 Van Dooren, Paul M. 35 Axelsson, Axel Owe Holger 35 Lin, Wen-Wei 35 Mehrmann, Volker 34 Dehghan Takht Fooladi, Mehdi 34 Khojasteh Salkuyeh, Davod 33 Cao, Yang 33 Simoncini, Valeria 33 Van Huffel, Sabine 32 Benzi, Michele 31 Liang, Zhao-Zheng 29 Wu, Shiliang 28 Jbilou, Khalide 28 Wei, Musheng 28 Wu, Yujiang 27 Jia, Zhongxiao 27 Li, Cuixia 27 Li, Rencang 27 Qi, Liqun 26 Milovanović, Gradimir V. 25 Jin, Xiaoqing 25 Saad, Yousef 25 Sadkane, Miloud 25 Yang, Aili 24 Bini, Dario Andrea 24 Chen, Guoliang 24 Lin, Yiqin 24 Martínez, José Mario 23 Calvetti, Daniela 23 Hu, Xiyan 23 Lu, Linzhang 22 Dai, Hua 22 Gemignani, Luca 22 Kressner, Daniel 22 Mastronardi, Nicola 22 Vandebril, Raf 22 Wu, Gang 21 Gu, Chuanqing 21 Hansen, Per Christian 21 Huang, Zhengge 21 Li, Wen 21 Nakatsukasa, Yuji 21 Sadok, Hassane 20 Cui, Jingjing 20 Mitrouli, Marilena 20 O’Leary, Dianne P. 20 Plemmons, Robert James 20 Rojo, Oscar L. 20 Verhaegen, Michel 20 Wathen, Andrew John 20 Zhang, Lei 19 Gondzio, Jacek 19 Nagy, James Gerard 19 Neumann, Michael 19 Stoll, Martin 19 Xu, Zhong 19 Ye, Qiang 19 Zheng, Bing 18 Bai, Zhaojun 18 De Moor, Bart L. R. 18 Gautschi, Walter 18 Hadjidimos, Apostolos 18 Li, Zi-Cai 18 Toutounian, Faezeh 17 Bai, Zhengjian 17 Cao, Zhihao 17 Chan, Tony Fan-Cheong 17 Chien, Cheng-Sheng 17 Hajarian, Masoud 17 Higham, Nicholas J. 17 King-wah Chu, Eric 17 Markovsky, Ivan 17 Rodriguez, Giuseppe 17 Vuik, Cornelis 17 Xiang, Hua 17 Zha, Hongyuan 17 Zhang, Jun 17 Zhang, Zhenyue 16 Ballico, Edoardo 16 Barlow, Jesse L. 16 Brezinski, Claude 16 Chan, Raymond Hon-Fu 16 Chen, Ke 16 Chu, Delin 16 Defez, Emilio 16 Ding, Feng ...and 14,392 more Authors all top 5 Cited in 683 Serials 1,064 Linear Algebra and its Applications 815 Journal of Computational and Applied Mathematics 532 Applied Mathematics and Computation 397 Journal of Computational Physics 395 Computers & Mathematics with Applications 310 Numerical Algorithms 276 Numerische Mathematik 273 Computer Methods in Applied Mechanics and Engineering 270 Applied Numerical Mathematics 233 BIT 210 SIAM Journal on Scientific Computing 203 Mathematics of Computation 196 Automatica 192 Numerical Linear Algebra with Applications 189 SIAM Journal on Matrix Analysis and Applications 171 International Journal of Computer Mathematics 122 Computational Statistics and Data Analysis 119 Applied Mathematics Letters 107 Journal of Scientific Computing 89 Computational Optimization and Applications 88 International Journal of Control 87 Computing 85 Pattern Recognition 79 Mathematical Programming. 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Theory and Methods 21 BIT. Nordisk Tidskrift for Informationsbehandling 20 Journal of Fluid Mechanics 20 Statistics & Probability Letters 20 Automation and Remote Control 20 Communications in Statistics. Simulation and Computation 20 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 20 Frontiers of Mathematics in China 20 Science China. Mathematics 19 Neural Computation 19 SIAM Review 19 Abstract and Applied Analysis 19 SIAM/ASA Journal on Uncertainty Quantification 18 Journal of Inequalities and Applications 17 Journal of Engineering Mathematics 17 Applications of Mathematics ...and 583 more Serials all top 5 Cited in 62 Fields 7,304 Numerical analysis (65-XX) 2,312 Linear and multilinear algebra; matrix theory (15-XX) 1,050 Partial differential equations (35-XX) 1,048 Statistics (62-XX) 1,046 Operations research, mathematical programming (90-XX) 899 Computer science (68-XX) 894 Systems theory; control (93-XX) 691 Fluid mechanics (76-XX) 496 Information and communication theory, circuits (94-XX) 467 Mechanics of deformable solids (74-XX) 351 Probability theory and stochastic processes (60-XX) 348 Ordinary differential equations (34-XX) 339 Approximations and expansions (41-XX) 322 Calculus of variations and optimal control; optimization (49-XX) 283 Biology and other natural sciences (92-XX) 219 Operator theory (47-XX) 201 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 170 Combinatorics (05-XX) 166 Quantum theory (81-XX) 155 Optics, electromagnetic theory (78-XX) 151 Harmonic analysis on Euclidean spaces (42-XX) 141 Dynamical systems and ergodic theory (37-XX) 140 Geophysics (86-XX) 131 Special functions (33-XX) 123 Mechanics of particles and systems (70-XX) 110 Statistical mechanics, structure of matter (82-XX) 107 Integral equations (45-XX) 80 Algebraic geometry (14-XX) 80 Functions of a complex variable (30-XX) 79 Real functions (26-XX) 63 Number theory (11-XX) 63 Classical thermodynamics, heat transfer (80-XX) 60 Field theory and polynomials (12-XX) 52 Functional analysis (46-XX) 51 Differential geometry (53-XX) 45 Integral transforms, operational calculus (44-XX) 40 Commutative algebra (13-XX) 36 Difference and functional equations (39-XX) 34 Potential theory (31-XX) 31 Convex and discrete geometry (52-XX) 31 Global analysis, analysis on manifolds (58-XX) 24 Astronomy and astrophysics (85-XX) 23 Geometry (51-XX) 21 History and biography (01-XX) 20 General and overarching topics; collections (00-XX) 17 Group theory and generalizations (20-XX) 15 Measure and integration (28-XX) 12 Several complex variables and analytic spaces (32-XX) 12 Sequences, series, summability (40-XX) 11 General topology (54-XX) 11 Manifolds and cell complexes (57-XX) 9 Topological groups, Lie groups (22-XX) 9 Relativity and gravitational theory (83-XX) 8 Mathematical logic and foundations (03-XX) 8 Associative rings and algebras (16-XX) 6 Mathematics education (97-XX) 5 Nonassociative rings and algebras (17-XX) 5 Algebraic topology (55-XX) 3 Order, lattices, ordered algebraic structures (06-XX) 3 General algebraic systems (08-XX) 3 Abstract harmonic analysis (43-XX) 1 Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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