在代数特征值问题、奇异值分解和广义奇异值分解问题、离散不适定问题和反问题的正则化理论和数值解法等领域做出了系统性的、有国际影响的重要研究成果，所提出的精化投影方法被公认为是求解大规模矩阵特征值问题和奇异值分解问题的三类投影方法之一（注：后来发展为标准RR投影方法、精化RR投影方法、调和RR投影方法、精化调和RR投影方法共四类投影方法）。在Inverse Problems, Mathematics of Computation, Numerische Mathematik, SIAM Journal on Matrix Analysis and Applications, SIAM Journal on Optimization, SIAM Journal on Scientific Computing 等国际著名杂志上发表论文80篇，据不完全统计，在国际上，贾仲孝的79篇论文和博士学位论文被国际学术界1214人（含中国学者562人）在20本经典著作、专著、手册和教材及731篇论文（注：已发表的国际刊物论文、预印本、国外学位论文）中他引1145篇次（包括专著和教材引用58篇次），其中特征值的工作被他引736篇次，奇异值分解和广义奇异值分解的工作被他引125篇次，最小二乘和总体最小二乘的工作他引90次，离散不适定问题和反问题的工作他引92篇次，线性方程组的工作被他引77篇次，矩阵函数的工作他引15篇次，最优化的工作他引10篇次；在国内，贾仲孝的研究工作被国内431研究人员发表在国内刊物上的351篇论文（注：国内刊物论文和不是自己指导的学生的学位论文）和1部专著他引630篇次。国际国内合计他引1775篇次，引用人数逾1390人。除了中国外，国际上引用的学者来自美、英、法、德、意、荷兰、瑞士、瑞典、加拿大、比利时、西班牙、葡萄牙、丹麦、俄罗斯、澳大利亚、摩洛哥、日本、希腊、捷克、克罗地亚、芬兰、波兰、土耳其、哈萨克斯坦、罗马尼亚、塞尔维亚、斯洛文尼亚、斯洛伐克、巴西、阿根廷、印度、南非、以色列、新加坡、伊朗、阿尔及利亚、阿联酋、韩国、印度尼西亚、马来西亚、尼日利亚、毛里求斯和台湾、香港、澳门共计46个国家和地区。引用者包括美国两院院士Golub、Demmel和Dongarra（2022图灵奖获得者），美国工程院院士Stewart, 英国皇家科学院和美国工程院院士Trefethen, 荷兰工程院院士Van der Vorst, 还有Bjorck、Saad、Sorensen等许多著名学者。引用的书目包括 Demmel 和Dongarra等人编辑的 “Templates for the Solution of Algebraic Eigenvalue Problems: a Practical Guide ”(2000)，Golub & van Loan 的经典著作“Matrix Computations” 第三、第四版 (1996,2013)，Stewart 的经典著作“Matrix Algorithms II: Eigensystems ”(2001)，Bjorck 的专著 Numerical Methods in Matrix Computations (2015)，van der Vorst 的专著 “Computational Methods for Large Eigenvalue Problems” (2002)，Trefethen & Embree 的专著“Spectra and Pseudospectra, The Behavior of Nonnormal Matrices and Operators” (2005)，Meurant & Tebbens 的专著 Krylov Methods for Nonsymmetric Linear Systems ”(2020)，Quarteroni、Sacco & Saleri 的专著 Numerical Mathematics (2000)，Brezinski、Meurant & Revido-Zaglia 的著作 “A Journey Through the History of Numerical Linear Algebra” (2022), Bjorck的专著“Numerical Methods for Least Squares Problems: Second Edition”(2024)，等等.
在著名刊物上发表的论文
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[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.
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[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 Computation，70(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.
[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.
[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] 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.
[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.
[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), e2080.
[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 pair, Numerical Algorithms, 87 (2021): 689—718.
[63] Jia Z. and Li H., The joint bidiagonalization process with partial reorthogonalization, Numerical Algorithms, 88 (2021): 965—992.
[64] Jia Z. and Wang F., The convergence of the generalized Lanczos trust-region method for the trust-region subproblem, SIAM Journal on Optimization, 31 (1) (2021): 887—914.
[65] Jia Z. and Lai F., A convergence analysis on the iterative trace ratio algorithm and its refinements, CSIAM Transaction on Applied Mathematics, 2(2) (2021): 297–312.
[66] Theoretical and computable optimal subspace expansions for matrix eigenvalue problems, SIAM Journal on Matrix Analysis and Applications, 43 (2) (2022): 584—604.
[67] Huang J. and Jia Z., Two harmonic Jacobi--Davidson methods for computing a partial generalized singular value decomposition of a large matrix pair, Journal of Scientific Computing, 93 (2022): Paper No. 41, 32pp.
[68] Huang J. and Jia Z., A cross-product free Jacobi—Davidson type method for computing a partial generalized singular value decomposition (GSVD) of a large matrix, Journal of Scientific Computing, 94 (2023): Paper No. 3, 32pp.
[69] Jia Z. and Li H., The joint bidiagonalization method for large GSVD computations in finite precision, SIAM Journal on Matrix Analysis and Applications, 44(1) (2023): 382—407.
[70] Jia Z. and Zhang K., A FEAST SVDsolver for the computation of singular value decompositions of large matrices based on the Chebyshev—Jackson series expansion, Journal of Scientific Computing, 97 (2023): Paper No. 21, 36pp.
[71] Jia Z. and Zhang K., An augmented matrix-based CJ-FEAST SVDsolver for computing a partial singular value decomposition with the singular values in a given interval, SIAM Journal on Matrix Analysis and Applications, 45 (1) (2024): 24—58.
[72] Huang J. and Jia Z., A skew-symmetric Lanczos bidiagonalization method for computing several extremal eigenpairs of a large skew-symmetric matrix, SIAM Journal on Matrix Analysis and Applications, 45 (2) (2024): 1114—1147.
[73] Huang J. and Jia Z., Refined and refined harmonic Jacobi–Davidson methods for computing several GSVD components of a large regular matrix pair, Numerical Algorithms, 99 (2025): 895—920.
[74] Jia Z. and Zheng QQ, An analysis of the Rayleigh—Ritz and refined Rayleigh—Ritz methods for regular nonlinear eigenvalue problems, SIAM Journal on Matrix Analysis and Applications, 46 (1) (2025): 676—701.
[75] Jia Z. and Zhang K., A CJ-FEAST GSVDsolver for computing a partial GSVD of a large matrix pair with the generalized singular values in a given interval, Numerische Mathematik, 157 (2025): 897—949.
[76] Fang K. and Jia Z., An implicitly restarted joint bidiagonalization algorithm for large GSVD computations, SIAM Journal on Matrix Analysis and Applications, 47(3) (2026): 1439—1470.
[77] Huang J. and Jia Z., Harmonic, refined and refined harmonic skew-symmetric Lanczos bidiagonal- lization methods for computing several extreme eigenpairs of a large skew-symmetric matrix, Journal of Computational and Applied Mathematics, 490 (2027): article no. 117930.
