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  1. Z. Bai, Note on the quadratic convergence of Kogbetliantz's algorithm for computing the singular value decomposition Linear Algebra and its Applications, Volume 104, June 1988, Pages 131-140 (pdf file)

  2. Z. Bai, Numerical Treatment of Restricted Gauss Markov Linear Model. Comm. in Stat. Simulat. and Comput., Vol.17, pp. 569--579,1988.

  3. Z. Bai and J. Demmel, On a Block Implementation of Hessenberg QR Iteration, Intl. J. of High Speed Computing, Vol.1, pp. 97--112, 1989. (pdf file)

  4. E. Anderson, Z. Bai and J. Dongrra, Generalized QR Decomposition and its Applications, Lin. Alg. Appl., Vol.162--164, pp. 243--271, Feb. 1992. (pdf file)

  5. Z. Bai, The CSD, GSVD, their Applications and Computation, IMA preprint series 958, Institute for Mathematics and its Applications, University of Minnesota, MN, 1992. (pdf file)

  6. Z. Bai, J. W. Demmel, Design of a parallel nonsymmetric eigenroutine toolbox, Part I, Computer Science Divsion Report UCB/CSD-92-718, Univ. of California, Berkeley. December 1992 (pdf file)

  7. Z. Bai, J. W. Demmel, On swapping diagonal blocks in real Schur form, Linear Algebra and its Applications, Volume 186, June 1993, Pages 75-95 (pdf file)

  8. Z. Bai, J. Demmel and A. McKenney, On Computing Condition Numbers for the Nonsymmetric Eigenproblem, ACM Trans. Math. Soft., Vol.19, pp. 202--223, 1993.

  9. Z. Bai and H. Zha, A New Preprocessing Algorithm for the Computation of the Generalized Singular Value Decomposition, SIAM J. Sci. Stat. Comp. Vol.14, pp. 1007--1012, 1993.

  10. Z. Bai and J. Demmel, Computing the Generalized Singular Value Decomposition, SIAM J. Sci. Comput. Vol.14, pp. 1464--1486, 1993

  11. Z. Bai, Error Analysis of Lanczos Algorithm for Nonsymmetric Eigenvalue Problem, Math. Comp. Vol.62, pp. 209--226, 1994. (pdf file)

  12. Z. Bai, A Parallel Algorithm for Computing the Generalized Singular Value Decomposition, J. of Parallel and Distributed Computing, Vol.20, pp. 280--288, 1994.

  13. Z. Bai, D. Hu and L. Reichel, A Newton Basis GMRES Implementation, IMA Journal of Numerical Analysis, Vol.14, No.4, 563--581, 1994. (pdf file)

  14. Z. Bai and Qingshan Qian, Inverse free parallel method for the numerical solution of algebraic Riccati equations. Processdings of the Fifth SIAM Conference on Applied Linear Algebra, SIAM, 1994. pp.167-171

  15. Z. Bai, A spectral transformation block Lanczos algorithm for solving sparse non-Hermitian eigenproblems. Processdings of the Fifth SIAM Conference on Applied Linear Algebra, SIAM, 1994. pp.307-311.

  16. Z. Bai, Progress in the Numerical Solution of the Nonsymmetric Eigenvalue Problem, Numer. Lin. Alg. Appl. Vol.2, No.3, pp. 219--234, 1995. (pdf file)

  17. Z. Bai, M. Fahey and G. Golub, Some large-scale matrix computation problems Journal of Computational and Applied Mathematics, Volume 74, Issues 1-2, 5 November 1996, Pages 71-89 (pdf file)

  18. Z. Bai and G. Golub, Bounds for the Trace of the Inverse and the Determinant of Symmetric Positive Definite Matrices, Annals of Numerical Mathematics, Vo.4, pp.29--38, 1997. (pdf file)

  19. Z. Bai, J. Demmel and M. Gu, An Inverse Free Parallel Spectral Divide and Conquer Algorithm for Nonsymmetric Eigenproblems, Numer. Math. vol.76, pp.279-308, 1997 pdf file

  20. Z. Bai, J. Demmel, J. Dongarra, A. Petitet, H. Robinson and K. Stanley, The Spectral Decomposition of Nonsymmetric Matrices on Distributed Memory Parallel Machines, SIAM J. Sci. Comput. Vol.18, pp. 1446--1461, 1997.

  21. Z. Bai and G. W. Stewart, Algorithm 775: SRRIT -- A FORTRAN Subroutine to Calculate the Dominant Invariant Subspace of a Nonsymmetric Matrix, ACM TOMS Vol. 23, No.4, 1997, pp.494-513. pdf file

  22. Z. Bai, A. Orlandi, W. T. Smith, Moment matching method for numerical solution of MTL equations in interconnect analysis Journal of Computational and Applied Mathematics, Volume 86, Issue 1, 28 November 1997, Pages 3-16 (pdf file)

  23. Z. Bai, M. Fahey, G. Golub, M. Menon and E. Richter, Computing Partial Eigenvalue Sum with Applications in Electronic Structure Calculations, Technical Report, SCCM-98-03, Stanford University, 1998 (pdf file)

  24. Z. Bai and J. Demmel, Using the Matrix Sign Function to Compute Invariant Subspaces, SIAM J. Mat. Anal. Appl., Vol.19, pp.205--225, 1998

  25. Z. Bai, P. Feldmann and R. Freund, How to Make Theoretically Passive Reduced-Order Models Passive in Practice, Proc. of the IEEE Custom Integrated Circuits Conference (CICC), pp.207--210, IEEE, 1998. (pdf file)

  26. Z. Bai and Q. Ye, Error Estimation of the Pad\'{e} Approximation of Transfer Functions via the Lanczos Process, Electronic Transaction on Numerical Analysis, Vol. 7, pp.1--17, 1998 (pdf file)

  27. Z. Bai, R. S. Slone, W. T. Smith and Q. Ye, Error bound for reduced system model by Pade Approximation via the Lanczos process, IEEE Trans. on Comput.-Aided Design of Intergrated Circuits and Systems, Vo. 18, No. 2, pp. 133-141, Feb. 1999

  28. Z. Bai, D. Day, Q. Ye, ABLE: an Adaptive Block Lanczos Method for Non-Hermitian Eigenvalue Problems, SIAM J. Mat. Anal. Appl. Vol.20, pp. 1060--1082, 1999 pdf file

  29. Z. Bai and R. Freund, Eigenvalue-based Characterization and Test for Positive Realness of Scalar Transfer Functions, IEEE Trans. Automat. Control., Vol. 45, No.12, Dec. 2000, pp.2396 -- 2402.

  30. Z. Bai, D. Bindel, J. Clark, J. Demmel, K. S. J. Pister, N. Zhou, New Numerical Techniques and Tools in SUGAR for 3D MEMS Simulations, Proc. of the Fourth International Conference on Modeling and Simulation of Microsystems, pp. 31--34, Hilton Head Island, South Carolina, March 19-21, 2001,

  31. Z. Bai and R. Freund, A Partial Pad\'{e}-via-Lanczos Method for Reduced-Order Modeling, Lin. Alg. Appl., vol.332-334, Aug. 2001, pp.139-164. (pdf file)

  32. Z. Bai and R. Freund, A symmetric band Lanczos process based on coupled recurrence and some applications, SIAM J. Sci. Comput., vol.23, pp.542--562, 2001 (pdf file)

  33. Z. Bai, Krylov subspace techniques for reduced-order modeling of large-scale dynamical systems Applied Numerical Mathematics, Volume 43, Issues 1-2, October 2002, Pages 9-44 pdf file

  34. Z. Bai and G. Golub, Computation of large-scale quadratic forms and transfer functions using the theory of moments, quadrature and Pade approximation, in ``Modern Methods in Scientific Computing and Applications'', A. Bourlioux and M. J. Gander, editors, NATO Science Series II Mathematics, Physics and Chemistry, Vol.75, pp.1--30, Kluwer, 2002 (preprint)

  35. G. Lou, T. W. Wu and Z. Bai, Disk brake squeal prediction using the ABLE algorithm, J. of Sound and Vibration, Vol.272, 731--748, 2004 pdf file

  36. Y. Su, J. Wang, X. Zeng, Z. Bai, C. Chiang and D. Zhou, SAPOR: second-order {A}rnoldi method for passive order reduction of RCS circuits. Proceedings of IEEE/ACM International Conference on Computer Aided Design(ICCAD-2004), pp.74--79, IEEE press, 2004 pdf file

  37. C. Yang, W. Gao, Z. Bai, X. Li, L. Lee, P. Husbands, E. Ng, An algebraic sub-structuring method for large-scale eigenvalue calculation , SIAM J. Sci. Computing, Vol.27, No.3, pp.873-892, 2005 pdf file

  38. Z. Bai, P. Dewilde and R. Freund, Reduced-order modeling , in Handbook of Numerical Analysis Vol. XIII, Numerical Methods in Electromagnetics, W. Schilders and E.J.W. ter Maten, eds. pp. 825--895, 2005

  39. R.-C. Li and Z. Bai, Structure-preserving model reduction using a Krylov subspace projection formation . Comm. Math. Sci. Vol.3, pp.179--199, 2005 pdf file

  40. Z. Bai, K. Meerbergen, Y. Su, Arnoldi methods for structure-preserving dimension reduction of second-order dynamical systems, Springer LNCSE Vol. 45, the Proceedings of Oberwolfach Workshop on Dimension Reduction, pp.173--189,2005 preprint

  41. Z. Bai and Y. Su, Dimension reduction of second-order dynamical systems via a second-order Arnoldi method, SIAM J. Sci. Comp., Vol.25, No.5, 2005, pp.1692-1709, 2005 pdf file

  42. Z. Bai and Y. Su, SOAR: A second-order Arnoldi method for the solution of the quadratic eigenvalue problem, SIAM J. Matrix Anal. Appl., Vol.26, No.3, pp.640-659, 2005 pdf file

  43. B. Liu, X. Zeng, Y. Su, J. Tao, Z. Bai, C. Chiang and D. Zhou, Block SAPOR: block second-order Arnoldi method for passive order reduction of multi-input multi-output RCS interconnect circuits. in Design Automation Conference, 2005. Proceedings of the ASC-DAC 2005. pp.244-249, 2005 pdf file

  44. I. Yamazaki, V. Natarajan, Z. Bai and B. Hamann, Segmenting point sets, Proceedings of IEEE International Conference on Shape Modeling and Applications 2006, Matsushima, Japan, pp.4--13, June 2006 pdf file

  45. Z. Bai, J. Demmel, J. Dongarra, J. Langou and J. Wang, LAPACK, Chapter 75 of CRC Handbook of Linear Algebra, Leslie Hogben ed., 24 pages, CRC Press, 2006 pdf file

  46. B. Wang, Y. Su and Z. Bai, The second-order biorthogonalization procedure and its application to quadratic eigenvalue problems, Appl. Math. and Comp., Vol.172, pp.788--796, 2006

  47. Z. Bai and C. Yang, From self-consistency to SOAR: Solving large-scale nonlinear eigenvalue problems. SIAM News, Vol.39, No.3, 2006

  48. Z. Bai and B. Liao, Towards an optimal substructuring method for model reduction. Lecture Notes in Computer Science Vol. 3732, pp.276--285, 2006 pdf file

  49. D. Bindel, Z. Bai and J. Demmel, Model reduction for RF MEMS simulation. Lecture Notes in Computer Science Vol. 3732, pp.286--295, 2006 pdf file

  50. Z. Bai and D. Skoogh, A projection method for model reduction of bilinear dynamical systems Linear Algebra and its Applications, Volume 415, Issues 2-3, 1 June 2006, Pages 406-425 pdf file

  51. J.-H. Ko and Z. Bai, An algebraic substructuring method for high-frequency response analysis of micro-systems, Lecture Notes in Computer Science, Vol. 4487, pp.521-528, 2007 (pdf file)

  52. Y.-T. Li, Z. Bai, Y. Su and X. Zeng, Parameterized Model Order Reduction via a Two-Directional Arnoldi Process, Proceedings of IEEE/ACM International Conference on Computer-Aided Design (ICCAD 2007), pp.868-873, 2007 (pdf file)

  53. B.-S. Liao, Z. and W. Gao, The important modes of subsystems: a moment-matching approach, Inter. J. Numer. Meth. Engng, Vol.70, 1581-1597, 2007 (pdf file)

  54. Z. Bai, W. Chen, R. Scalettar, I. Yamazaki, Robust and Efficient Numerical Linear Algebra Solvers and Applications in Quantum Mechanical Simulations. Proceedings of the 4th International Congress of Chinese Mathematician (ICCM), Edited by Lizhan Ji, Kefeng Liu, Lo Yang, Shing-Tung Yau, Vol.III, pp.253--268, Higher Education Press, China. 2007 (ISBN 978-7-04-023267-7) (preprint)

  55. W. Gao, X. S. Li, C. Yang and Z. Bai, Performance evaluation of a multilevel sub-structuring method for sparse eigenvalue problems, Lecture Notes in Computational Science and Engineering, Vol.55 (Domain Decomposition. Methods in Science and Engineering XVI), O. B. Widlund and D. E. Keyes eds., pp.231-238, Springer, 2007.

  56. J.-H. Ko and Z. Bai, High-frequency response analysis via algebraic substructuring, Inter. J. Numer. Meth. Engng. Vol.76, 2008, Pages: 295-313 (pdf file)

  57. J. H. Ko, S. N. Jun, D. Byun and Z. Bai, An algebraic substructuring using multiple shifts for eigenvalue computations. J. Mechanical Science and Engineering, Vol.22, 2008, pp.440-449 (pdf file)

  58. Z. Bai, R-C. Li and Y. Su, A Unified Krylov Projection Framework for Structure-Preserving Model Reduction. In ``Model Order Reduction: Theory, Research Aspects and Applications'', Springer Series of Mathematics in Industry, Vol.13. Schilders, Wilhelmus H.A.; van der Vorst, Henk A.; Rommes, Joost (Eds.) pp.75-93, 2008 (preprint)

  59. Y.-T. Li, Z. Bai, Y. Su and X. Zeng, Model order reduction of parameterized interconnect networks via a two-directional Arnoldi Process. IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, Vol.27, pp.1571--1582. 2008 (pdf file)

  60. W. Gao, X. Li, C. Yang and Z. Bai, An implementation and evaluation of the AMLS method for Sparse Eigenvalue Problems, ACM Trans. Math. Software. Vol.34, pp.20:2--20:28, 2008 (pdf file)

  61. Sourav Chatterji, Ichitaro Yamazaki, Zhaojun Bai and Jonathan Eisen. CompostBin: A DNA composition-based algorithm for binning environmental shotgun reads. 12th Annual International Conference on Research in Computational Molecular Biology (RECOMB 2008). Lecture Notes in Computer Science: Research in Computational Molecular Biology, Vol.4955, pp.17-28, 2008 (pdf file)

  62. Zhaojun Bai, Wenbin Chen, Richard Scalettar and Ichitaro Yamazaki, Numerical Methods for Quantum Monte Carlo Simulations of the Hubbard Model, In ``Multi-Scale Phenomena in Complex Fluids'' edited by Thomas Y. Hou, Chun Liu and Jian-Guo Liu, pp. 1-110, Higher Education Press and World Scientific, 2009 (ISBN-9787040173581) (preprint)

  63. C. N. Varney, C.-R. Lee, Z. Bai, S. Chiesa, M. Jarrell and R. T. Scalettar, Quantum Monte Carlo study of the two-dimensional fermion Hubbard model. Phy. Rev. B, 80, 075116, 2009 (DOI:10.1103/PhysRevB.80.075116) (pdf file) (selected for the September 2009 issue of Virtual Journal of Atomic Quantum Fluids, published by the American Physical Society and the American Institute of Physics in cooperation with numerous other societies and publishers).

  64. I. Yamazaki, Z. Bai, W. Chen and R. Scalettar, A high-quality preconditioning technique for multi-length-scale symmetric positive definite linear systems. Numer. Math. Theor. Meth. Appl. Vol.2, No.4, pp.469-484, 2009 (pdf file)

  65. Y.-T. Li, Z. Bai and Y. Su, A two-directional Arnoldi process and its application to parametric model order reduction. J. Comput. and Appl. Math. Vol.226, pp.10-21, 2009 (pdf file)

  66. I. Yamazaki, V. Natarajan, Z. Bai and B. Hamann, Segmenting Point-sampled Surfaces. Journal of Visual Computer, Vol.26, pp.1421-1433, 2010, (preprint)

  67. Y. Nakatsukasa, Z. Bai and F. Gygi, Optimizing Halley's Iteration for Computing the Matrix Polar Decomposition, SIAM J. of Matrix Analysis and Applications, Vol.31, No.5, pp.2700-2720, 2010. (preprint)

  68. E. Khatami, C.-R. Lee, Z. Bai, R. T. Scalettar and M. Jarrell, Cluster solver for dynamical mean field theory with linear scaling in inverse temperature. Phys. Rev. E, Vol.81, 056703, 2010 (7 pages) (pdf file)

  69. R.-C. Lee, I.H. Chung, Z. Bai, Parallelization of Determinant Quantum Monte Carlo Simulation of Strongly Correlated Electron Systems, in the Proceedings of 24th IEEE International Parallel and Distributed Processing Symposium (IPDPS 2010), Atlanta, USA, April 2010. (preprint),

  70. I. Yamazaki, Z. Bai, H. Simon, L.-W. Wang and K. Wu, Adaptive projection subspace dimension for the thick-restart Lanczos method, ACM Trans. of Math. Software, Vol.37, No.3. 2010 (preprint),

  71. K. Meerbergen and Z. Bai, The Lanczos method for parameterized symmetric linear systems with multiple right-hand sides . SIAM J. of Matrix Analysis and Applications, Vol. 31, No.4, pp.1642-1662, 2010 (preprint)

  72. X. Huang, Z. Bai and Y. Su, Nonlinear rank-one modification of the symmetric eigenvalue problem. Journal of Computational Mathematics, Vol.28, pp.218-234, 2010 (pdf file)

  73. K. Senzaki, H. Tadano, T. Sakurai and Z. Bai, A method for profiling the distribution of eigenvalues using the AS method , Taiwanese Journal of Mathematics, Vol.14, No.3A, pp.839-853, 2010 (preprint)

  74. B.-S. Liao, Z. Bai, L.-Q. Lee and K. Ko, Nonlinear Rayleigh-Ritz iteratve method for solving large scale nonlinear eigenvalue problems, Taiwanese Journal of Mathematics, Vol.14, No.3A, pp.869-883, 2010 (preprint)

  75. R.-C. Lee and Z. Bai, Redesign of higher-level matrix algorithms for multicore and hybrid architectures and applications in quantum Monte Carlo simulation, in Proceedings of 25th IEEE International Parallel and Distributed Processing Symposium (IPDPS 2011) (preprint)

  76. Z. Bai, R.-C. Lee, R.-C. Li and S. Xu, Stable solutions of linear systems involving long chain of matrix multiplications, Linear Algebra and its Applications, Vol.435, pp.659-673, 2011 (preprint)

  77. Y. Su and Z. Bai, Solving rational eigenvalue problems via linearization, SIAM J. of Matrix Analysis and Applications, Vol.32, No.1, pp.201-216, 2011 (preprint)

  78. F. Hebert, M. Schram, R. T. Scalettar, W. B. Chen and Z. Bai, Hatano-Nelson model with a periodic potential, European Physical Journal B, Vol.79, pp.465-471, 2011 (preprint)

  79. M. Dixon, Z. Bai, C. Brush, F. Chung, E. Dogrul and T. Kadir, Error Control of Iterative Linear Solvers for Integrated Groundwater Models, Ground Water, Vol.49, No.6, pp.859-865, 2011. (preprint)

  80. D. Rocca, Z. Bai, R.-C. Li and G. Galli, A block variational procedure for the iterative diagonalization of non-Hermitian random-phase approximation matrices, J. Chem. Phys, 136, 034111 (2012); doi: 10.1063/1.3677667 (preprint)

  81. H. Nguyen, Z. Bai, E. C. Dogrul, T. N. Kadir, C. F. Brush and F. I Chung, Adaptive accuracy control of nonlinear Newton-Krylov methods for multiscale integrated hydrologic models, in Proceedings of XIX International Conference on Water Resources (CMWR 2012), pp.204-211, June 2012. (preprint)

  82. A. Tomas, C.-C. Chang, R. Scalettar and Z. Bai, Advancing large scale many-body QMC simulations on GPU accelerated multicore systems, in Proceedings of 26th IEEE International Parallel and Distributed Processing Symposium (IPDPS 2012), IEEE, 2012 (preprint)

  83. Y.-T. Li, Z. Bai, W.-W. Lin and Y. Su, A structure quasi-Arnoldi procedure for model order reduction of second-order systems, Lin. Alg. Appl. Vol.436, pp.2780-2794, 2012 (preprint)

  84. Z. Bai and R.-C. Li, Minimization principles of the linear response eigenvalue problem I: Theory, SIAM J. Matrix Anal. Apps., Vol.33 No.4 pp.1075-1100, 2012 (preprint)/(tech.report)

  85. Z. Bai and R.-C. Li, Minimization principles of the linear response eigenvalue problem II: Computation, SIAM J. Matrix Anal. Appl. Vol.34, No.2, pp.392-416, 2013 (preprint)/(tech.report)

  86. X. Liang, R.-C. Li and Z. Bai, Trace minimization principles for positive semi-definite pencils, Linear Algebra and its Applications, Vol.438, No.7, pp.3085-3106, 2013. (preprint)

  87. A. Tomas, Z. Bai and V. Hernandez, Parallelization of the QR decomposition with column pivoting using column cyclic distribution on multicore and GPU processors, VECPAR, Lecture Notes in Computer Science. Vol.7851, pp.50-58, Springer, 2013 (preprint)

  88. Y. Cai, Z. Bai, J. Pask and N. Sukumar, Hybrid preconditioning for iterative diagonalization of ill-conditioned generalized eigenvalue problems in electronic structure calculations, J. of Computational Physics, Vol.255, pp.16-33, 2013 (preprint)

  89. Z. Bai and R.-C. Li, Minimization principles and computation for the generalized linear response eigenvalue problem, BIT Numerical Mathematics: Vol.54, pp.31-54, 2014 (preprint)

  90. S. Gogolenko, Z. Bai and R. Scalettar, Structured orthogonal inversion of block p-cyclic matrices on multicores with GPU accelerators, Lecture Notes in Computer Science, Vol.8632, Euro-Par 2014, F. Silva, I. Dutra and V. Santos Costa, eds. pp.524--535, Springer, 2014. (preprint)

  91. Z. Bai, J. Demmel, J. Dongarra, J. Langou and J. Wang, Introduction to LAPACK in Handbook of Linear Algebra (2nd edition), edited by L. Hogben ed., CRC Press, 2014 preprint
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Copyrights are owned by the publisher of the journal/conference. PDF files here are provided as a convenience for one-time individual use only
Maintained by Zhaojun Bai, bai@cs.ucdavis.edu.