English 清华大学 旧版入口 人才招聘

贾仲孝

  • 教授
  • 电话:62795349
  • 邮箱:jiazx@tsinghua.edu.cn

基本信息

博士(德国比勒费尔德大学),清华大学数学科学系教授、博导,系学术委员会副主任,中国工业与应用数学学会(CSIAM)监事会监事,《计算数学》编委。

 

工作履历

1987.5-1989.12: 山西师范大学数学系助教。

1990.1-1990.12: 山西师范大学数学系讲师。

1995.9-2001.11: 大连理工大学应用数学系教授、博士生导师。

2001.11--至今:清华大学数学科学系教授、博士生导师。

 

研究领域

数值线性代数,代数特征值问题和奇异值分解与广义奇异值分解问题的数值方法及应用,大规模线性方程组的迭代法和预处理技术,最小二乘问题和总体最小二乘问题的理论分析和数值解法,离散不适定问题和反问题的正则化理论和数值解法。

所授课程

数值分析(数学系本科生),数值分析A(全校研究生),高等数值分析(全校研究生),矩阵计算(研究生专业课)。

 

奖励与荣誉

1993年获得英国“数学及其应用学会(Institute of Mathematics and Its Applications(IMA))”两年一届的“第六届国际青年数值分析家奖-Leslie Fox奖”(数值分析最佳研究论文奖),六名获奖者之一;1999年国务院政府专家特殊津贴;1999度“国家百千万人才工程”;清华大学“百人计划”特聘教授(2001).

 

学术成果

在矩阵特征值问题、奇异值分解问题的数值解法的理论和算法领域做出了系统的、有重要国际影响的研究成果,在国际学术界引发了大量的后续研究。所提出的精化Rayleigh-Ritz方法与传统的标准Rayleigh-Ritz方法和调和Rayleigh-Ritz方法一道,自国际计算数学界权威Demmel(美国科学院院士和工程院院士)、Dongarra(美国工程院院士)等五人编辑的“Templates for the Solution of Algebraic Eigenvalue Problems: a Practical Guide, SIAM, Philadelphia2000出版以来,被公认为是求解这两大类问题的三类投影方法之一。对于非对称情形的特征值问题,首次建立了这三类方法的普适性收敛性理论。国际计算数学界权威Stewart(美国工程院院士)的经典专著Matrix Algorithms: Vol. II Eigensystems, SIAM, Philadelphia, 2001470页)和国际权威计算数学家van der Vorst(荷兰工程院院士)的专著Computational Methods for Large Eigenvalue Problems, North-Holland (Elsevier), 2002177页)分别用10页多和4页多的篇幅系统描述和讨论贾仲孝的精化Rayleigh-Ritz方法。在稀疏线性方程组的迭代法和有效预处理技术、线性最小二乘和总体最小二乘问题的扰动理论、离散不适定和反问题的正则化理论和数值解法等领域,均做出了国际水平的研究成果。1995-2020年期间,在Mathematics of Computation, Numerische Mathematik, SIAM 系列杂志, Inverse Problems等国际顶尖杂志上发表论文60余篇,研究成果被国际学术界的40个国家与地区的约700名专家、研究人员在17部经典著作、专著、教材,包括Golub(美国科学院院士和工程院院士) & Van Loan的经典著作Matrix Computations第三、第四版(1996 2013)等,及600余篇论文中引用1100多篇次。


主要论著:

[1] The convergence of generalized Lanczos methods for large unsymmetric eigenproblems, SIAM Journal on Matrix Analysis and Applications, 16 (3) (1995): 843-862. 

[2] A block incomplete orthogonalization method for large nonsymmetric eigenproblems, BIT, 34 (4) (1995): 516-539.

[3] On IOM(q): the incomplete orthogonalization method for large unsymmetric linear systems, Numerical Linear Algebra with Applications, 3 (6) (1996): 491-512

[4] Refined iterative algorithms based on Arnoldi's process for large unsymmetric eigenproblems, Linear Algebra and Its Applications,259 (1997): 1-23

[5] A refined iterative algorithm based on the block Arnoldi process for large unsymmetric eigenproblems, Linear Algebra and Its Applications, 270(1998): 171-189

[6] Generalized block Lanczos methods for large unsymmetric eigenproblems, Numerische Mathematik, 80 (2)(1998):239-266

[7] 解非对称线性方程组的不完全广义最小残量法, 中国科学(A辑), 28 (8)1998: 694-702.

On IGMRES: an incomplete generalized minimal residual method for large unsymmetric linear systems, Science in China (Series A), 41 (12)(1998): 1178-1188. 

[8] A variation on the block Arnoldi method for large unsymmetric eigenproblems, Acta Mathematica  Applicatae Sinica, 14 (4) (1998): 425-432.

[9] 求解大规模非Hermite线性方程组的Krylov子空间型方法的收敛性分析,  数学学报, 41 (5) (1998): 915-924.The convergence of Krylov subspace methods for large unsymmetric linear systems, Acta Mathematica Sinica-New Series, 14 (4) (1998): 507-518. 

[10] Polynomial characterizations of the approximate eigenvectors by the refined Arnoldi method and an implicitly restarted refined Arnoldi algorithm, Linear Algebra and Its Applications, 287 (1999): 191-214

[11] 解大规模矩阵特征问题的复合正交投影方法, 中国科学(A辑),29 (3)(1999): 224-232. Composite orthogonal projection methods for large matrix eigenproblems, Science in  China (Series A), 42 (6) (1999): 577-585

[12] Arnoldi type algorithms for large unsymmetric multiple eigenvalue problems, Journal of Computational Mathematics17 (3) (1999): 257-274. 

[13] A refined subspace iteration algorithm for large sparse eigenproblems, Applied Numerical Mathematics32(1)(2000): 35-52. 

[14] Some recursions on Arnoldi's method and IOM for large non-Hermitian linear systems, Computers and Mathematics with Applications, 39 (3/4) (2000): 125-129. 

[15] Jia Z. and Elsner L., Improving eigenvectors in Arnoldi's method, Journal of Computational Mathematics, 18 (3) (2000): 365-376. 

[16] Jia Z. and Stewart G.W., An analysis of the Rayleigh-Ritz method  for  approximating eigenspaces, Mathematics of Computation70(234)(2001):637-647. 

[17] On residuals of refined projection methods for large matrix eigenproblems, Computers and Mathematics with Applications. 41 (7/8) (2001): 813-820. (SCI)

[18] The refined harmonic Arnoldi method and an implicitly restarted refined algorithm for computing interior eigenpairs of large matrices, Applied Numerical Mathematics, 42 (4) (2002): 489-512.

[19] Chen G. and Jia Z. A reverse order implicit Q-theorem and the Arnoldi process, Journal of Computational Mathematics, 20 (5) (2002): 519-524. 

[20] Jia Z. and Zhang Y., A refined invert-and-shift Arnoldi algorithm for large generalized unsymmetric eigenproblems, Computers and Mathematics with Applications, 44 (8/9) (2002): 1117-1127. 

[21] Jia Z. and Niu D., An implicitly restarted refined bidiagonalization Lanczos method for computing a partial singular value decomposition, SIAM Journal on Matrix Analysis and Applications, 25(1)(2003):246-265.

[22] Chen G and Jia Z, Theoretical and numerical comparisons of GMRES and WZ-GMRES, Computers and Mathematics with Applications, 47 (8/9) (2004):1335-1350. (SCI)

[23] Chen G and Jia Z., An analogue of the results of Saad and Stewart for harmonic Ritz vectors, Journal of Computational and Applied Mathematics,167 (2004): 493-498. 

[24] Some theoretical comparisons of refined Ritz vectors and Ritz vectors, Science in China, Series A, 47 (Suppl.) (2004): 222-233.

[25] Feng S. and Jia Z., A refined Jacobi-Davidson method and its correction equation, Computers and Mathematics with Applications, 49 (2/3) (2005): 417-427.

[26] The convergence of harmonic Ritz values, harmonic Ritz vectors and refined harmonic Ritz vectors, Mathematics of Computation,  74 (251) (2005): 1441-1456.

[27] Chen G. and Jia Z., A refined harmonic Rayleigh-Ritz procedure and an explicitly restarted refined harmonic Arnoldi algorithm, Mathematical and Computer Modelling, 41 (2005): 615-627.

[28] Using cross-product matrices to compute the SVD, Numerical Algorithms, 42 (1) (2006): 31-61.

[29] Jia Z. and Sun Y., A QR decomposition based solver for the least squares problem from the minimal residual method, Journal of Computational Mathematics, 25 (5) (2007): 531-542.

[30] 贾仲孝,王震,非精确Rayleigh商迭代和非精确的简化Jacobi-Davidson方法的收敛性分析,中国科学,A38 (4) (2008): 365-376. Jia Z. and Wang Z., A convergence analysis of the inexact Rayleigh quotient iteration and simplified Jacobi-Davidson method for the large Hermitian matrix eigenproblem, Science in China Series A, 51 (12) (2008): 2205-2216. 

[31] Jia Z. and Zhu B., A power sparse approximate inverse preconditioning procedure for large linear systems, Numerical Linear Algebra with Applications, 16 (4) (2009): 259-299. 

[32] Applications of the Conjugate Gradient (CG) method in optimal surface parameterizations, International Journal of Computer Mathematics, 87 (5) (2010): 1032-1039. 

[33] Jia Z. and Niu D., A refined harmonic Lanczos bidiagonalization method and an implicitly restarted algorithm for computing the smallest singular triplets of large matrices, SIAM Journal on Scientific Computing, 32 (2) (2010): 714-744. 

[34] Some properties of LSQR for large sparse linear least squares problems, Journal of Systems Science and Complexity, 23 (4) (2010): 815-821. 

[35] Duan C. and Jia Z., A global harmonic Arnoldi method for large non-Hermitian eigenproblems with an application to multiple eigenvalue problems, Journal of Computational and Applied Mathematics, 234 (2010): 845-860. 

[36] E K.-W Chu, H.-Y Fan, Z. Jia, T. Li and W.-W Lin, The Rayleigh-Ritz method, refinement and Arnoldi process for periodic matrix pairs, Journal of Computational and Applied Mathematics, 235 (2011): 2626-2639. 

[37] Duan D and Jia Z., A global Arnoldi method for large non-Hermitian eigenproblems with special applications to multiple eigenproblems, Taiwanese Journal of Mathematics, 15 (4) (2011): 1497-1525. 

[38] Li B. and Jia Z., Some results on condition numbers of the scaled total least squares problems, Linear Algebra and Its Applications, 435 (3)(2011): 674—686. 

[39] On convergence of the inexact Rayleigh quotient iteration with MINRES, Journal of Computational and Applied Mathematics, 236 (2012): 4276—4295. 

[40] Jia Z. and Sun Y., SHIRRA: A refined variant of SHIRA for the Skew-Hamiltonian/Hamiltonian (SHH) pencil eigenvalue problem, Taiwanese Journal of Mathematics, 17 (1) (2013): 259-274. (SCI)

[41] On convergence of the inexact Rayleigh quotient iteration with the Lanczos method used for solving linear systems, Science China Mathematics, 56 (10)(2013): 2145-2160. 

[42] Jia Z. and Li B., On the condition number of the total least squares problem, Numerische Mathematik, 125 (1) (2013): 61-87. 

[43] Jia Z. and Zhang Q., An approach to making SPAI and PSAI preconditioning effective for large irregular sparse linear systems, SIAM Journal on Scientific Computing, 35 (4) (2013): A1903-A1927. 

[44] Huang T-M, Jia Z. and Lin W-W., On the convergence of Ritz pairs and refined Ritz vectors for quadratic eigenvalue problems, BIT Numerical Mathematics, 53 (4) (2013): 941-958. 

[45] Jia Z. and Zhang Q., Robust dropping criteria for F-norm minimization based sparse approximate inverse preconditioning, BIT Numerical Mathematics, 53( 4) (2013): 959-985. 

[46] Jia Z. and Li C., Inner iterations in the shift-invert residual Arnoldi method and the Jacobi--Davidson method, Science China Mathematics, 57 (8) (2014): 1733-1752.

[47] Jia Z. and Li C., Harmonic and refined harmonic shift-invert residual Arnoldi and Jacobi--Davidson methods for interior eigenvalue problems, Journal of Computational and Applied Mathematics, 282 (2015): 83-97. 

[48] Jia Z. and Sun Y., Implicitly restarted generalized second-order Arnoldi type algorithms for the  quadratic eigenvalue problem, Taiwanese Journal of Mathematics, 19 (1) (2015): 1-30.

[49] Jia Z. and Lv H., A posteriori error estimates of Krylov subspace approximations to matrix functions, Numerical Algorithms, 69 (1) (2015): 1-28. 

[50] Jia Z., Lin W.-W and Liu C.-S. A positivity preserving inexact Noda iteration for computing the  smallest eigenpair of a large irreducible M-matrix, Numerische Mathematik, 130 (4) (2015): 645-679

[51] Huang Y. and Jia Z., Some results on regularization of LSQR for large-scale discrete ill-posed problems, Science China Mathematics, 60 (4) (2017): 701-718. doi: 10.1007/s11425-015-0568-4.

[52] Jia Z. and Kang WJ., A residual based sparse approximate inverse preconditioning procedure for large sparse linear systems, Numerical Linear Algebra with Applications, 24 (2) (2017), 1-13.

[53] Huang Y. and Jia Z., On regularizing effects of MINRES and MR-II for large-scale symmetric discrete ill-posed problems, Journal of Computational and Applied Mathematics, 320 (2017): 145-163. 

[54] Jia Z. and Yang Y., Modified truncated randomized singular value decomposition (MTRSVD) algorithms for large scale discrete ill-posed problems with general-form regularization, Inverse Problems, 34 (2018): 055013 (28pp).

[55] Jia Z. and Kang WJ., A transformation approach that makes SPAI, PSAI and RSAI procedures efficient for large double irregular nonsymmetric sparse linear systems, Journal of Computational and Applied Mathematics, 384 (2019): 200—213.

[56] Huang J. and Jia Z., On inner iterations of Jacobi-Davidson type methods for large SVD computations, SIAM Journal on Scientific Computing, 41 (3) (2019): A1574—A1603.

[57] Approximation accuracy of the Krylov subspaces for linear discrete ill-posed problems, Journal of Computational and Applied Mathematics, 374 (2020): 112786.

[58] The low rank approximations and Ritz values in LSQR for linear discrete ill-posed problems, Inverse Problems, 36 (4) 2020: 045013 (32pp). 

[59] Regularization properties of the Krylov iterative solvers CGME and LSMR for linear discrete ill-posed problems with an application to truncated randomized SVDs, Numerical Algorithms, 85 (4) 2020, 1281-1310.

[60] Regularization properties of LSQR for linear discrete ill-posed problems in the multiple singular value and best, near best and general low rank approximations, Inverse Problems, 36 (8) (2020): 085009 (38pp).  

[61] Jia Z. and Yang Y., A joint bidiagonalization based algorithm for large scale general-form Tikhonov regularization, Applied Numerical Mathematics, 157 (2020), 159-177.

[62] Huang J. and Jia Z., On choices of formulations of computing the generalized singular value decomposition of a matrix pairNumerical Algorithms, 2020, https://doi: 10.1007/s11075-020-00984-9.

[63]   Jia Z. and Lai. F., A convergence analysis on the iterative trace ratio algorithm and its refinements,CSIAM Transactions on Applied Mathematics , accepted, 2020.

[64] Jia Z. and Wang F., The convergence of the generalized Lanczos trust-region method for the trust-region subproblem, ArXiv,: 1908.02094 [math.na].

[65] Theoretical and computable optimal subspace expansions for matrix eigenvalue problems, ArXiv: 2004.04928 [math.na].

[66] Huang J. and Jia Z., A cross-product free Jacobi--Davidson type method for computing a partial generalized singular value decomposition of a large matrix pair, ArXiv: 2004.13975 [math.na].

人才培养

指导毕业博士14名:张勇(大连理工大学, 1999),陈桂芝(大连理工大学, 2000),闫庆友(大连理工大学, 2002),冯绍强(大连理工大学, 2003),牛大田(大连理工大学,2003),孙玉泉(2006),段聪颖(2010),李岑(2013),张芡(2013),吕慧(2014),黄漪(2016),康文洁(2017),杨艳飞(2018),黄金枝(2020;硕士14名:其中大连理工大学6名,清华大学8名。


现有在读博士生5名:王法、李海波、张锴亮、房凯霄、杨雪琴。


博士后3名: 谢冬秀(大连理工, 2001出站),李冰玉(清华,2010出站),郑青青(在站).