基本介紹
- 中文名：賈仲孝
- 外文名：Zhongxiao Jia
- 國籍：中國
- 民族：漢族
- 出生地：山西
- 出生日期：公元1963年7月
- 職業：教師
- 畢業院校：德國比勒菲爾德大學
- 職稱：清華大學數學科學系教授
個人簡介,研究方向,學術成果,
個人簡介
賈仲孝，1963年7月生，山西 萬榮 上義村人。清華大學－數學科學系－教授、博導。1984年畢業於山西大學，獲得學士學位；1987年畢業於大連工學院獲得碩士學位；1994年畢業於德國Bielefeld大學獲得博士學位。
所在院系 ： 數學系。 研究方向 ： 數值代數、科學工程計算，代數特徵值問題的數值方法，大規模奇異值分解的有效計算，大規模稀疏線性方程組的疊代法和預處理，最小二乘問題和整體最小二乘問題，不適定問題的理論和算法。
第七、八屆中國計算數學學會常務理事（2006.10-2014.10）、第五、六屆中國工業和套用數學學會（CSIAM）常務理事（2008.9—2016.8），北京市數學會副理事長（2014.1--）。
研究方向
主要從事計算數學和科學工程計算方面的研究工作。從1995年以來，在國內外著名雜誌上發表文章多篇，SCI收錄40多篇，研究成果在國際上有相當大的影響，被31個國家和地區的學者廣泛引用。1993年6月在英國牛津大學被授予“第六屆國際青年數值分析家獎—Leslie Fox獎”（數值分析最佳研究論文獎），是六名獲獎者之一。該獎由英國“數學及其套用學會（Institute of Mathematics and Its Applications(IMA）”頒發， 每兩年一次在世界範圍內授予幾名對數值分析和科學計算做出重要貢獻的青年數學家（不超過31歲）。1999年度入選“國家百千萬人才工程”第一、二層次，並享受國務院政府專家特殊津貼，2001年1月入選清華大學傑出人才“百人計畫”等等。主持國家自然科學基金·、教育部博士點基金多項，是國家攀登項目和973項目“大規模科學計算方法”與“數學機械化”的骨幹成員。
學術成果
[1] The convergence of generalized Lanczos methods for largeunsymmetric eigenproblems, SIAM Journal on Matrix Analysis and Applications,16 (3) (1995): 843-862.
[2] A block incomplete orthogonalization method for largenonsymmetric eigenproblems, BIT, 34 (4) (1995): 516-539.
[3] On IOM(q): the incomplete orthogonalization method forlarge unsymmetric linear systems, Numerical Linear Algebra with Applications,3 (6) (1996): 491-512.
[4] Refined iterative algorithms based onArnoldi's process for large unsymmetric eigenproblems, Linear Algebra andIts Applications, 259 (1997): 1-23.
[5] A refined iterative algorithm based on theblock Arnoldi process for large unsymmetric eigenproblems, Linear Algebraand Its Applications, 270（1998）: 171-189.
[6] Generalized block Lanczosmethods for large unsymmetric eigenproblems, Numerische Mathematik, 80(2（1998）:239-266.
[7] 解非對稱線性方程組的不完全廣義最小殘量法, 中國科學（A輯）, 28 (8)（1998）: 694-702.
On IGMRES: an incomplete generalized minimalresidual method for large unsymmetric
linear systems, Science in China, Series A, 41 (12)(1998): 1178-1188.
[8] 求解大規模非Hermite線性方程組的Krylov子空間型方法的收斂性分析, 數學學報, 41 (5) (1998): 915-924.
The convergence of Krylov subspace methods forlarge unsymmetric linear systems, Acta Mathematica Sinica-New Series, 14(4) (1998): 507-518.
[9]Polynomial characterizations of the approximate eigenvectors by the refinedArnoldi method and an implicitly restarted refined Arnoldi algorithm, LinearAlgebra and Its Applications, 287 (1999): 191-214.
[10] 解大規模矩陣特徵問題的複合正交投影方法, 中國科學（A輯），29 (3)(1999): 224-232.
Compositeorthogonal projection methods for large matrix eigenproblems, Science in China， Series A, 42 (6) (1999): 577-585.
[11]Arnoldi type algorithms for large unsymmetric multiple eigenvalue problems, Journalof Computational Mathematics，17 (3)(1999): 257-274.
[12] A refined subspaceiteration algorithm for large sparse eigenproblems, Applied NumericalMathematics，32（1）(2000): 35-52.
[13]Some recursions on Arnoldi's method and IOM for large non-Hermitian linearsystems, Computers and Mathematics with Applications, 39 (3/4) (2000):125-129.
[14] Jia Z. and Elsner L., Improving eigenvectors in Arnoldi'smethod, Journal of Computational Mathematics, 18 (3) (2000): 365-376.
[15] JiaZ. and Stewart G.W., An analysis of the Rayleigh-Ritz method for approximating eigenspaces, Mathematics of Computation，70（234）（2001）：637-647.
[16] On residuals of refinedprojection methods for large matrix eigenproblems, Computers and Mathematicswith Applications. 41 (7/8) (2001): 813-820.
[17] The refined harmonicArnoldi method and an implicitly restarted refined algorithm for computinginterior eigenpairs of large matrices, Applied Numerical Mathematics, 42(4) (2002): 489-512.
[18] Chen G. and Jia Z.A reverse order implicit Q-theorem and the Arnoldi process, Journal ofComputational Mathematics, 20 (5) (2002): 519-524.
[19] JiaZ. and Zhang Y., A refined invert-and-shift Arnoldi algorithm for largegeneralized unsymmetric eigenproblems, Computers and Mathematics withApplications, 44 (8/9) (2002): 1117-1127.
[20] Jia Z. and Niu D.,An implicitly restarted refined bidiagonalization Lanczos method for computinga partial singular value decomposition, SIAM Journal on Matrix Analysis andApplications, 25(1)(2003)：246-265.
[21] Chen G and Jia Z,Theoretical and numerical comparisons of GMRES and WZ-GMRES, Computers and Mathematicswith Applications, 47 (8/9) (2004):1335-1350.
[22] Chen G and Jia Z.,An analogue of the results of Saad and Stewart for harmonic Ritz vectors, Journalof Computational and Applied Mathematics, 167 (2004): 493-498.
[23] Some theoretical comparisons of refined Ritz vectors and Ritz vectors, Sciencein China, Series A, 47 (Suppl.) (2004): 222-233.
[24]Feng S. and Jia Z., A refined Jacobi-Davidson method and its correctionequation, Computers and Mathematics with Applications, 49 (2/3) (2005):417-427.
[25]The convergence of harmonic Ritz values, harmonic Ritz vectors and refinedharmonic Ritz vectors, Mathematics of Computation, 74 (251)(2005): 1441-1456.
[26] Chen G. and Jia Z.,A refined harmonic Rayleigh-Ritz procedure and an explicitly restarted refinedharmonic Arnoldi algorithm, Mathematical and Computer Modelling, 41（2005）：615-627.
[27] Using cross-productmatrices to compute the SVD,Numerical Algorithms, 42 (1) (2006): 31-61.
[28] Jia Z. and Sun Y., AQR decomposition based solver for the least squares problem from the minimalresidual method,Journal ofComputational Mathematics, 25 (5) (2007): 531—542.
[29] 賈仲孝，王震，非精確Rayleigh商疊代和非精確的簡化Jacobi-Davidson方法的收斂性分析，中國科學,A輯，38 (4) (2008): 365-376.
Jia Z. and Wang Z., Aconvergence analysis of the inexact Rayleigh quotient iteration and simplifiedJacobi-Davidson method for the large Hermitian matrix eigenproblem,Science in China Series A, 51 (12)(2008): 2205—2216.
[30] Jia Z. and Zhu B., A power sparse approximate inversepreconditioning procedure for large linear systems, Numerical Linear Algebra with Applications, 16 (4) (2009):259—299.
[31] Applications of the Conjugate Gradient (CG) method in optimal surfaceparameterizations, International Journalof Computer Mathematics, 87 (5)(2010): 1032—1039.
[32] Jia Z. andNiu D., A refined harmonic Lanczos bidiagonalization method and an implicitlyrestarted algorithm for computing the smallest singular triplets of largematrices, SIAM Journal on ScientificComputing, 32 (2) (2010): 714--744.
[33] Some properties of LSQR for large sparse linearleast squares problems, Journal ofSystems Science and Complexity, 23 (4)(2010): 815--821.
[34] Duan C. and Jia Z., A global harmonicArnoldi method for large non-Hermitian eigenproblems with an application tomultiple eigenvalue problems, Journal ofComputational and Applied Mathematics, 234 (2010): 845—860.
[35] E K.-W Chu, H.-Y Fan, Z.Jia, T. Li and W.-W Lin, The Rayleigh-Ritz method, refinement and Arnoldiprocess for periodic matrix pairs, Journal of Computational andApplied Mathematics, 235 (2011): 2626—2639.
[36] Duan D and Jia Z.,A global Arnoldi method for large non-Hermitian eigenproblems with specialapplications to multiple eigenproblems,Taiwanese Journal of Mathematics, 15 (4) (2011): 1497—1525.
[37] 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.
[38] On convergence of the inexact Rayleigh quotientiteration with MINRES, Journal of Computational andApplied Mathematics, 236 (2012): 4276—4295.
[39] Jia Z. and Sun Y., SHIRRA: A refined variant of SHIRAfor the Skew-Hamiltonian/Hamiltonian (SHH) pencil eigenvalue problem, Taiwanese Journal of Mathematics, 17(1) (2013): 259—274.
[40] On convergence of theinexact Rayleigh quotient iteration with the Lanczos method used for solvinglinear systems, Science ChinaMathematics, 56 (10)(2013): 2145—2160.
[41] Jia Z. and Li B., Onthe condition number of the total least squares problem, Numerische Mathematik, 125 (1) (2013): 61—87.
[42] Jia Z. and Zhang Q.,An approach to making SPAI and PSAI preconditioning effective for largeirregular sparse linear systems, SIAM Journal onScientific Computing, 35 (4) (2013):A1903—A1927.
[43] Huang T-M, Jia Z.and Lin W-W., On the convergence of Ritz pairs andrefined Ritz vectors for quadratic eigenvalue problems, BIT Numerical Mathematics, 53 (4) (2013): 941—958.
[44] Jia Z. and Zhang Q., Robustdropping criteria for F-norm minimization based sparse approximate inversepreconditioning, BIT NumericalMathematics, 53( 4) (2013): 959—985.
[45] Jia Z. and LiC., On inner iterations in the shift-invert residual Arnoldi method andthe Jacobi--Davidson method, ScienceChina Mathematics,accepted, August, 2013.
[46] Jia Z.and Li C., Harmonic and refined harmonic shift-invert residual Arnoldi andJacobi--Davidson
methods for interior eigenvalue problems,arXiv: math/1210.4658, 2012.
[47] Jia Z.and Lv H., A posteriori error estimates of Krylov subspace approximations tomatrix functions, arXiv: math/1303.7219, 2013.
[48] Jia Z., Lin W.-W and Liu C.-S. An inexact Noda iteration for computingthe smallest eigenpair of an irreducible $M$-matrix, arXiv:math/1309.3926, 2013.
