Edit Profile (opens in new tab) Bai, Zhaojun Co-Author Distance Author ID: bai.zhaojun Published as: Bai, Zhaojun; Bai, Z.; Bai, ZhaoJun more...less Homepage: http://web.cs.ucdavis.edu/~bai/ External Links: MGP · dblp · GND Documents Indexed: 84 Publications since 1988, including 3 Books and 10 Additional arXiv Preprints 5 Contributions as Editor Co-Authors: 98 Co-Authors with 81 Joint Publications 3,745 Co-Co-Authors all top 5 Co-Authors 8 single-authored 15 Su, Yangfeng 14 Li, Rencang 10 Demmel, James Weldon 6 Lu, Ding 5 Dongarra, Jack J. 5 Freund, Roland W. 4 Cai, Yunfeng 4 Gao, Weiguo 4 Yang, Chao 3 Bischof, Christian H. 3 Golub, Gene Howard 3 Lu, Tianyi 3 Zhang, Lei-Hong 2 Chen, Wenbin 2 Dewilde, Patrick M. 2 Du Croz, Jeremy J. 2 Greenbaum, Anne 2 Hammarling, Sven J. 2 Hu, Dan 2 Huang, Xin 2 Lee, Lie-Quan 2 Li, Yung-Ta 2 Liao, Ben-Shan 2 Lin, Chao-Ping 2 McKenney, Alan 2 Meerbergen, Karl 2 Ng, Esmond G. 2 Pask, John Ernest 2 Reichel, Lothar 2 Sorensen, Danny C. 2 Sukumar, Natarajan 2 Wang, Li 2 Yamazaki, Ichitaro 2 Ye, Qiang 1 Benzi, Michele 1 Blackford, S. 1 Brush, Charles 1 Chung, Francis J. 1 Dai, Yu-Hong 1 Dixon, Matthew F. 1 Dogrul, Emin 1 E, Weinan 1 Elman, Howard C. 1 Fahey, Mark R. 1 Garrett, C. Kristopher 1 Ge, Lixin 1 Grimes, Roger G. 1 Gu, Ming 1 Gygi, François 1 Higham, Nicholas J. 1 Husbands, Parry 1 Kadir, Tariq 1 Kilmer, Misha Elena 1 King-wah Chu, Eric 1 Ko, Jin Hwan 1 Ko, Kwok 1 Kononenko, Oleksiy 1 Lee, Cherung 1 Li, Zenghai 1 Liang, Xin 1 Lin, Wen-Wei 1 Lin, Wenwei 1 Marques, Osni A. 1 McKenny, A. 1 Mehrmann, Volker 1 Nakatsukasa, Yuji 1 Neymeyr, Klaus 1 Ng, Cho-Kuen 1 Orlandi, Antonio 1 Ostrouchov, Susan 1 Petitet, Antoine 1 Qian, Qingshan 1 Roh, Dong Min 1 Ruhe, Axel 1 Sakurai, Tetsuya 1 Scalettar, Richard T. 1 Senzaki, Kenta 1 Shao, Nian 1 Shu, Chi-Wang 1 Simon, Horst D. 1 Skoogh, Daniel 1 Smith, William T. 1 Stewart, Gilbert Wright 1 Tadano, Hiroto 1 Van Beeumen, Roel 1 Van der Vorst, Henk Albertus 1 Vandereycken, Bart 1 Wang, Bin 1 Wang, Chern-Shuh 1 Wang, Lin-Wang 1 Wu, Kesheng 1 Xiao, Liling 1 Xie, Huiqing 1 Xu, Shufang 1 Zha, Hongyuan 1 Zhang, Pingwen 1 Zhou, Ming 1 Zhou, Yunshen all top 5 Serials 12 SIAM Journal on Matrix Analysis and Applications 9 Linear Algebra and its Applications 7 SIAM Journal on Scientific Computing 5 ACM Transactions on Mathematical Software 3 International Journal for Numerical Methods in Engineering 3 Journal of Computational and Applied Mathematics 3 Taiwanese Journal of Mathematics 2 Journal of Computational Physics 2 Journal of Computational Mathematics 2 Numerical Linear Algebra with Applications 2 Software - Environments - Tools 2 Science China. Mathematics 1 IMA Journal of Numerical Analysis 1 Mathematics of Computation 1 Applied Mathematics and Computation 1 BIT 1 IEEE Transactions on Automatic Control 1 Numerische Mathematik 1 Applied Numerical Mathematics 1 Journal of Fudan University. Natural Science 1 Journal of Parallel and Distributed Computing 1 International Journal of High Speed Computing 1 Communications in Statistics. Simulation and Computation 1 ETNA. Electronic Transactions on Numerical Analysis 1 Annals of Numerical Mathematics 1 Optimization Methods & Software 1 Communications in Mathematical Sciences 1 Series in Contemporary Applied Mathematics CAM 1 Numerical Mathematics: Theory, Methods and Applications all top 5 Fields 72 Numerical analysis (65-XX) 22 Linear and multilinear algebra; matrix theory (15-XX) 8 Systems theory; control (93-XX) 5 General and overarching topics; collections (00-XX) 5 Quantum theory (81-XX) 4 Ordinary differential equations (34-XX) 4 Computer science (68-XX) 4 Optics, electromagnetic theory (78-XX) 2 Approximations and expansions (41-XX) 2 Operator theory (47-XX) 2 Statistics (62-XX) 2 Mechanics of deformable solids (74-XX) 2 Operations research, mathematical programming (90-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Mechanics of particles and systems (70-XX) 1 Biology and other natural sciences (92-XX) 1 Information and communication theory, circuits (94-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 67 Publications have been cited 2,237 times in 1,802 Documents Cited by ▼ Year ▼ LAPACK user’s guide. This work is dedicated to Jim Wilkinson. 3rd ed. Zbl 0934.65030 Anderson, E.; Bai, Z.; Bischof, C.; Blackford, S.; Demmel, J.; Dongarra, J.; Du Croz, J.; Greenbaum, A.; Hammarling, S.; McKenney, A.; Sorensen, D. 578 1999 Templates for the solution of algebraic eigenvalue problems. A practical guide. Zbl 0965.65058 327 2000 LAPACK user’s guide. 2nd ed. Zbl 0843.65018 Anderson, E.; Bai, Z.; Bischof, C.; Demmel, J.; Dongarra, J.; Du Croz, J.; Greenbaum, A.; Hammarling, S.; McKenney, A.; Ostrouchov, S.; Sorensen, D. 137 1995 Krylov subspace techniques for reduced-order modeling of large-scale dynamical systems. Zbl 1012.65136 Bai, Zhaojun 130 2002 SOAR: A second-order Arnoldi method for the solution of the quadratic eigenvalue problem. Zbl 1080.65024 Bai, Zhaojun; Su, Yangfeng 81 2005 LAPACK users’ guide. Zbl 0755.65028 Anderson, E.; Bai, Z.; Bischof, C. 80 1992 Dimension reduction of large-scale second-order dynamical systems via a second-order Arnoldi method. Zbl 1078.65058 Bai, Zhaojun; Su, Yangfeng 78 2005 A projection method for model reduction of bilinear dynamical systems. Zbl 1107.93012 Bai, Zhaojun; Skoogh, Daniel 59 2006 Some large-scale matrix computation problems. Zbl 0870.65035 Bai, Zhaojun; Fahey, Mark; Golub, Gene 50 1996 Solving rational eigenvalue problems via linearization. Zbl 1222.65034 Su, Yangfeng; Bai, Zhaojun 43 2011 An inverse free parallel spectral divide and conquer algorithm for nonsymmetric eigenproblems. Zbl 0876.65021 Bai, Zhaojun; Demmel, James; Gu, Ming 41 1997 ABLE: An adaptive block Lanczos method for non-Hermitian eigenvalue problems. Zbl 0932.65045 Bai, Zhaojun; Day, David; Ye, Qiang 39 1999 Minimization principles for the linear response eigenvalue problem. II: Computation. Zbl 1311.65102 Bai, Zhaojun; Li, Ren-Cang 32 2013 Minimization principles for the linear response eigenvalue problem I: Theory. Zbl 1263.65078 Bai, Zhaojun; Li, Ren-Cang 30 2012 Computing the generalized singular value decomposition. Zbl 0789.65024 Bai, Zhaojun; Demmel, James W. 27 1993 On swapping diagonal blocks in real Schur form. Zbl 0783.65030 Bai, Zhaojun; Demmel, James W. 23 1993 A Newton basis GMRES implementation. Zbl 0818.65022 Bai, Zhaojun; Hu, Dan; Reichel, Lothar 23 1994 Stability analysis of the two-level orthogonal Arnoldi procedure. Zbl 1382.65102 Lu, Ding; Su, Yangfeng; Bai, Zhaojun 23 2016 Using the matrix sign function to compute invariant subspaces. Zbl 0914.65035 Bai, Zhaojun; Demmel, James 22 1998 On an eigenvector-dependent nonlinear eigenvalue problem. Zbl 1401.65036 Cai, Yunfeng; Zhang, Lei-Hong; Bai, Zhaojun; Li, Ren-Cang 20 2018 A partial Padé-via-Lanczos method for reduced-order modeling. Zbl 0980.93012 Bai, Zhaojun; Freund, Roland W. 19 2001 Structure-preserving model reduction using a Krylov subspace projection formulation. Zbl 1100.65028 Li, Ren-Cang; Bai, Zhaojun 19 2005 Bounds for the trace of the inverse and the determinant of symmetric positive definite matrices. Zbl 0883.15013 Bai, Zhaojun; Golub, Gene H. 18 1997 Optimizing Halley’s iteration for computing the matrix polar decomposition. Zbl 1215.65081 Nakatsukasa, Yuji; Bai, Zhaojun; Gygi, François 17 2010 Nonlinear Rayleigh-Ritz iterative method for solving large scale nonlinear eigenvalue problems. Zbl 1198.65072 Liao, Ben-Shan; Bai, Zhaojun; Lee, Lie-Quan; Ko, Kwok 17 2010 Error analysis of the Lanczos algorithm for the nonsymmetric eigenvalue problem. Zbl 0809.65029 Bai, Zhaojun 16 1994 Error estimation on the Padé approximation of transfer functions via the Lanczos process. Zbl 0913.41013 Bai, Zhaojun; Ye, Qiang 14 1998 On a block implementation of Hessenberg multishift QR iteration. Zbl 0726.65035 Bai, Zhaojun; Demmel, James 14 1989 Adaptive projection subspace dimension for the thick-restart Lanczos method. Zbl 1364.65089 Yamazaki, Ichitaro; Bai, Zhaojun; Simon, Horst; Wang, Lin-Wang; Wu, Kesheng 14 2010 Trace minimization principles for positive semi-definite pencils. Zbl 1262.15010 Liang, Xin; Li, Ren-Cang; Bai, Zhaojun 14 2013 Robust Rayleigh quotient minimization and nonlinear eigenvalue problems. Zbl 1416.65148 Bai, Zhaojun; Lu, Ding; Vandereycken, Bart 14 2018 Generalized QR factorization and its applications. Zbl 0747.65022 Anderson, E.; Bai, Z.; Dongarra, J. 12 1992 Nonlinear rank-one modifications of the symmetric eigenvalue problem. Zbl 1224.65093 Huang, Xin; Bai, Zhaojun; Su, Yangfeng 11 2010 An algebraic substructuring method for large-scale eigenvalue calculation. Zbl 1092.65032 Yang, Chao; Gao, Weiguo; Bai, Zhaojun; Li, Xiaoye S.; Lee, Lie-Quan; Husbands, Parry; Ng, Esmond 11 2005 A two-directional Arnoldi process and its application to parametric model order reduction. Zbl 1160.65012 Li, Yung-Ta; Bai, Zhaojun; Su, Yangfeng 11 2009 A new preprocessing algorithm for the computation of the generalized singular value decomposition. Zbl 0785.65046 Bai, Zhaojun; Zha, Hongyuan 11 1993 Minimization principles and computation for the generalized linear response eigenvalue problem. Zbl 1293.65053 Bai, Zhaojun; Li, Ren-Cang 11 2014 The Lanczos method for parameterized symmetric linear systems with multiple right-hand sides. Zbl 1205.65149 Meerbergen, Karl; Bai, Zhaojun 11 2010 Eigenvalue-based characterization and test for positive realness of scalar transfer functions. Zbl 0990.93044 Bai, Zhaojun; Freund, Roland W. 10 2000 An implementation and evaluation of the AMLS method for sparse eigenvalue problems. Zbl 1291.65121 Gao, Weiguo; Li, Xiaoye S.; Yang, Chao; Bai, Zhaojun 10 2008 Linear response eigenvalue problem solved by extended locally optimal preconditioned conjugate gradient methods. Zbl 1358.65021 Bai, ZhaoJun; Li, RenCang; Lin, WenWei 9 2016 The important modes of subsystems: a moment-matching approach. Zbl 1194.74119 Liao, Ben-Shan; Bai, Zhaojun; Gao, Weiguo 9 2007 Algorithm 776: SRRIT: A Fortran subroutine to calculate the dominant invariant subspace of a nonsymmetric matrix. Zbl 0912.65029 Bai, Zhaojun; Stewart, G. W. 8 1997 A symmetric band Lanczos process based on coupled recurrences and some applications. Zbl 0997.65064 Bai, Zhaojun; Freund, Roland W. 8 2001 Reduced-order modeling. Zbl 1180.78032 Bai, Zhaojun; Dewilde, Patrick M.; Freund, Roland W. 8 2005 The spectral decomposition of nonsymmetric matrices on distributed memory parallel computers. Zbl 0890.65034 Bai, Z.; Demmel, J.; Dongarra, J.; Petitet, A.; Robinson, H. 7 1997 A Padé approximate linearization algorithm for solving the quadratic eigenvalue problem with low-rank damping. Zbl 1352.65120 Lu, Ding; Huang, Xin; Bai, Zhaojun; Su, Yangfeng 6 2015 Progress in the numerical solution of the nonsymmetric eigenvalue problem. Zbl 0838.65033 Bai, Zhaojun 5 1995 On computing condition numbers to the nonsymmetric eigenproblem. Zbl 0889.65044 Bai, Z.; Demmel, J.; McKenny, A. 5 1993 Hybrid preconditioning for iterative diagonalization of ill-conditioned generalized eigenvalue problems in electronic structure calculations. Zbl 1349.81204 Cai, Yunfeng; Bai, Zhaojun; Pask, John E.; Sukumar, N. 5 2013 The second-order biorthogonalization procedure and its application to quadratic eigenvalue problems. Zbl 1088.65035 Wang, Bin; Su, Yangfeng; Bai, Zhaojun 4 2006 An implementation of the GMRES method using QR factorization. Zbl 0818.65023 Bai, Zhaojun; Hu, Dan; Reichel, Lothar 4 1992 A unified Krylov projection framework for structure-preserving model reduction. Zbl 1154.93010 Bai, Zhaojun; Li, Ren-cang; Su, Yangfeng 4 2008 A nonlinear QR algorithm for banded nonlinear eigenvalue problems. Zbl 1369.65057 Garrett, C. Kristopher; Bai, Zhaojun; Li, Ren-Cang 4 2016 Sharp estimation of convergence rate for self-consistent field iteration to solve eigenvector-dependent nonlinear eigenvalue problems. Zbl 1492.65142 Bai, Zhaojun; Li, Ren-Cang; Lu, Ding 4 2022 Computing resonant modes of accelerator cavities by solving nonlinear eigenvalue problems via rational approximation. Zbl 1416.78039 Van Beeumen, Roel; Marques, Osni; Ng, Esmond G.; Yang, Chao; Bai, Zhaojun; Ge, Lixin; Kononenko, Oleksiy; Li, Zenghai; Ng, Cho-Kuen; Xiao, Liling 4 2018 Note on the quadratic convergence of Kogbetliantz’s algorithm for computing the singular value decomposition. Zbl 0652.65028 Bai, Zhaojun 3 1988 A high-quality preconditioning technique for multi-length-scale symmetric positive definite linear systems. Zbl 1212.65122 Yamazaki, Ichitaro; Bai, Zhaojun; Chen, Wenbin; Scalettar, Richard 3 2009 Inverse free parallel method for the numerical solution of algebraic Riccati equations. Zbl 0820.65019 Bai, Zhaojun; Qian, Qingshan 3 1994 Arnoldi methods for structure-preserving dimension reduction of second-order dynamical systems. Zbl 1079.65530 Bai, Zhaojun; Meerbergen, Karl; Su, Yangfeng 3 2005 Orthogonal canonical correlation analysis and applications. Zbl 1455.65059 Wang, Li; Zhang, Lei-hong; Bai, Zhaojun; Li, Ren-Cang 3 2020 High-frequency response analysis via algebraic substructuring. Zbl 1195.74074 Ko, Jin Hwan; Bai, Zhaojun 3 2008 A structured quasi-Arnoldi procedure for model order reduction of second-order systems. Zbl 1237.93036 Li, Yung-Ta; Bai, Zhaojun; Lin, Wen-Wei; Su, Yangfeng 2 2012 Stable solutions of linear systems involving long chain of matrix multiplications. Zbl 1220.65035 Bai, Zhaojun; Lee, Cherung; Li, Ren-Cang; Xu, Shufang 2 2011 Convergence analysis of a locally accelerated preconditioned steepest descent method for Hermitian-definite generalized eigenvalue problems. Zbl 1424.65039 Cai, Yunfeng; Bai, Zhaojun; Pask, John E.; Sukumar, N. 2 2018 A parallel algorithm for computing the generalized singular value decomposition. Zbl 0797.65038 Bai, Zhaojun 1 1994 A method for profiling the distribution of eigenvalues using the AS method. Zbl 1198.65076 Senzaki, Kenta; Tadano, Hiroto; Sakurai, Tetsuya; Bai, Zhaojun 1 2010 Sharp estimation of convergence rate for self-consistent field iteration to solve eigenvector-dependent nonlinear eigenvalue problems. Zbl 1492.65142 Bai, Zhaojun; Li, Ren-Cang; Lu, Ding 4 2022 Orthogonal canonical correlation analysis and applications. Zbl 1455.65059 Wang, Li; Zhang, Lei-hong; Bai, Zhaojun; Li, Ren-Cang 3 2020 On an eigenvector-dependent nonlinear eigenvalue problem. Zbl 1401.65036 Cai, Yunfeng; Zhang, Lei-Hong; Bai, Zhaojun; Li, Ren-Cang 20 2018 Robust Rayleigh quotient minimization and nonlinear eigenvalue problems. Zbl 1416.65148 Bai, Zhaojun; Lu, Ding; Vandereycken, Bart 14 2018 Computing resonant modes of accelerator cavities by solving nonlinear eigenvalue problems via rational approximation. Zbl 1416.78039 Van Beeumen, Roel; Marques, Osni; Ng, Esmond G.; Yang, Chao; Bai, Zhaojun; Ge, Lixin; Kononenko, Oleksiy; Li, Zenghai; Ng, Cho-Kuen; Xiao, Liling 4 2018 Convergence analysis of a locally accelerated preconditioned steepest descent method for Hermitian-definite generalized eigenvalue problems. Zbl 1424.65039 Cai, Yunfeng; Bai, Zhaojun; Pask, John E.; Sukumar, N. 2 2018 Stability analysis of the two-level orthogonal Arnoldi procedure. Zbl 1382.65102 Lu, Ding; Su, Yangfeng; Bai, Zhaojun 23 2016 Linear response eigenvalue problem solved by extended locally optimal preconditioned conjugate gradient methods. Zbl 1358.65021 Bai, ZhaoJun; Li, RenCang; Lin, WenWei 9 2016 A nonlinear QR algorithm for banded nonlinear eigenvalue problems. Zbl 1369.65057 Garrett, C. Kristopher; Bai, Zhaojun; Li, Ren-Cang 4 2016 A Padé approximate linearization algorithm for solving the quadratic eigenvalue problem with low-rank damping. Zbl 1352.65120 Lu, Ding; Huang, Xin; Bai, Zhaojun; Su, Yangfeng 6 2015 Minimization principles and computation for the generalized linear response eigenvalue problem. Zbl 1293.65053 Bai, Zhaojun; Li, Ren-Cang 11 2014 Minimization principles for the linear response eigenvalue problem. II: Computation. Zbl 1311.65102 Bai, Zhaojun; Li, Ren-Cang 32 2013 Trace minimization principles for positive semi-definite pencils. Zbl 1262.15010 Liang, Xin; Li, Ren-Cang; Bai, Zhaojun 14 2013 Hybrid preconditioning for iterative diagonalization of ill-conditioned generalized eigenvalue problems in electronic structure calculations. Zbl 1349.81204 Cai, Yunfeng; Bai, Zhaojun; Pask, John E.; Sukumar, N. 5 2013 Minimization principles for the linear response eigenvalue problem I: Theory. Zbl 1263.65078 Bai, Zhaojun; Li, Ren-Cang 30 2012 A structured quasi-Arnoldi procedure for model order reduction of second-order systems. Zbl 1237.93036 Li, Yung-Ta; Bai, Zhaojun; Lin, Wen-Wei; Su, Yangfeng 2 2012 Solving rational eigenvalue problems via linearization. Zbl 1222.65034 Su, Yangfeng; Bai, Zhaojun 43 2011 Stable solutions of linear systems involving long chain of matrix multiplications. Zbl 1220.65035 Bai, Zhaojun; Lee, Cherung; Li, Ren-Cang; Xu, Shufang 2 2011 Optimizing Halley’s iteration for computing the matrix polar decomposition. Zbl 1215.65081 Nakatsukasa, Yuji; Bai, Zhaojun; Gygi, François 17 2010 Nonlinear Rayleigh-Ritz iterative method for solving large scale nonlinear eigenvalue problems. Zbl 1198.65072 Liao, Ben-Shan; Bai, Zhaojun; Lee, Lie-Quan; Ko, Kwok 17 2010 Adaptive projection subspace dimension for the thick-restart Lanczos method. Zbl 1364.65089 Yamazaki, Ichitaro; Bai, Zhaojun; Simon, Horst; Wang, Lin-Wang; Wu, Kesheng 14 2010 Nonlinear rank-one modifications of the symmetric eigenvalue problem. Zbl 1224.65093 Huang, Xin; Bai, Zhaojun; Su, Yangfeng 11 2010 The Lanczos method for parameterized symmetric linear systems with multiple right-hand sides. Zbl 1205.65149 Meerbergen, Karl; Bai, Zhaojun 11 2010 A method for profiling the distribution of eigenvalues using the AS method. Zbl 1198.65076 Senzaki, Kenta; Tadano, Hiroto; Sakurai, Tetsuya; Bai, Zhaojun 1 2010 A two-directional Arnoldi process and its application to parametric model order reduction. Zbl 1160.65012 Li, Yung-Ta; Bai, Zhaojun; Su, Yangfeng 11 2009 A high-quality preconditioning technique for multi-length-scale symmetric positive definite linear systems. Zbl 1212.65122 Yamazaki, Ichitaro; Bai, Zhaojun; Chen, Wenbin; Scalettar, Richard 3 2009 An implementation and evaluation of the AMLS method for sparse eigenvalue problems. Zbl 1291.65121 Gao, Weiguo; Li, Xiaoye S.; Yang, Chao; Bai, Zhaojun 10 2008 A unified Krylov projection framework for structure-preserving model reduction. Zbl 1154.93010 Bai, Zhaojun; Li, Ren-cang; Su, Yangfeng 4 2008 High-frequency response analysis via algebraic substructuring. Zbl 1195.74074 Ko, Jin Hwan; Bai, Zhaojun 3 2008 The important modes of subsystems: a moment-matching approach. Zbl 1194.74119 Liao, Ben-Shan; Bai, Zhaojun; Gao, Weiguo 9 2007 A projection method for model reduction of bilinear dynamical systems. Zbl 1107.93012 Bai, Zhaojun; Skoogh, Daniel 59 2006 The second-order biorthogonalization procedure and its application to quadratic eigenvalue problems. Zbl 1088.65035 Wang, Bin; Su, Yangfeng; Bai, Zhaojun 4 2006 SOAR: A second-order Arnoldi method for the solution of the quadratic eigenvalue problem. Zbl 1080.65024 Bai, Zhaojun; Su, Yangfeng 81 2005 Dimension reduction of large-scale second-order dynamical systems via a second-order Arnoldi method. Zbl 1078.65058 Bai, Zhaojun; Su, Yangfeng 78 2005 Structure-preserving model reduction using a Krylov subspace projection formulation. Zbl 1100.65028 Li, Ren-Cang; Bai, Zhaojun 19 2005 An algebraic substructuring method for large-scale eigenvalue calculation. Zbl 1092.65032 Yang, Chao; Gao, Weiguo; Bai, Zhaojun; Li, Xiaoye S.; Lee, Lie-Quan; Husbands, Parry; Ng, Esmond 11 2005 Reduced-order modeling. Zbl 1180.78032 Bai, Zhaojun; Dewilde, Patrick M.; Freund, Roland W. 8 2005 Arnoldi methods for structure-preserving dimension reduction of second-order dynamical systems. Zbl 1079.65530 Bai, Zhaojun; Meerbergen, Karl; Su, Yangfeng 3 2005 Krylov subspace techniques for reduced-order modeling of large-scale dynamical systems. Zbl 1012.65136 Bai, Zhaojun 130 2002 A partial Padé-via-Lanczos method for reduced-order modeling. Zbl 0980.93012 Bai, Zhaojun; Freund, Roland W. 19 2001 A symmetric band Lanczos process based on coupled recurrences and some applications. Zbl 0997.65064 Bai, Zhaojun; Freund, Roland W. 8 2001 Templates for the solution of algebraic eigenvalue problems. A practical guide. Zbl 0965.65058 327 2000 Eigenvalue-based characterization and test for positive realness of scalar transfer functions. Zbl 0990.93044 Bai, Zhaojun; Freund, Roland W. 10 2000 LAPACK user’s guide. This work is dedicated to Jim Wilkinson. 3rd ed. Zbl 0934.65030 Anderson, E.; Bai, Z.; Bischof, C.; Blackford, S.; Demmel, J.; Dongarra, J.; Du Croz, J.; Greenbaum, A.; Hammarling, S.; McKenney, A.; Sorensen, D. 578 1999 ABLE: An adaptive block Lanczos method for non-Hermitian eigenvalue problems. Zbl 0932.65045 Bai, Zhaojun; Day, David; Ye, Qiang 39 1999 Using the matrix sign function to compute invariant subspaces. Zbl 0914.65035 Bai, Zhaojun; Demmel, James 22 1998 Error estimation on the Padé approximation of transfer functions via the Lanczos process. Zbl 0913.41013 Bai, Zhaojun; Ye, Qiang 14 1998 An inverse free parallel spectral divide and conquer algorithm for nonsymmetric eigenproblems. Zbl 0876.65021 Bai, Zhaojun; Demmel, James; Gu, Ming 41 1997 Bounds for the trace of the inverse and the determinant of symmetric positive definite matrices. Zbl 0883.15013 Bai, Zhaojun; Golub, Gene H. 18 1997 Algorithm 776: SRRIT: A Fortran subroutine to calculate the dominant invariant subspace of a nonsymmetric matrix. Zbl 0912.65029 Bai, Zhaojun; Stewart, G. W. 8 1997 The spectral decomposition of nonsymmetric matrices on distributed memory parallel computers. Zbl 0890.65034 Bai, Z.; Demmel, J.; Dongarra, J.; Petitet, A.; Robinson, H. 7 1997 Some large-scale matrix computation problems. Zbl 0870.65035 Bai, Zhaojun; Fahey, Mark; Golub, Gene 50 1996 LAPACK user’s guide. 2nd ed. Zbl 0843.65018 Anderson, E.; Bai, Z.; Bischof, C.; Demmel, J.; Dongarra, J.; Du Croz, J.; Greenbaum, A.; Hammarling, S.; McKenney, A.; Ostrouchov, S.; Sorensen, D. 137 1995 Progress in the numerical solution of the nonsymmetric eigenvalue problem. Zbl 0838.65033 Bai, Zhaojun 5 1995 A Newton basis GMRES implementation. Zbl 0818.65022 Bai, Zhaojun; Hu, Dan; Reichel, Lothar 23 1994 Error analysis of the Lanczos algorithm for the nonsymmetric eigenvalue problem. Zbl 0809.65029 Bai, Zhaojun 16 1994 Inverse free parallel method for the numerical solution of algebraic Riccati equations. Zbl 0820.65019 Bai, Zhaojun; Qian, Qingshan 3 1994 A parallel algorithm for computing the generalized singular value decomposition. Zbl 0797.65038 Bai, Zhaojun 1 1994 Computing the generalized singular value decomposition. Zbl 0789.65024 Bai, Zhaojun; Demmel, James W. 27 1993 On swapping diagonal blocks in real Schur form. Zbl 0783.65030 Bai, Zhaojun; Demmel, James W. 23 1993 A new preprocessing algorithm for the computation of the generalized singular value decomposition. Zbl 0785.65046 Bai, Zhaojun; Zha, Hongyuan 11 1993 On computing condition numbers to the nonsymmetric eigenproblem. Zbl 0889.65044 Bai, Z.; Demmel, J.; McKenny, A. 5 1993 LAPACK users’ guide. Zbl 0755.65028 Anderson, E.; Bai, Z.; Bischof, C. 80 1992 Generalized QR factorization and its applications. Zbl 0747.65022 Anderson, E.; Bai, Z.; Dongarra, J. 12 1992 An implementation of the GMRES method using QR factorization. Zbl 0818.65023 Bai, Zhaojun; Hu, Dan; Reichel, Lothar 4 1992 On a block implementation of Hessenberg multishift QR iteration. Zbl 0726.65035 Bai, Zhaojun; Demmel, James 14 1989 Note on the quadratic convergence of Kogbetliantz’s algorithm for computing the singular value decomposition. Zbl 0652.65028 Bai, Zhaojun 3 1988 all cited Publications top 5 cited Publications all top 5 Cited by 2,983 Authors 59 Benner, Peter 29 Jiang, Yaolin 28 Li, Rencang 25 Reichel, Lothar 21 Bai, Zhaojun 20 Dongarra, Jack J. 20 Lin, Wen-Wei 20 Nakatsukasa, Yuji 18 Kressner, Daniel 18 Zhang, Lei-Hong 17 Quintana-Ortí, Enrique S. 16 Mehrmann, Volker 16 Wei, Yimin 15 Higham, Nicholas J. 15 Jarlebring, Elias 14 Román, Jose E. 13 Dopico, Froilán M. 13 Jbilou, Khalide 13 Saad, Yousef 12 Wu, Gang 11 Aishima, Kensuke 11 Gugercin, Serkan 11 Jia, Zhongxiao 11 Meerbergen, Karl 11 Simoncini, Valeria 11 Stykel, Tatjana 11 Zlatev, Zahari 10 Desmet, Wim 10 Eberhard, Peter 10 Huang, Tsungming 10 Tomov, Stanimire Z. 10 Van Dooren, Paul M. 10 Yang, Chao 9 Lin, Yiqin 9 Sadkane, Miloud 9 Wang, Weichung 8 Bao, Liang 8 Demmel, James Weldon 8 Michiels, Wim 8 Nechepurenko, Yuri M. 8 Quintana-Ortí, Gregorio 8 Xu, Kangli 8 Yamamoto, Yusaku 8 Ye, Qiang 7 Alam, Rafikul 7 Baglama, James 7 Bentbib, Abdeslem Hafid 7 Drmač, Zlatko 7 Keyes, David Elliot 7 Li, Wen 7 Lin, Lin 7 Maier, Matthias Sebastian 7 Neymeyr, Klaus 7 Shen, Chungen 7 Solov’ëv, Sergeĭ Ivanovich 7 Su, Yangfeng 7 Tisseur, Françoise 7 Van der Vorst, Henk Albertus 7 Voss, Heinrich 7 Watkins, David S. 7 Xi, Yuanzhe 7 Xiao, Zhihua 7 Xu, Wei-Wei 6 Arndt, Daniel 6 Baboulin, Marc 6 Bangerth, Wolfgang 6 Campos, Carmen 6 Carson, Erin Claire 6 Deckers, Elke 6 Faragó, István 6 Freund, Roland W. 6 Grigori, Laura 6 Heister, Timo 6 Heltai, Luca 6 Hernández, Vicente G. 6 Huang, Weiqiang 6 Hwang, Tsung-Min 6 Kågström, Bo 6 Kronbichler, Martin 6 Lu, Ding 6 Lu, Linzhang 6 Mach, Thomas 6 Pelteret, Jean-Paul 6 Quintana, María C. 6 Sakurai, Tetsuya 6 Shao, Meiyue 6 Sleijpen, Gerard L. G. 6 Turcksin, Bruno 6 Wang, Xiaolong 6 Xie, Xiang 5 Bientinesi, Paolo 5 Breiten, Tobias 5 Chen, Xiaoshan 5 Dax, Achiya 5 Demyanko, Kirill V. 5 Faßbender, Heike 5 Feng, Lihong 5 Fenu, Caterina 5 Fika, Paraskevi 5 Ghafoor, Abdul ...and 2,883 more Authors all top 5 Cited in 263 Serials 136 Linear Algebra and its Applications 104 Journal of Computational and Applied Mathematics 96 Journal of Computational Physics 78 SIAM Journal on Scientific Computing 71 Computer Physics Communications 71 SIAM Journal on Matrix Analysis and Applications 63 Computer Methods in Applied Mechanics and Engineering 52 Numerical Algorithms 52 Numerical Linear Algebra with Applications 49 International Journal for Numerical Methods in Engineering 35 Computers & Mathematics with Applications 35 BIT 33 Applied Mathematics and Computation 28 Applied Numerical Mathematics 28 Journal of Scientific Computing 23 Numerische Mathematik 18 ACM Transactions on Mathematical Software 16 Computers and Fluids 16 Mathematics of Computation 16 Systems & Control Letters 15 International Journal of Control 15 Engineering Analysis with Boundary Elements 15 Optimization Methods & Software 15 Mathematical and Computer Modelling of Dynamical Systems 14 Automatica 14 Computational Mechanics 14 Advances in Computational Mathematics 13 Journal of Fluid Mechanics 13 Japan Journal of Industrial and Applied Mathematics 13 Computational Optimization and Applications 11 Journal of the Franklin Institute 11 Calcolo 11 Mathematics and Computers in Simulation 11 Applied Mathematical Modelling 11 Mathematical Programming. Series A. Series B 10 International Journal of Computer Mathematics 10 ETNA. Electronic Transactions on Numerical Analysis 9 Linear and Multilinear Algebra 9 SIAM Journal on Numerical Analysis 9 SIAM Journal on Optimization 8 Computational Statistics and Data Analysis 8 Multibody System Dynamics 8 Acta Numerica 7 Computing 7 Applied Mathematics Letters 7 Mathematical and Computer Modelling 7 European Journal of Operational Research 7 SIAM Review 7 Mathematical Problems in Engineering 7 International Journal of Systems Science. Principles and Applications of Systems and Integration 6 Physica D 6 Parallel Computing 6 Archives of Computational Methods in Engineering 6 Journal of Numerical Mathematics 6 GAMM-Mitteilungen 6 Statistics and Computing 5 Journal of Optimization Theory and Applications 5 COMPEL 5 Russian Journal of Numerical Analysis and Mathematical Modelling 5 ELA. The Electronic Journal of Linear Algebra 5 European Journal of Control 5 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik 5 Lobachevskii Journal of Mathematics 5 Foundations of Computational Mathematics 5 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 5 Numerical Algebra, Control and Optimization 5 JSIAM Letters 4 Acta Mechanica 4 International Journal for Numerical Methods in Fluids 4 Journal of Mathematical Physics 4 Theoretical Computer Science 4 Annals of Operations Research 4 Machine Learning 4 Physics of Fluids 4 Computational and Applied Mathematics 4 Computing and Visualization in Science 4 Communications in Nonlinear Science and Numerical Simulation 4 Concurrency and Computation: Practice & Experience 4 Journal of Machine Learning Research (JMLR) 4 Journal of Applied Mathematics and Computing 4 International Journal of Computational Methods 4 Mathematical Programming Computation 4 Science China. Mathematics 4 East Asian Journal on Applied Mathematics 3 Classical and Quantum Gravity 3 Inverse Problems 3 Computer Aided Geometric Design 3 Numerical Methods for Partial Differential Equations 3 Journal of Global Optimization 3 Annals of Physics 3 Journal of Nonlinear Science 3 Communications in Numerical Methods in Engineering 3 Parallel Algorithms and Applications 3 International Journal of Numerical Modelling 3 European Journal of Mechanics. A. Solids 3 Computational Geosciences 3 Combustion Theory and Modelling 3 Journal of High Energy Physics 3 Multiscale Modeling & Simulation 3 Advances in Difference Equations ...and 163 more Serials all top 5 Cited in 47 Fields 1,227 Numerical analysis (65-XX) 349 Linear and multilinear algebra; matrix theory (15-XX) 208 Systems theory; control (93-XX) 158 Fluid mechanics (76-XX) 141 Mechanics of deformable solids (74-XX) 134 Partial differential equations (35-XX) 123 Computer science (68-XX) 107 Operations research, mathematical programming (90-XX) 77 Statistics (62-XX) 73 Quantum theory (81-XX) 65 Optics, electromagnetic theory (78-XX) 65 Statistical mechanics, structure of matter (82-XX) 56 Ordinary differential equations (34-XX) 41 Mechanics of particles and systems (70-XX) 34 Calculus of variations and optimal control; optimization (49-XX) 31 Biology and other natural sciences (92-XX) 30 Dynamical systems and ergodic theory (37-XX) 29 Approximations and expansions (41-XX) 26 Operator theory (47-XX) 25 Combinatorics (05-XX) 23 Probability theory and stochastic processes (60-XX) 21 Information and communication theory, circuits (94-XX) 19 Classical thermodynamics, heat transfer (80-XX) 17 Geophysics (86-XX) 10 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 8 Algebraic geometry (14-XX) 8 Integral equations (45-XX) 7 Harmonic analysis on Euclidean spaces (42-XX) 7 Astronomy and astrophysics (85-XX) 6 Functions of a complex variable (30-XX) 6 Special functions (33-XX) 6 Relativity and gravitational theory (83-XX) 5 Difference and functional equations (39-XX) 5 Differential geometry (53-XX) 5 Global analysis, analysis on manifolds (58-XX) 4 Field theory and polynomials (12-XX) 3 History and biography (01-XX) 3 Real functions (26-XX) 3 Convex and discrete geometry (52-XX) 2 Commutative algebra (13-XX) 2 Potential theory (31-XX) 2 Integral transforms, operational calculus (44-XX) 2 Functional analysis (46-XX) 2 Mathematics education (97-XX) 1 General and overarching topics; collections (00-XX) 1 Number theory (11-XX) 1 Algebraic topology (55-XX) Citations by Year