Edit Profile (opens in new tab) Golub, Gene Howard (b. 1932 d. 2007) Co-Author Distance Author ID: golub.gene-h Published as: Golub, Gene H.; Golub, G. H.; Golub, Gene; Golub, G. more...less External Links: MacTutor · MGP · Wikidata · dblp · GND · IdRef Documents Indexed: 258 Publications since 1961, including 14 Books 9 Contributions as Editor Biographic References: 5 Publications Co-Authors: 186 Co-Authors with 244 Joint Publications 5,871 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 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 3 Yuan, Jinyun 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 Alter, Orly 1 Andersson, Lars-Erik 1 Baglama, James 1 Beckermann, Bernhard 1 Björk, Åke 1 Bochev, M. 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. ...and 88 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 Proceedings of the National Academy of Sciences of the United States of America 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 E. Applied Sciences 1 NATO ASI Series. Series F. Computer and Systems Sciences 1 Proceedings of Symposia in Applied Mathematics 1 Publications of the Mathematics Research Center, The University of Wisconsin - Madison 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) 21 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) 1 Biology and other natural sciences (92-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 236 Publications have been cited 18,654 times in 13,060 Documents Cited by ▼ Year ▼ Matrix computations. 3rd ed. Zbl 0865.65009Golub, Gene; Van Loan, Charles F. 3,345 1996 Matrix computations. 2nd ed. Zbl 0733.65016Golub, Gene H.; Van Loan, Charles F. 1,474 1989 Matrix computations. 4th ed. Zbl 1268.65037Golub, Gene H.; Van Loan, Charles F. 1,108 2013 Numerical solution of saddle point problems. Zbl 1115.65034Benzi, Michele; Golub, Gene H.; Liesen, Jörg 959 2005 Matrix computations. Zbl 0559.65011Golub, Gene H.; Van Loan, Charles F. 924 1983 Hermitian and skew-Hermitian splitting methods for non-Hermitian positive definite linear systems. Zbl 1036.65032Bai, Zhong-Zhi; Golub, Gene H.; Ng, Michael K. 671 2003 Generalized cross-validation as a method for choosing a good ridge parameter. Zbl 0461.62059Golub, Gene H.; Heath, Michael; Wahba, Grace 464 1979 Preconditioned Hermitian and skew-Hermitian splitting methods for non-Hemitian positive semidefinite linear systems. Zbl 1056.65025Bai, Zhongzhi; Golub, Gene H.; Pan, Jianyu 365 2004 Calculation of Gauss quadrature rules. Zbl 0179.21901Golub, Gene H.; Welsch, John H. 361 1969 Accelerated Hermitian and skew-Hermitian splitting iteration methods for saddle-point problems. Zbl 1134.65022Bai, Zhongzhi; Golub, Gene H. 287 2007 Calculating the singular values and pseudo-inverse of a matrix. Zbl 0194.18201Golub, G.; Kahan, W. 265 1965 A Hessenberg-Schur method for the problem AX+XB=C. Zbl 0421.65022Golub, Gene H.; Nash, S.; Van Loan, Charles F. 262 1979 A preconditioner for generalized saddle point problems. Zbl 1082.65034Benzi, Michele; Golub, Gene H. 261 2004 Inexact and preconditioned Uzawa algorithms for saddle point problems. Zbl 0815.65041Elman, Howard C.; Golub, Gene H. 249 1994 A note on preconditioning for indefinite linear systems. Zbl 0959.65063Murphy, Malcolm F.; Golub, Gene H.; Wathen, Andrew J. 234 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 226 2005 On direct methods for solving Poisson’s equations. Zbl 0217.52902Buzbee, B. L.; Golub, G. H.; Nielson, C. W. 213 1970 A nonlinear primal-dual method for total variation-based image restoration. Zbl 0929.68118Chan, Tony F.; Golub, Gene H.; Mulet, Pep 204 1999 The differentiation of pseudo-inverses and nonlinear least squares problems whose variables separate. Zbl 0258.65045Golub, G. H.; Pereyra, V. 192 1973 An analysis of the total least squares problem. Zbl 0468.65011Golub, Gene H.; Van Loan, Charles F. 185 1980 Symmetric tensors and symmetric tensor rank. Zbl 1181.15014Comon, Pierre; Golub, Gene; Lim, Lek-Heng; Mourrain, Bernard 182 2008 Some modified matrix eigenvalue problems. Zbl 0254.65027Golub, Gene H. 178 1973 SOR-like methods for augmented systems. Zbl 0991.65036Golub, Gene H.; Wu, X.; Yuan, Jin-Yun 169 2001 Singular value decomposition and least squares solutions. Zbl 0181.17602Golub, G. H.; Reinsch, C. 165 1970 Rank-one approximation to high order tensors. Zbl 1001.65036Zhang, Tong; Golub, Gene H. 146 2001 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 146 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. 144 1961 Numerical methods for solving linear least squares problems. Zbl 0142.11502Golub, G. 138 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. 135 2008 On successive-overrelaxation acceleration of the Hermitian and skew-Hermitian splitting iterations. Zbl 1199.65097Bai, Zhong-Zhi; Golub, Gene H.; Ng, Michael K. 133 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 128 2006 Methods for modifying matrix factorizations. Zbl 0289.65021Gill, P. E.; Golub, G. H.; Murray, W.; Saunders, M. A. 125 1974 Numerical methods for computing angles between linear subspaces. Zbl 0282.65031Björck, Åke; Golub, Gene H. 118 1973 Inverse eigenvalue problems: theory, algorithms, and applications. Zbl 1075.65058Chu, Moody T.; Golub, Gene H. 110 2005 Matrices, moments and quadrature with applications. Zbl 1217.65056Golub, Gene H.; Meurant, Gérard 110 2010 Handbook series linear algebra. Linear least squares solutions by Householder transformations. Zbl 0142.11503Businger, P.; Golub, G. H. 106 1965 A survey of matrix inverse eigenvalue problems. Zbl 0633.65036Boley, Daniel; Golub, Gene H. 104 1987 Separable nonlinear least squares: The variable projection method and its applications. Zbl 1022.65014Golub, Gene; Pereyra, Victor 98 2003 Block preconditioning for the conjugate gradient method. Zbl 0556.65022Concus, P.; Golub, G. H.; Meurant, G. 97 1985 Tikhonov regularization and total least squares. Zbl 0945.65042Golub, Gene H.; Hansen, Per Christian; O’Leary, Dianne P. 96 1999 Structured inverse eigenvalue problems. Zbl 1105.65326Chu, Moody T.; Golub, Gene H. 85 2002 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. 84 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. 82 1978 On solving block-structured indefinite linear systems. Zbl 1036.65033Golub, Gene H.; Greif, Chen 78 2003 Adaptive methods for the computation of PageRank. Zbl 1091.68044Kamvar, Sepandar; Haveliwala, Taher; Golub, Gene 75 2004 Matrices, moments and quadrature. Zbl 0795.65019Golub, G. H.; Meurant, Gerard 74 1994 The numerically stable reconstruction of a Jacobi matrix from spectral data. Zbl 0388.15010de Boor, C.; Golub, G. H. 71 1978 Ill-conditioned eigensystems and the computation of the Jordan canonical form. Zbl 0341.65027Golub, G. H.; Wilkinson, J. H. 69 1976 Optimization of the Hermitian and skew-Hermitian splitting iteration for saddle-point problems. Zbl 1052.65015Benzi, Michele; Gander, Martin J.; Golub, Gene H. 65 2003 Least-squares fitting of circles and ellipses. Zbl 0817.65008Gander, Walter; Golub, Gene H.; Strebel, Rolf 64 1994 Iterative solution of linear systems. Zbl 0762.65019Freund, Roland W.; Golub, Gene H.; Nachtigal, Noël M. 61 1992 The Block Lanczos method for computing eigenvalues. Zbl 0407.68040Golub, G. H.; Underwood, R. 58 1977 Matrix computations. 3rd ed. Zbl 1118.65316Golub, Gene; Van Loan, Charles F. 57 2007 An iteration for indefinite systems and its application to the Navier-Stokes equations. Zbl 0912.76053Golub, Gene H.; Wathen, Andrew J. 55 1998 Scientific computing. An introduction with parallel computing. Zbl 0790.65001Golub, Gene; Ortega, James M. 50 1993 Some large-scale matrix computation problems. Zbl 0870.65035Bai, Zhaojun; Fahey, Mark; Golub, Gene 49 1996 Quadratically constrained least squares and quadratic problems. Zbl 0745.65029Golub, Gene H.; von Matt, Urs 49 1991 An Arnoldi-type algorithm for computing Page Rank. Zbl 1105.65034Golub, G. H.; Greif, C. 49 2006 Estimation of the \(L\)-curve via Lanczos bidiagonalization. Zbl 0945.65044Calvetti, D.; Golub, G. H.; Reichel, L. 49 1999 The simplex method of linear programming using LU decomposition. Zbl 0181.19104Bartels, R. H.; Golub, G. H. 49 1969 An inverse free preconditioned Krylov subspace method for symmetric generalized eigenvalue problems. Zbl 1016.65017Golub, Gene H.; Ye, Qiang 48 2002 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 47 2005 Matrices, moments and quadrature. II: How to compute the norm of the error iterative methods. Zbl 0888.65050Golub, G. H.; Meurant, G. 46 1997 Bounds for the entries of matrix functions with applications to preconditioning. Zbl 0934.65054Benzi, Michele; Golub, Gene H. 46 1999 Computation of Gauss-Kronrod quadrature rules. Zbl 0947.65022Calvetti, D.; Golub, G. H.; Gragg, W. B.; Reichel, L. 46 2000 A stable numerical method for inverting shape from moments. Zbl 0956.65030Golub, Gene H.; Milanfar, Peyman; Varah, James 46 2000 A generalization of the Eckart-Young-Mirsky matrix approximation theorem. Zbl 0623.15020Golub, G. H.; Hoffman, Alan; Stewart, G. W. 45 1987 Scientific computing and differential equations: an introduction to numerical methods. Rev. ed. Zbl 0749.65041Golub, Gene H.; Ortega, James M. 43 1992 A constrained eigenvalue problem. Zbl 0666.15006Gander, Walter; Golub, Gene H.; von Matt, Urs 43 1989 Some history of the conjugate gradient and Lanczos algorithms: 1948-1976. Zbl 0673.65017Golub, Gene H.; O’Leary, Dianne P. 43 1989 Calculation of Gauss quadratures with multiple free and fixed knots. Zbl 0525.65010Golub, G. H.; Kautsky, J. 41 1983 Eigenvalue computation in the 20th century. Zbl 0965.65057Golub, Gene H.; van der Vorst, Henk A. 41 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. 39 1981 On the solution of large, structured linear complementarity problems: the block partitioned case. Zbl 0391.90087Cottle, Richard W.; Golub, Gene H.; Sacher, Richard S. 38 1978 Inexact preconditioned conjugate gradient method with inner-outer iteration. Zbl 0955.65022Golub, Gene H.; Ye, Qiang 38 2000 Adaptively preconditioned GMRES algorithms. Zbl 0954.65026Baglama, J.; Calvetti, D.; Golub, G. H.; Reichel, L. 37 1999 Imposing curvature restrictions on flexible functional forms. Zbl 0573.62098Gallant, A. Ronald; Golub, Gene H. 36 1984 Use of fast direct methods for the efficient numerical solution of nonseparable elliptic equations. Zbl 0245.65043Concus, Paul; Golub, Gene H. 35 1973 On the calculation of Jacobi matrices. Zbl 0512.65030Kautsky, J.; Golub, G. H. 34 1983 Iterative methods for cyclically reduced non-self-adjoint linear systems. Zbl 0699.65021Elman, Howard C.; Golub, Gene H. 34 1990 The convergence of inexact Chebyshev and Richardson iterative methods for solving linear systems. Zbl 0661.65033Golub, Gene H.; Overton, Michael L. 32 1988 Note on the iterative refinement of least squares solution. Zbl 0156.16106Golub, G. H.; Wilkinson, J. H. 32 1966 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. 31 1986 Estimates in quadratic formulas. Zbl 0822.65022Golub, Gene H.; Strakoš, Zdeněk 30 1994 First international symposium on domain decomposition methods for partial differential equations (Proceedings, Paris, France, January 7-9, 1987). Zbl 0649.00019 30 1988 On Fourier-Toeplitz methods for separable elliptic problems. Zbl 0277.65065Fischer, D.; Golub, G.; Hald, O.; Leiva, C.; Widlund, O. 30 1974 A rank-one reduction formula and its applications to matrix factorizations. Zbl 0844.65033Chu, Moody T.; Funderlic, Robert E.; Golub, Gene H. 29 1995 A generalized conjugate gradient method for nonsymmetric systems of linear equations. Zbl 0344.65020Concus, Paul; Golub, Gene H. 29 1976 Perturbation analysis of the canonical correlations of matrix pairs. Zbl 0811.15011Golub, Gene H.; Zha, Hongyuan 28 1994 Regularization by truncated total least squares. Zbl 0891.65040Fierro, R. D.; Golub, G. H.; Hansen, P. C.; O’Leary, D. P. 28 1997 A class of nonsymmetric preconditioners for saddle point problems. Zbl 1104.65038Botchev, Mike A.; Golub, Gene H. 27 2006 The restricted singular value decomposition: Properties and applications. Zbl 0738.15006De Moor, Bart L. R.; Golub, Gene H. 27 1991 Symmetric-triangular decomposition and its applications. II: Preconditioners for indefinite systems. Zbl 1151.65027Wu, Xiaonan; Golub, Gene H.; Cuminato, José A.; Yuan, Jin Yun 27 2008 A bibliography on semiseparable matrices. Zbl 1168.15312Vandebril, R.; Van Barel, M.; Golub, G.; Mastronardi, N. 27 2005 Matrix computations. Paperback ed., 4th printing. Zbl 0592.65011Golub, Gene H.; Van Loan, Charles F. 26 1985 Tikhonov regularization for large scale problems. Zbl 0927.65058Golub, Gene H.; von Matt, Urs 25 1998 Regularized total least squares based on quadratic eigenvalue problem solvers. Zbl 1079.65048Sima, Diana M.; Van Huffel, Sabine; Golub, Gene H. 25 2004 On the spectral decomposition of Hermitian matrices modified by low rank perturbations with applications. Zbl 0646.65033Arbenz, Peter; Golub, Gene H. 25 1988 On the preconditioning of matrices with skew-symmetric splittings. Zbl 0983.65041Golub, Gene H.; Vanderstraeten, Denis 25 2000 Inexact inverse iteration for generalized eigenvalue problems. Zbl 0984.65032Golub, Gene H.; Ye, Qiang 24 2000 Matrix computations. 4th ed. Zbl 1268.65037Golub, Gene H.; Van Loan, Charles F. 1,108 2013 Matrices, moments and quadrature with applications. Zbl 1217.65056Golub, Gene H.; Meurant, Gérard 110 2010 Solving ellipsoid-constrained integer least squares problems. Zbl 1195.65049Chang, Xiao-Wen; Golub, Gene H. 3 2010 The QR algorithm: 50 years later its genesis by John Francis and Vera Kublanovskaya and subsequent developments. Zbl 1169.65032Golub, Gene; Uhlig, Frank 7 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 182 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. 135 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 27 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 7 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. 287 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 146 2007 On successive-overrelaxation acceleration of the Hermitian and skew-Hermitian splitting iterations. Zbl 1199.65097Bai, Zhong-Zhi; Golub, Gene H.; Ng, Michael K. 133 2007 Matrix computations. 3rd ed. Zbl 1118.65316Golub, Gene; Van Loan, Charles F. 57 2007 On the numerical condition of a generalized Hankel eigenvalue problem. Zbl 1121.65036Beckermann, B.; Golub, G. H.; Labahn, G. 12 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 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 9 2007 A two-stage algorithm for computing pagerank and multistage generalizations. Zbl 1206.68050Lee, Chris P.; Golub, Gene H.; Zenios, Stefanos A. 2 2007 A two-stage algorithm for computing PageRank and multistage generalizations. Zbl 1221.68041Lee, 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 128 2006 An Arnoldi-type algorithm for computing Page Rank. Zbl 1105.65034Golub, G. H.; Greif, C. 49 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. 16 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. 10 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 959 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 226 2005 Inverse eigenvalue problems: theory, algorithms, and applications. Zbl 1075.65058Chu, Moody T.; Golub, Gene H. 110 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 47 2005 A bibliography on semiseparable matrices. Zbl 1168.15312Vandebril, R.; Van Barel, M.; Golub, G.; Mastronardi, N. 27 2005 The generalized eigenvalue problem for nonsquare pencils using a minimal perturbation approach. Zbl 1100.65035Boutry, Gregory; Elad, Michael; Golub, Gene H.; Milanfar, Peyman 18 2005 Multidimensional integral inversion, with applications in shape reconstruction. Zbl 1099.65128Cuyt, Annie; Golub, Gene; Milanfar, Peyman; Verdonk, Brigitte 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. 12 2005 A bibliography on semiseparable matrices. Zbl 1168.15306Van Barel, Marc; Vandebril, Raf; Golub, G.; Mastronardi, Nicola 8 2005 A subspace approximation method for the quadratic eigenvalue problem. Zbl 1079.65039Holz, U. B.; Golub, G. H.; Law, K. H. 5 2005 Preconditioned Hermitian and skew-Hermitian splitting methods for non-Hemitian positive semidefinite linear systems. Zbl 1056.65025Bai, Zhongzhi; Golub, Gene H.; Pan, Jianyu 365 2004 A preconditioner for generalized saddle point problems. Zbl 1082.65034Benzi, Michele; Golub, Gene H. 261 2004 Adaptive methods for the computation of PageRank. Zbl 1091.68044Kamvar, Sepandar; Haveliwala, Taher; Golub, Gene 75 2004 Regularized total least squares based on quadratic eigenvalue problem solvers. Zbl 1079.65048Sima, Diana M.; Van Huffel, Sabine; Golub, Gene H. 25 2004 Shape from moments – an estimation theory perspective. Zbl 1369.62145Elad, Michael; Milanfar, Peyman; Golub, Gene H. 16 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. 10 2004 Integrative analysis of genome-scale data by using pseudoinverse projection predicts novel correlation between DNA replication and RNA transcription. Zbl 1491.92048Alter, Orly; Golub, Gene H. 1 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. 671 2003 Separable nonlinear least squares: The variable projection method and its applications. Zbl 1022.65014Golub, Gene; Pereyra, Victor 98 2003 On solving block-structured indefinite linear systems. Zbl 1036.65033Golub, Gene H.; Greif, Chen 78 2003 Optimization of the Hermitian and skew-Hermitian splitting iteration for saddle-point problems. Zbl 1052.65015Benzi, Michele; Gander, Martin J.; Golub, Gene H. 65 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. 85 2002 An inverse free preconditioned Krylov subspace method for symmetric generalized eigenvalue problems. Zbl 1016.65017Golub, Gene H.; Ye, Qiang 48 2002 Symmetric-triangular decomposition and its applications. I: Theorems and algorithms. Zbl 1017.65020Golub, Gene H.; Yuan, Jin-Yun 14 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 169 2001 Rank-one approximation to high order tensors. Zbl 1001.65036Zhang, Tong; Golub, Gene H. 146 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. 234 2000 Computation of Gauss-Kronrod quadrature rules. Zbl 0947.65022Calvetti, D.; Golub, G. H.; Gragg, W. B.; Reichel, L. 46 2000 A stable numerical method for inverting shape from moments. Zbl 0956.65030Golub, Gene H.; Milanfar, Peyman; Varah, James 46 2000 Eigenvalue computation in the 20th century. Zbl 0965.65057Golub, Gene H.; van der Vorst, Henk A. 41 2000 Inexact preconditioned conjugate gradient method with inner-outer iteration. Zbl 0955.65022Golub, Gene H.; Ye, Qiang 38 2000 On the preconditioning of matrices with skew-symmetric splittings. Zbl 0983.65041Golub, Gene H.; Vanderstraeten, Denis 25 2000 Inexact inverse iteration for generalized eigenvalue problems. Zbl 0984.65032Golub, Gene H.; Ye, Qiang 24 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 204 1999 Tikhonov regularization and total least squares. Zbl 0945.65042Golub, Gene H.; Hansen, Per Christian; O’Leary, Dianne P. 96 1999 Estimation of the \(L\)-curve via Lanczos bidiagonalization. Zbl 0945.65044Calvetti, D.; Golub, G. H.; Reichel, L. 49 1999 Bounds for the entries of matrix functions with applications to preconditioning. Zbl 0934.65054Benzi, Michele; Golub, Gene H. 46 1999 Adaptively preconditioned GMRES algorithms. Zbl 0954.65026Baglama, J.; Calvetti, D.; Golub, G. H.; Reichel, L. 37 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 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 2 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. 55 1998 Tikhonov regularization for large scale problems. Zbl 0927.65058Golub, Gene H.; von Matt, Urs 25 1998 Solution of biharmonic equations with application to radar imaging. Zbl 0933.65128Andersson, Lars-Erik; Elfving, Tommy; Golub, Gene H. 21 1998 Parameter estimation in the presence of bounded data uncertainties. Zbl 0914.65147Chandrasekaran, S.; Golub, G. H.; Gu, M.; Sayed, A. H. 16 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 11 1998 Inner and outer iterations for the Chebyshev algorithm. Zbl 0911.65024Giladi, Eldar; Golub, Gene H.; Keller, Joseph B. 8 1998 On the homotopy method for perturbed symmetric generalized eigenvalue problems. Zbl 0917.65035Zhang, T.; Law, K. H.; Golub, G. H. 8 1998 Rank modifications of semidefinite matrices associated with a secant update formula. Zbl 0922.65031Chu, Moody T.; Funderlic, R. E.; Golub, Gene H. 8 1998 Cyclic reduction – history and applications. Zbl 0921.65023Gander, Walter; Golub, Gene H. 6 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. 46 1997 Regularization by truncated total least squares. Zbl 0891.65040Fierro, R. D.; Golub, G. H.; Hansen, P. C.; O’Leary, D. P. 28 1997 Generalized cross-validation for large scale problems. Zbl 0878.65032Golub, Gene H.; von Matt, Urs 22 1997 Bounds for the trace of the inverse and the determinant of symmetric positive definite matrices. Zbl 0883.15013Bai, Zhaojun; Golub, Gene H. 17 1997 On a variational formulation of the generalized singular value decomposition. Zbl 0891.65038Chu, Moody T.; Funderlic, Robert. E.; Golub, Gene H. 13 1997 150 years old and still alive: Eigenproblems. Zbl 0881.65026van der Vorst, Henk A.; Golub, Gene H. 11 1997 Closer to the solution: Iterative linear solvers. Zbl 0881.65025Golub, Gene H.; van der Vorst, Henk A. 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 ...and 136 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 15,958 Authors 132 Reichel, Lothar 101 Wei, Yimin 69 Ma, Changfeng 68 Bai, Zhongzhi 68 Pan, Victor Yakovlevich 67 Huang, Ting-Zhu 64 Golub, Gene Howard 62 Zhang, Guofeng 57 Jódar Sanchez, Lucas Antonio 52 Benner, Peter 46 Khojasteh Salkuyeh, Davod 45 Serra-Capizzano, Stefano 43 Ng, Michael Kwok-Po 42 Evans, David John 41 Van Dooren, Paul M. 40 Van Barel, Marc 39 Jbilou, Khalide 39 Mehrmann, Volker 38 Dehghan Takht Fooladi, Mehdi 38 Simoncini, Valeria 37 Axelsson, Axel Owe Holger 37 Benzi, Michele 37 Liang, Zhaozheng 37 Wu, Shiliang 35 Li, Cuixia 34 Van Huffel, Sabine 33 Cao, Yang 32 Jia, Zhongxiao 32 Wu, Yujiang 31 Chen, Guoliang 31 Lin, Wen-Wei 31 Milovanović, Gradimir V. 31 Qi, Liqun 30 Li, Rencang 30 Nakatsukasa, Yuji 30 Yang, Aili 29 Wei, Musheng 28 Huang, Zhengge 28 Jin, Xiaoqing 27 Hajarian, Masoud 27 Kressner, Daniel 27 Stoll, Martin 26 Dai, Hua 26 Saad, Yousef 26 Sadkane, Miloud 25 Chen, Fang 25 Cui, Jingjing 25 Martínez, José Mario 25 Mastronardi, Nicola 25 Mitrouli, Marilena 25 Vandebril, Raf 25 Wu, Gang 24 De Moor, Bart L. 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