Edit Profile (opens in new tab) Golub, Gene Howard Compute Distance To: Compute Author ID: golub.gene-h Published as: Golub, Gene H.; Golub, G. H.; Golub, Gene; Golub, G. External Links: MacTutor · MGP · Wikidata · dblp · GND · IdRef Documents Indexed: 257 Publications since 1961, including 14 Books 9 Contributions as Editor Biographic References: 5 Publications Co-Authors: 185 Co-Authors with 243 Joint Publications 5,517 Co-Co-Authors all top 5 Co-Authors 18 single-authored 10 Van Loan, Charles Francis 9 Boley, Daniel L. 8 Bai, Zhongzhi 8 Concus, Paul 8 O’Leary, Dianne P. 7 Gander, Walter 7 Meurant, Gérard A. 7 Milanfar, Peyman 6 Calvetti, Daniela 6 Elhay, Sylvan 6 Elman, Howard C. 6 Reichel, Lothar 5 Chan, Tony Fan-Cheong 5 Chu, Moody T. 5 Greif, Chen 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 Ortega, James M. 4 Van Barel, Marc 4 Vandebril, Raf 4 Varah, James M. 4 Yuan, Jinyun 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 Chan, Raymond Hon-Fu 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 Gautschi, Walter 2 Greenbaum, Anne 2 Gutknecht, Martin H. 2 Hald, Ole Hansen 2 Kågström, Bo 2 Lee, Chris P. 2 Li, Chi-Kwong 2 Liao, Li-Zhi 2 Mastronardi, Nicola 2 Mulet, Pep 2 Ram, Yitshak M. 2 Seneta, Eugene 2 Sølna, Knut 2 Stewart, Gilbert Wright 2 Tang, Wei-Pai 2 Underwood, Richard 2 Varga, Richard Steven 2 Verdonk, Brigitte M. 2 Widlund, Olof B. 2 Wu, Xiaonan 2 Zenios, Stefanos A. 2 Zhang, Zhenyue 1 Andersson, Lars-Erik 1 Baglama, James 1 Beckermann, Bernhard 1 Björk, Åke 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 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 87 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 Collection de la Direction des Études et Recherches d’Électricité de France 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 Proceedings of Symposia in Applied Mathematics 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 216 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 General and overarching topics; collections (00-XX) 11 History and biography (01-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 Open 235 Publications have been cited 16,759 times in 11,760 Documents Cited by ▼ Year ▼ Matrix computations. 3rd ed. Zbl 0865.65009Golub, Gene; Van Loan, Charles F. 3,053 1996 Matrix computations. 2nd ed. Zbl 0733.65016Golub, Gene H.; Van Loan, Charles F. 1,370 1989 Numerical solution of saddle point problems. Zbl 1115.65034Benzi, Michele; Golub, Gene H.; Liesen, Jörg 861 2005 Matrix computations. Zbl 0559.65011Golub, Gene H.; Van Loan, Charles F. 856 1983 Matrix computations. 4th ed. Zbl 1268.65037Golub, Gene H.; Van Loan, Charles F. 832 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. 592 2003 Generalized cross-validation as a method for choosing a good ridge parameter. Zbl 0461.62059Golub, Gene H.; Heath, Michael; Wahba, Grace 386 1979 Preconditioned Hermitian and skew-Hermitian splitting methods for non-Hemitian positive semidefinite linear systems. Zbl 1056.65025Bai, Zhongzhi; Golub, Gene H.; Pan, Jianyu 336 2004 Calculation of Gauss quadrature rules. Zbl 0179.21901Golub, Gene H.; Welsch, John H. 323 1969 Accelerated Hermitian and skew-Hermitian splitting iteration methods for saddle-point problems. Zbl 1134.65022Bai, Zhongzhi; Golub, Gene H. 264 2007 A preconditioner for generalized saddle point problems. Zbl 1082.65034Benzi, Michele; Golub, Gene H. 240 2004 A Hessenberg-Schur method for the problem AX+XB=C. Zbl 0421.65022Golub, Gene H.; Nash, S.; Van Loan, Charles F. 238 1979 Calculating the singular values and pseudo-inverse of a matrix. Zbl 0194.18201Golub, G.; Kahan, W. 238 1965 Inexact and preconditioned Uzawa algorithms for saddle point problems. Zbl 0815.65041Elman, Howard C.; Golub, Gene H. 227 1994 A note on preconditioning for indefinite linear systems. Zbl 0959.65063Murphy, Malcolm F.; Golub, Gene H.; Wathen, Andrew J. 205 2000 On direct methods for solving Poisson’s equations. Zbl 0217.52902Buzbee, B. L.; Golub, G. H.; Nielson, C. W. 203 1970 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 202 2005 A nonlinear primal-dual method for total variation-based image restoration. Zbl 0929.68118Chan, Tony F.; Golub, Gene H.; Mulet, Pep 179 1999 The differentiation of pseudo-inverses and nonlinear least squares problems whose variables separate. Zbl 0258.65045Golub, G. H.; Pereyra, V. 167 1973 An analysis of the total least squares problem. Zbl 0468.65011Golub, Gene H.; Van Loan, Charles F. 165 1980 Some modified matrix eigenvalue problems. Zbl 0254.65027Golub, Gene H. 165 1973 SOR-like methods for augmented systems. Zbl 0991.65036Golub, Gene H.; Wu, X.; Yuan, Jin-Yun 160 2001 Singular value decomposition and least squares solutions. Zbl 0181.17602Golub, G. H.; Reinsch, C. 152 1970 Symmetric tensors and symmetric tensor rank. Zbl 1181.15014Comon, Pierre; Golub, Gene; Lim, Lek-Heng; Mourrain, Bernard 147 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 135 2007 Rank-one approximation to high order tensors. Zbl 1001.65036Zhang, Tong; Golub, Gene H. 131 2001 Numerical methods for solving linear least squares problems. Zbl 0142.11502Golub, G. 128 1965 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. 126 2008 Chebyshev semi-iterative methods, successive overrelaxation iterative methods, and second order Richardson iterative methods. I, II. Zbl 0099.10903Golub, Gene H.; Varga, Richard S. 123 1961 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 120 2006 Methods for modifying matrix factorizations. Zbl 0289.65021Gill, P. E.; Golub, G. H.; Murray, W.; Saunders, M. A. 119 1974 On successive-overrelaxation acceleration of the Hermitian and skew-Hermitian splitting iterations. Zbl 1199.65097Bai, Zhong-Zhi; Golub, Gene H.; Ng, Michael K. 115 2007 Handbook series linear algebra. Linear least squares solutions by Householder transformations. Zbl 0142.11503Businger, P.; Golub, G. H. 101 1965 Numerical methods for computing angles between linear subspaces. Zbl 0282.65031Björck, Åke; Golub, Gene H. 98 1973 A survey of matrix inverse eigenvalue problems. Zbl 0633.65036Boley, Daniel; Golub, Gene H. 97 1987 Block preconditioning for the conjugate gradient method. Zbl 0556.65022Concus, P.; Golub, G. H.; Meurant, G. 94 1985 Inverse eigenvalue problems: theory, algorithms, and applications. Zbl 1075.65058Chu, Moody T.; Golub, Gene H. 92 2005 Matrices, moments and quadrature with applications. Zbl 1217.65056Golub, Gene H.; Meurant, Gérard 85 2010 Tikhonov regularization and total least squares. Zbl 0945.65042Golub, Gene H.; Hansen, Per Christian; O’Leary, Dianne P. 81 1999 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. 81 1971 Separable nonlinear least squares: The variable projection method and its applications. Zbl 1022.65014Golub, Gene; Pereyra, Victor 81 2003 Structured inverse eigenvalue problems. Zbl 1105.65326Chu, Moody T.; Golub, Gene H. 80 2002 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. 76 1978 On solving block-structured indefinite linear systems. Zbl 1036.65033Golub, Gene H.; Greif, Chen 72 2003 The numerically stable reconstruction of a Jacobi matrix from spectral data. Zbl 0388.15010de Boor, C.; Golub, G. H. 69 1978 Ill-conditioned eigensystems and the computation of the Jordan canonical form. Zbl 0341.65027Golub, G. H.; Wilkinson, J. H. 65 1976 Matrices, moments and quadrature. Zbl 0795.65019Golub, G. H.; Meurant, Gerard 64 1994 Least-squares fitting of circles and ellipses. Zbl 0817.65008Gander, Walter; Golub, Gene H.; Strebel, Rolf 59 1994 Optimization of the Hermitian and skew-Hermitian splitting iteration for saddle-point problems. Zbl 1052.65015Benzi, Michele; Gander, Martin J.; Golub, Gene H. 59 2003 Iterative solution of linear systems. Zbl 0762.65019Freund, Roland W.; Golub, Gene H.; Nachtigal, Noël M. 58 1992 Matrix computations. 3rd ed. Zbl 1118.65316Golub, Gene; Van Loan, Charles F. 56 2007 An iteration for indefinite systems and its application to the Navier-Stokes equations. Zbl 0912.76053Golub, Gene H.; Wathen, Andrew J. 54 1998 The Block Lanczos method for computing eigenvalues. Zbl 0407.68040Golub, G. H.; Underwood, R. 53 1977 Scientific computing. An introduction with parallel computing. Zbl 0790.65001Golub, Gene; Ortega, James M. 49 1993 Adaptive methods for the computation of PageRank. Zbl 1091.68044Kamvar, Sepandar; Haveliwala, Taher; Golub, Gene 49 2004 Quadratically constrained least squares and quadratic problems. Zbl 0745.65029Golub, Gene H.; von Matt, Urs 47 1991 The simplex method of linear programming using LU decomposition. Zbl 0181.19104Bartels, R. H.; Golub, G. H. 47 1969 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 44 2005 Estimation of the \(L\)-curve via Lanczos bidiagonalization. Zbl 0945.65044Calvetti, D.; Golub, G. H.; Reichel, L. 44 1999 An Arnoldi-type algorithm for computing Page Rank. Zbl 1105.65034Golub, G. H.; Greif, C. 44 2006 Some large-scale matrix computation problems. Zbl 0870.65035Bai, Zhaojun; Fahey, Mark; Golub, Gene 43 1996 An inverse free preconditioned Krylov subspace method for symmetric generalized eigenvalue problems. Zbl 1016.65017Golub, Gene H.; Ye, Qiang 42 2002 Matrices, moments and quadrature. II: How to compute the norm of the error iterative methods. Zbl 0888.65050Golub, G. H.; Meurant, G. 42 1997 A constrained eigenvalue problem. Zbl 0666.15006Gander, Walter; Golub, Gene H.; von Matt, Urs 42 1989 A stable numerical method for inverting shape from moments. Zbl 0956.65030Golub, Gene H.; Milanfar, Peyman; Varah, James 42 2000 A generalization of the Eckart-Young-Mirsky matrix approximation theorem. Zbl 0623.15020Golub, G. H.; Hoffman, Alan; Stewart, G. W. 41 1987 Bounds for the entries of matrix functions with applications to preconditioning. Zbl 0934.65054Benzi, Michele; Golub, Gene H. 41 1999 Some history of the conjugate gradient and Lanczos algorithms: 1948-1976. Zbl 0673.65017Golub, Gene H.; O’Leary, Dianne P. 40 1989 Calculation of Gauss quadratures with multiple free and fixed knots. Zbl 0525.65010Golub, G. H.; Kautsky, J. 40 1983 Scientific computing and differential equations: an introduction to numerical methods. Rev. ed. Zbl 0749.65041Golub, Gene H.; Ortega, James M. 38 1992 Computation of Gauss-Kronrod quadrature rules. Zbl 0947.65022Calvetti, D.; Golub, G. H.; Gragg, W. B.; Reichel, L. 37 2000 Eigenvalue computation in the 20th century. Zbl 0965.65057Golub, Gene H.; van der Vorst, Henk A. 37 2000 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 Inexact preconditioned conjugate gradient method with inner-outer iteration. Zbl 0955.65022Golub, Gene H.; Ye, Qiang 35 2000 On the calculation of Jacobi matrices. Zbl 0512.65030Kautsky, J.; Golub, G. H. 34 1983 Adaptively preconditioned GMRES algorithms. Zbl 0954.65026Baglama, J.; Calvetti, D.; Golub, G. H.; Reichel, L. 33 1999 Imposing curvature restrictions on flexible functional forms. Zbl 0573.62098Gallant, A. Ronald; Golub, Gene H. 33 1984 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 Iterative methods for cyclically reduced non-self-adjoint linear systems. Zbl 0699.65021Elman, Howard C.; Golub, Gene H. 33 1990 Use of fast direct methods for the efficient numerical solution of nonseparable elliptic equations. Zbl 0245.65043Concus, Paul; Golub, Gene H. 33 1973 The convergence of inexact Chebyshev and Richardson iterative methods for solving linear systems. Zbl 0661.65033Golub, Gene H.; Overton, Michael L. 31 1988 Note on the iterative refinement of least squares solution. Zbl 0156.16106Golub, G. H.; Wilkinson, J. H. 30 1966 On Fourier-Toeplitz methods for separable elliptic problems. Zbl 0277.65065Fischer, D.; Golub, G.; Hald, O.; Leiva, C.; Widlund, O. 29 1974 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. 28 1986 The restricted singular value decomposition: Properties and applications. Zbl 0738.15006De Moor, Bart L. R.; Golub, Gene H. 27 1991 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 A class of nonsymmetric preconditioners for saddle point problems. Zbl 1104.65038Botchev, Mike A.; Golub, Gene H. 27 2006 A generalized conjugate gradient method for nonsymmetric systems of linear equations. Zbl 0344.65020Concus, Paul; Golub, Gene H. 26 1976 Matrix computations. Paperback ed., 4th printing. Zbl 0592.65011Golub, Gene H.; Van Loan, Charles F. 26 1985 Regularization by truncated total least squares. Zbl 0891.65040Fierro, R. D.; Golub, G. H.; Hansen, P. C.; O’Leary, D. P. 25 1997 Estimates in quadratic formulas. Zbl 0822.65022Golub, Gene H.; Strakoš, Zdeněk 25 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 25 2008 Inexact inverse iteration for generalized eigenvalue problems. Zbl 0984.65032Golub, Gene H.; Ye, Qiang 24 2000 On the spectral decomposition of Hermitian matrices modified by low rank perturbations with applications. Zbl 0646.65033Arbenz, Peter; Golub, Gene H. 23 1988 On the preconditioning of matrices with skew-symmetric splittings. Zbl 0983.65041Golub, Gene H.; Vanderstraeten, Denis 23 2000 First international symposium on domain decomposition methods for partial differential equations (Proceedings, Paris, France, January 7-9, 1987). Zbl 0649.00019 22 1988 Tikhonov regularization for large scale problems. Zbl 0927.65058Golub, Gene H.; von Matt, Urs 22 1998 Regularized total least squares based on quadratic eigenvalue problem solvers. Zbl 1079.65048Sima, Diana M.; Van Huffel, Sabine; Golub, Gene H. 22 2004 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. 832 2013 Matrices, moments and quadrature with applications. Zbl 1217.65056Golub, Gene H.; Meurant, Gérard 85 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 6 2009 A quasi-separable approach to solve the symmetric definite tridiagonal generalized eigenvalue problem. Zbl 1186.65046Vandebril, Raf; Golub, Gene; van Barel, Marc 2 2009 Symmetric tensors and symmetric tensor rank. Zbl 1181.15014Comon, Pierre; Golub, Gene; Lim, Lek-Heng; Mourrain, Bernard 147 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. 126 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 25 2008 Continuous methods for symmetric generalized eigenvalue problems. Zbl 1140.65029Gao, Xing-Bao; Golub, Gene H.; Liao, Li-Zhi 9 2008 Approximation of the scattering amplitude and linear systems. Zbl 1188.65032Golub, Gene H.; Stoll, Martin; Wathen, Andy 6 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. 264 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 135 2007 On successive-overrelaxation acceleration of the Hermitian and skew-Hermitian splitting iterations. Zbl 1199.65097Bai, Zhong-Zhi; Golub, Gene H.; Ng, Michael K. 115 2007 Matrix computations. 3rd ed. Zbl 1118.65316Golub, Gene; Van Loan, Charles F. 56 2007 Spectral analysis of a preconditioned iterative method for the convection-diffusion equation. Zbl 1140.65024Bertaccini, Daniele; Golub, Gene H.; Serra-Capizzano, Stefano 12 2007 On the numerical condition of a generalized Hankel eigenvalue problem. Zbl 1121.65036Beckermann, B.; Golub, G. H.; Labahn, G. 11 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 7 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. 1 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 120 2006 An Arnoldi-type algorithm for computing Page Rank. Zbl 1105.65034Golub, G. H.; Greif, C. 44 2006 A class of nonsymmetric preconditioners for saddle point problems. Zbl 1104.65038Botchev, Mike A.; Golub, Gene H. 27 2006 An algebraic analysis of a block diagonal preconditioner for saddle point systems. Zbl 1105.65048Golub, Gene H.; Greif, Chen; Varah, James M. 14 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. 9 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 861 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 202 2005 Inverse eigenvalue problems: theory, algorithms, and applications. Zbl 1075.65058Chu, Moody T.; Golub, Gene H. 92 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 44 2005 A bibliography on semiseparable matrices. Zbl 1168.15312Vandebril, R.; Van Barel, M.; Golub, G.; Mastronardi, N. 22 2005 The generalized eigenvalue problem for nonsquare pencils using a minimal perturbation approach. Zbl 1100.65035Boutry, Gregory; Elad, Michael; Golub, Gene H.; Milanfar, Peyman 14 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. 10 2005 Multidimensional integral inversion, with applications in shape reconstruction. Zbl 1099.65128Cuyt, Annie; Golub, Gene; Milanfar, Peyman; Verdonk, Brigitte 9 2005 A bibliography on semiseparable matrices. Zbl 1168.15306Van Barel, Marc; Vandebril, Raf; Golub, G.; Mastronardi, Nicola 5 2005 A subspace approximation method for the quadratic eigenvalue problem. Zbl 1079.65039Holz, U. B.; Golub, G. H.; Law, K. H. 4 2005 Preconditioned Hermitian and skew-Hermitian splitting methods for non-Hemitian positive semidefinite linear systems. Zbl 1056.65025Bai, Zhongzhi; Golub, Gene H.; Pan, Jianyu 336 2004 A preconditioner for generalized saddle point problems. Zbl 1082.65034Benzi, Michele; Golub, Gene H. 240 2004 Adaptive methods for the computation of PageRank. Zbl 1091.68044Kamvar, Sepandar; Haveliwala, Taher; Golub, Gene 49 2004 Regularized total least squares based on quadratic eigenvalue problem solvers. Zbl 1079.65048Sima, Diana M.; Van Huffel, Sabine; Golub, Gene H. 22 2004 Shape from moments – an estimation theory perspective. Zbl 1369.62145Elad, Michael; Milanfar, Peyman; Golub, Gene H. 14 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. 592 2003 Separable nonlinear least squares: The variable projection method and its applications. Zbl 1022.65014Golub, Gene; Pereyra, Victor 81 2003 On solving block-structured indefinite linear systems. Zbl 1036.65033Golub, Gene H.; Greif, Chen 72 2003 Optimization of the Hermitian and skew-Hermitian splitting iteration for saddle-point problems. Zbl 1052.65015Benzi, Michele; Gander, Martin J.; Golub, Gene H. 59 2003 Scaling by binormalization. Zbl 1050.65049Livne, Oren E.; Golub, Gene H. 8 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. 80 2002 An inverse free preconditioned Krylov subspace method for symmetric generalized eigenvalue problems. Zbl 1016.65017Golub, Gene H.; Ye, Qiang 42 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 160 2001 Rank-one approximation to high order tensors. Zbl 1001.65036Zhang, Tong; Golub, Gene H. 131 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 15 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 6 2001 A note on preconditioning for indefinite linear systems. Zbl 0959.65063Murphy, Malcolm F.; Golub, Gene H.; Wathen, Andrew J. 205 2000 A stable numerical method for inverting shape from moments. Zbl 0956.65030Golub, Gene H.; Milanfar, Peyman; Varah, James 42 2000 Computation of Gauss-Kronrod quadrature rules. Zbl 0947.65022Calvetti, D.; Golub, G. H.; Gragg, W. B.; Reichel, L. 37 2000 Eigenvalue computation in the 20th century. Zbl 0965.65057Golub, Gene H.; van der Vorst, Henk A. 37 2000 Inexact preconditioned conjugate gradient method with inner-outer iteration. Zbl 0955.65022Golub, Gene H.; Ye, Qiang 35 2000 Inexact inverse iteration for generalized eigenvalue problems. Zbl 0984.65032Golub, Gene H.; Ye, Qiang 24 2000 On the preconditioning of matrices with skew-symmetric splittings. Zbl 0983.65041Golub, Gene H.; Vanderstraeten, Denis 23 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 14 2000 Computing the SVD of a general matrix product/quotient. Zbl 0969.65032Golub, Gene; Sølna, Knut; Van Dooren, Paul 9 2000 A nonlinear primal-dual method for total variation-based image restoration. Zbl 0929.68118Chan, Tony F.; Golub, Gene H.; Mulet, Pep 179 1999 Tikhonov regularization and total least squares. Zbl 0945.65042Golub, Gene H.; Hansen, Per Christian; O’Leary, Dianne P. 81 1999 Estimation of the \(L\)-curve via Lanczos bidiagonalization. Zbl 0945.65044Calvetti, D.; Golub, G. H.; Reichel, L. 44 1999 Bounds for the entries of matrix functions with applications to preconditioning. Zbl 0934.65054Benzi, Michele; Golub, Gene H. 41 1999 Adaptively preconditioned GMRES algorithms. Zbl 0954.65026Baglama, J.; Calvetti, D.; Golub, G. H.; Reichel, L. 33 1999 On some eigenvector-eigenvalue relations. Zbl 0929.15008Elhay, S.; Gladwell, G. M. L.; Golub, G. H.; Ram, Y. M. 10 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 Applications and computation of orthogonal polynomials. Conference at the Mathematical Research Institute Oberwolfach, Germany, March 22–29, 1998. Dedicated to the memory of Günther Hämmerlin. Zbl 0919.00065 1 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. 54 1998 Tikhonov regularization for large scale problems. Zbl 0927.65058Golub, Gene H.; von Matt, Urs 22 1998 Solution of biharmonic equations with application to radar imaging. Zbl 0933.65128Andersson, Lars-Erik; Elfving, Tommy; Golub, Gene H. 17 1998 Parameter estimation in the presence of bounded data uncertainties. Zbl 0914.65147Chandrasekaran, S.; Golub, G. H.; Gu, M.; Sayed, A. H. 15 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 10 1998 Rank modifications of semidefinite matrices associated with a secant update formula. Zbl 0922.65031Chu, Moody T.; Funderlic, R. E.; Golub, Gene H. 10 1998 On the homotopy method for perturbed symmetric generalized eigenvalue problems. Zbl 0917.65035Zhang, T.; Law, K. H.; Golub, G. H. 8 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 0910.00057 2 1998 Efficient solution of the Jacobian system in Newton’s method close to a root. Zbl 0921.65039Drexler, Michael; Golub, Gene H. 1 1998 Eigenvalue perturbation and generalized Krylov subspace method. Zbl 0931.65039Zhang, T.; Golub, G. H.; Law, K. 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. 42 1997 Regularization by truncated total least squares. Zbl 0891.65040Fierro, R. D.; Golub, G. H.; Hansen, P. C.; O’Leary, D. P. 25 1997 Generalized cross-validation for large scale problems. Zbl 0878.65032Golub, Gene H.; von Matt, Urs 21 1997 Bounds for the trace of the inverse and the determinant of symmetric positive definite matrices. Zbl 0883.15013Bai, Zhaojun; Golub, Gene H. 15 1997 On a variational formulation of the generalized singular value decomposition. Zbl 0891.65038Chu, Moody T.; Funderlic, Robert. E.; Golub, Gene H. 12 1997 Closer to the solution: Iterative linear solvers. Zbl 0881.65025Golub, Gene H.; van der Vorst, Henk A. 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. 1 1997 Matrix computations. 3rd ed. Zbl 0865.65009Golub, Gene; Van Loan, Charles F. 3,053 1996 ...and 135 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 14,073 Authors 122 Reichel, Lothar 97 Wei, Yimin 67 Bai, Zhongzhi 66 Huang, Ting-Zhu 65 Pan, Victor Yakovlevich 63 Golub, Gene Howard 63 Ma, Changfeng 61 Zhang, Guofeng 56 Jódar Sanchez, Lucas Antonio 47 Benner, Peter 43 Khojasteh Salkuyeh, Davod 42 Evans, David John 41 Ng, Michael Kwok-Po 40 Serra-Capizzano, Stefano 38 Van Barel, Marc 37 Axelsson, Axel Owe Holger 37 Dehghan Takht Fooladi, Mehdi 36 Benzi, Michele 36 Liang, Zhaozheng 35 Mehrmann, Volker 35 Simoncini, Valeria 34 Cao, Yang 34 Wu, Shiliang 33 Jbilou, Khalide 32 Li, Cuixia 32 Van Dooren, Paul M. 32 Van Huffel, Sabine 31 Lin, Wen-Wei 31 Milovanović, Gradimir V. 30 Chen, Guoliang 30 Wu, Yujiang 29 Qi, Liqun 28 Jia, Zhongxiao 28 Wei, Musheng 27 Jin, Xiaoqing 27 Yang, Aili 26 Li, Rencang 26 Nakatsukasa, Yuji 25 Dai, Hua 25 Huang, Zhengge 25 Saad, Yousef 24 Martínez, José Mario 24 Stoll, Martin 23 Calvetti, Daniela 23 Kressner, Daniel 23 Lu, Linzhang 23 Mastronardi, Nicola 23 Vandebril, Raf 22 Bini, Dario Andrea 22 Cui, Jingjing 22 Gu, Chuanqing 22 Hu, Xiyan 22 Lin, Yiqin 22 Mitrouli, Marilena 22 Sadkane, Miloud 22 Wu, Gang 22 Zheng, Bing 21 Gemignani, Luca 21 Hajarian, Masoud 21 Li, Wen 21 Sadok, Hassane 20 Higham, Nicholas J. 20 Nagy, James Gerard 20 Rojo, Oscar L. 20 Toutounian, Faezeh 20 Wathen, Andrew John 20 Xiang, Hua 20 Xu, Zhong 19 Chen, Fang 19 Gondzio, Jacek 19 Hansen, Per Christian 19 Miao, Shu-Xin 19 O’Leary, Dianne P. 19 Plemmons, Robert James 19 Rodriguez, Giuseppe 19 Wang, Xiang 19 Zhang, Lei 18 Bai, Zhaojun 18 Bai, Zhengjian 18 Gautschi, Walter 18 Hadjidimos, Apostolos 18 Verhaegen, Michel 18 Ye, Qiang 17 Ballico, Edoardo 17 Barlow, Jesse L. 17 Chu, Delin 17 Chu, Moody T. 17 De Moor, Bart L. R. 17 Fan, Hongtao 17 King-wah Chu, Eric 17 Paige, Christopher C. 17 Spalević, Miodrag M. 17 Wang, Ligong 17 Wu, Qingbiao 17 Zha, Hongyuan 17 Zhang, Jun 17 Zhang, Lei-Hong 16 Brezinski, Claude 16 Cao, Zhihao 16 Chan, Raymond Hon-Fu ...and 13,973 more Authors all top 5 Cited in 717 Serials 1,014 Linear Algebra and its Applications 784 Journal of Computational and Applied Mathematics 520 Applied Mathematics and Computation 376 Computers & Mathematics with Applications 357 Journal of Computational Physics 345 Numerical Algorithms 283 Numerische Mathematik 271 Computer Methods in Applied Mechanics and Engineering 258 Applied Numerical Mathematics 246 SIAM Journal on Scientific Computing 242 BIT 209 SIAM Journal on Matrix Analysis and Applications 206 Mathematics of Computation 192 Numerical Linear Algebra with Applications 190 International Journal of Computer Mathematics 163 Automatica 128 Journal of Scientific Computing 115 Computational Statistics and Data Analysis 114 Applied Mathematics Letters 100 Computational Optimization and Applications 88 International Journal of Control 87 Computing 87 Computational and Applied Mathematics 80 Journal of Optimization Theory and Applications 80 Mathematical Programming. 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Simulation and Computation 20 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 20 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis ...and 617 more Serials all top 5 Cited in 61 Fields 7,549 Numerical analysis (65-XX) 2,422 Linear and multilinear algebra; matrix theory (15-XX) 1,145 Statistics (62-XX) 1,100 Operations research, mathematical programming (90-XX) 1,049 Partial differential equations (35-XX) 932 Computer science (68-XX) 853 Systems theory; control (93-XX) 716 Fluid mechanics (76-XX) 512 Information and communication theory, circuits (94-XX) 448 Mechanics of deformable solids (74-XX) 355 Probability theory and stochastic processes (60-XX) 346 Approximations and expansions (41-XX) 340 Calculus of variations and optimal control; optimization (49-XX) 330 Ordinary differential equations (34-XX) 292 Biology and other natural sciences (92-XX) 230 Operator theory (47-XX) 202 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 183 Combinatorics (05-XX) 155 Quantum theory (81-XX) 154 Harmonic analysis on Euclidean spaces (42-XX) 151 Optics, electromagnetic theory (78-XX) 138 Special functions (33-XX) 138 Dynamical systems and ergodic theory (37-XX) 138 Geophysics (86-XX) 121 Mechanics of particles and systems (70-XX) 110 Statistical mechanics, structure of matter (82-XX) 106 Integral equations (45-XX) 89 Algebraic geometry (14-XX) 83 Real functions (26-XX) 81 Functions of a complex variable (30-XX) 69 Number theory (11-XX) 63 Functional analysis (46-XX) 59 Differential geometry (53-XX) 57 Field theory and polynomials (12-XX) 57 Classical thermodynamics, heat transfer (80-XX) 52 Integral transforms, operational calculus (44-XX) 41 Commutative algebra (13-XX) 38 Difference and functional equations (39-XX) 36 Potential theory (31-XX) 34 Global analysis, analysis on manifolds (58-XX) 29 Convex and discrete geometry (52-XX) 24 Geometry (51-XX) 23 Astronomy and astrophysics (85-XX) 20 History and biography (01-XX) 18 General and overarching topics; collections (00-XX) 18 Group theory and generalizations (20-XX) 16 Measure and integration (28-XX) 16 Manifolds and cell complexes (57-XX) 15 General topology (54-XX) 12 Several complex variables and analytic spaces (32-XX) 12 Sequences, series, summability (40-XX) 11 Topological groups, Lie groups (22-XX) 9 Associative rings and algebras (16-XX) 8 Mathematical logic and foundations (03-XX) 7 Relativity and gravitational theory (83-XX) 6 Nonassociative rings and algebras (17-XX) 5 Algebraic topology (55-XX) 4 Mathematics education (97-XX) 3 Order, lattices, ordered algebraic structures (06-XX) 3 General algebraic systems (08-XX) 3 Abstract harmonic analysis (43-XX) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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