Zhongxiao Jia

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All published works

Action	Title	Year	Authors
+	The General Solution to a System of Tensor Equations over the Split Quaternion Algebra with Applications	2025	Zhongxiao Jia Qing‐Wen Wang
+	A Skew-Symmetric Lanczos Bidiagonalization Method for Computing Several Extremal Eigenpairs of a Large Skew-Symmetric Matrix	2024	Jinzhi Huang Zhongxiao Jia
+ PDF Chat	Preconditioning correction equations in Jacobi--Davidson type methods for computing partial singular value decompositions of large matrices	2024	Jinzhi Huang Zhongxiao Jia
+ PDF Chat	An Augmented Matrix-Based CJ-FEAST SVDsolver for Computing a Partial Singular Value Decomposition with the Singular Values in a Given Interval	2024	Zhongxiao Jia Kailiang Zhang
+ PDF Chat	The Joint Bidiagonalization Method for Large GSVD Computations in Finite Precision	2023	Zhongxiao Jia Haibo Li
+	An augmented matrix-based CJ-FEAST SVDsolver for computing a partial singular value decomposition with the singular values in a given interval	2023	Zhongxiao Jia Kailiang Zhang
+	Refined and refined harmonic Jacobi--Davidson methods for computing several GSVD components of a large regular matrix pair	2023	Jinzhi Huang Zhongxiao Jia
+	A CJ-FEAST GSVDsolver for computing a partial GSVD of a large matrix pair with the generalized singular values in a given interval	2023	Zhongxiao Jia Kailiang Zhang
+ PDF Chat	A Cross-Product Free Jacobi–Davidson Type Method for Computing a Partial Generalized Singular Value Decomposition of a Large Matrix Pair	2022	Jinzhi Huang Zhongxiao Jia
+ PDF Chat	Two Harmonic Jacobi–Davidson Methods for Computing a Partial Generalized Singular Value Decomposition of a Large Matrix Pair	2022	Jinzhi Huang Zhongxiao Jia
+ PDF Chat	Theoretical and Computable Optimal Subspace Expansions for Matrix Eigenvalue Problems	2022	Zhongxiao Jia
+ PDF Chat	A FEAST SVDsolver for the computation of singular value decompositions of large matrices based on the Chebyshev--Jackson series expansion	2022	Zhongxiao Jia Kailiang Zhang
+	A FEAST SVDsolver based on Chebyshev--Jackson series for computing partial singular triplets of large matrices	2022	Zhongxiao Jia Kailiang Zhang
+	An analysis of the Rayleigh-Ritz and refined Rayleigh-Ritz methods for nonlinear eigenvalue problems	2022	Zhongxiao Jia Qingqing Zheng
+	A skew-symmetric Lanczos bidiagonalization method for computing several largest eigenpairs of a large skew-symmetric matrix	2022	Jinzhi Huang Zhongxiao Jia
+ PDF Chat	The joint bidiagonalization process with partial reorthogonalization	2021	Zhongxiao Jia Haibo Li
+	A comparison of eigenvalue-based algorithms and the generalized Lanczos trust-region algorithm for Solving the trust-region subproblem	2021	Zhongxiao Jia Fa Wang
+ PDF Chat	The Convergence of the Generalized Lanczos Trust-Region Method for the Trust-Region Subproblem	2021	Zhongxiao Jia Fa Wang
+ PDF Chat	On choices of formulations of computing the generalized singular value decomposition of a large matrix pair	2020	Jinzhi Huang Zhongxiao Jia
+ PDF Chat	Regularization properties of LSQR for linear discrete ill-posed problems in the multiple singular value case and best, near best and general low rank approximations	2020	Zhongxiao Jia
+ PDF Chat	A joint bidiagonalization based iterative algorithm for large scale general-form Tikhonov regularization	2020	Zhongxiao Jia Yanfei Yang
+ PDF Chat	Regularization properties of LSQR for linear discrete ill-posed problems in the multiple singular value case and best, near best and general low rank approximations	2020	Zhongxiao Jia
+	A cross-product free Jacobi-Davidson type method for computing a partial generalized singular value decomposition (GSVD) of a large matrix pair.	2020	Jinzhi Huang Zhongxiao Jia
+	Optimal Subspace Expansion for Matrix Eigenvalue Problems.	2020	Zhongxiao Jia
+ PDF Chat	Regularization properties of Krylov iterative solvers CGME and LSMR for linear discrete ill-posed problems with an application to truncated randomized SVDs	2020	Zhongxiao Jia
+	Approximation accuracy of the Krylov subspaces for linear discrete ill-posed problems	2020	Zhongxiao Jia
+ PDF Chat	The low rank approximations and Ritz values in LSQR for linear discrete ill-posed problem	2020	Zhongxiao Jia
+	Theoretical and Computable Optimal Subspace Expansions for Matrix Eigenvalue Problems	2020	Zhongxiao Jia
+ PDF Chat	On Inner Iterations of Jacobi--Davidson Type Methods for Large SVD Computations	2019	Jinzhi Huang Zhongxiao Jia
+	The convergence of the Generalized Lanczos Trust-Region Method for the Trust-Region Subproblem	2019	Zhongxiao Jia Wang Fa
+	The joint bidiagonalization method for large GSVD computations in finite precision	2019	Zhongxiao Jia Haibo Li
+	A transformation approach that makes SPAI, PSAI and RSAI procedures efficient for large double irregular nonsymmetric sparse linear systems	2018	Zhongxiao Jia Wenjie Kang
+ PDF Chat	Modified truncated randomized singular value decomposition (MTRSVD) algorithms for large scale discrete ill-posed problems with general-form regularization	2018	Zhongxiao Jia Yanfei Yang
+ PDF Chat	On regularizing effects of MINRES and MR-II for large scale symmetric discrete ill-posed problems	2017	Yi Huang Zhongxiao Jia
+	The regularization theory of the Krylov iterative solvers LSQR and CGLS for linear discrete ill-posed problems, part I: the simple singular value case	2017	Zhongxiao Jia
+	On inner iterations of Jacobi-Davidson type methods for large SVD computations	2017	Jinzhi Huang Zhongxiao Jia
+ PDF Chat	A residual based sparse approximate inverse preconditioning procedure for large sparse linear systems	2016	Zhongxiao Jia Wenjie Kang
+ PDF Chat	Some results on the regularization of LSQR for large-scale discrete ill-posed problems	2016	Yi Huang Zhongxiao Jia
+	The Regularization Theory of the Krylov Iterative Solvers LSQR, CGLS, LSMR and CGME For Linear Discrete Ill-Posed Problems	2016	Zhongxiao Jia
+	Iterative Regularization of Minimum-Residual Methods for Large-Scale Symmetric Discrete Ill-Posed Problems	2015	Yi Huang Zhongxiao Jia
+ PDF Chat	IMPLICITLY RESTARTED GENERALIZED SECOND-ORDER ARNOLDI TYPE ALGORITHMS FOR THE QUADRATIC EIGENVALUE PROBLEM	2015	Zhongxiao Jia Yuquan Sun
+	Harmonic and refined harmonic shift-invert residual Arnoldi and Jacobi–Davidson methods for interior eigenvalue problems	2015	Zhongxiao Jia Cen Li
+	Some Results on the Regularization of LSQR for Large-Scale Discrete Ill-Posed Problems	2015	Yi Huang Zhongxiao Jia
+	A Residual Based Sparse Approximate Inverse Preconditioning Procedure for Large Sparse Linear Systems	2015	Zhongxiao Jia Wenjie Kang
+	A Transformation Approach that Makes SPAI, PSAI and RSAI Procedures Efficient for Large Double Irregular Nonsymmetric Sparse Linear Systems	2015	Zhongxiao Jia Wenjie Kang
+	On Regularizing Effects of MINRES and MR-II for Large-Scale Symmetric Discrete Ill-Posed Problems	2015	Yi Huang Zhongxiao Jia
+ PDF Chat	IMPLICITLY RESTARTED GENERALIZED SECOND-ORDER ARNOLDI TYPE ALGORITHMS FOR THE QUADRATIC EIGENVALUE PROBLEM	2015	Zhongxiao Jia Yuquan Sun
+	A positivity preserving inexact Noda iteration for computing the smallest eigenpair of a large irreducible $$M$$ M -matrix	2014	Zhongxiao Jia Wen‐Wei Lin Ching-Sung Liu
+ PDF Chat	A posteriori error estimates of krylov subspace approximations to matrix functions	2014	Zhongxiao Jia Hui Lv
+ PDF Chat	Inner iterations in the shift-invert residual Arnoldi method and the Jacobi-Davidson method	2014	Zhongxiao Jia Cen Li
+	Some Results on Regularization of LSQR and CGLS for Large-Scale Discrete Ill-Posed Problems	2014	Yi Huang Zhongxiao Jia
+	AN INEXACT NODA ITERATION FOR COMPUTING THE SMALLEST EIGENPAIR OF AN IRREDUCIBLE M-MATRIX	2013	Zhongxiao Jia Wen‐Wei Lin Ching-Sung Liu
+ PDF Chat	On the convergence of Ritz pairs and refined Ritz vectors for quadratic eigenvalue problems	2013	Tsung‐Ming Huang Zhongxiao Jia Wen‐Wei Lin
+ PDF Chat	Robust dropping criteria for F-norm minimization based sparse approximate inverse preconditioning	2013	Zhongxiao Jia Qian Zhang
+ PDF Chat	On the condition number of the total least squares problem	2013	Zhongxiao Jia Bingyu Li
+ PDF Chat	On convergence of the inexact Rayleigh quotient iteration with the Lanczos method used for solving linear systems	2013	Zhongxiao Jia
+ PDF Chat	SHIRRA: A REFINED VARIANT OF SHIRA FOR THE SKEW-HAMILTONIAN/HAMILTONIAN (SHH) PENCIL EIGENVALUE PROBLEM	2013	Zhongxiao Jia Yuquan Sun
+ PDF Chat	An Approach to Making SPAI and PSAI Preconditioning Effective for Large Irregular Sparse Linear Systems	2013	Zhongxiao Jia Qian Zhang
+	A positivity preserving inexact Noda iteration for computing the smallest eigenpair of a large irreducible M-matrix	2013	Zhongxiao Jia Wen‐Wei Lin Ching-Sung Liu
+	On convergence of the inexact Rayleigh quotient iteration with MINRES	2012	Zhongxiao Jia
+	Robust Selection Criteria for Dropping Tolerances in Power Sparse Approximate Inverse (PSAI) Preconditioning and Static SAI Preconditioning	2012	Zhongxiao Jia Qian Zhang
+	An Approach to Making SPAI and PSAI Preconditioning Effective for Large Irregular Sparse Linear Systems	2012	Zhongxiao Jia Qian Zhang
+	Subspace Expansion in the Shift-Invert Residual Arnoldi Method and the Jacobi--Davidson Method: Theory and Algorithms	2011	Zhongxiao Jia Cen Li
+	The Shift-Invert Residual Arnoldi Method and the Jacobi-Davidson Method: Theory and Algorithms ∗	2011	Zhongxiao Jia Cen Li
+ PDF Chat	A Global Arnoldi Method for Large Non-Hermitian Eigenproblems with Special Applications to Multiple Eigenproblems	2011	Congying Duan Zhongxiao Jia
+	A Global Arnoldi Method for Large Non-Hermitian Eigenproblems with Special Applications to Multiple Eigenproblems	2011	Congying Duan Zhongxiao Jia
+	A contribution to the condition number of the total least squares problem	2011	Zhongxiao Jia Bingyu Li
+	A Refined Second-order Arnoldi (RSOAR) Method for the Quadratic Eigenvalue Problem and Implicitly Restarted Algorithms ∗	2011	Zhongxiao Jia Yuquan Sun
+	The Rayleigh–Ritz method, refinement and Arnoldi process for periodic matrix pairs	2010	Eric King‐wah Chu Hung‐Yuan Fan Zhongxiao Jia Tiexiang Li Wen‐Wei Lin
+	Some results on condition numbers of the scaled total least squares problem	2010	Bingyu Li Zhongxiao Jia
+	Some properties of LSQR for large sparse linear least squares problems	2010	Zhongxiao Jia
+	A global harmonic Arnoldi method for large non-Hermitian eigenproblems with an application to multiple eigenvalue problems	2010	Congying Duan Zhongxiao Jia
+ PDF Chat	A Refined Harmonic Lanczos Bidiagonalization Method and an Implicitly Restarted Algorithm for Computing the Smallest Singular Triplets of Large Matrices	2010	Zhongxiao Jia Datian Niu
+	Implicitly Restarted Generalized Second-order Arnoldi Type Algorithms for the Quadratic Eigenvalue Problem	2010	Zhongxiao Jia Yuquan Sun
+	On Convergence of the Inexact Rayleigh Quotient Iteration without and with MINRES	2009	Zhongxiao Jia
+	A Refined Harmonic Lanczos Bidiagonalization Method and an Implicitly Restarted Algorithm for Computing the Smallest Singular Triplets of Large Matrices	2009	Zhongxiao Jia Datian Niu
+	On Convergence of the Inexact Rayleigh Quotient Iteration with MINRES	2009	Zhongxiao Jia
+	A convergence analysis of the inexact Rayleigh quotient iteration and simplified Jacobi-Davidson method for the large Hermitian matrix eigenproblem	2008	Zhongxiao Jia Zhen Wang
+	A refined Jacobi-Davidson method for the quadratic eigenvalue problem	2006	Zhongxiao Jia Yuquan Sun
+	Using cross-product matrices to compute the SVD	2006	Zhongxiao Jia
+	A refined harmonic Rayleigh-Ritz procedure and an explicitly restarted refined harmonic Arnoldi algorithm	2005	Guizhi Chen Zhongxiao Jia
+	A refined jacobi-davidson method and its correction equation	2005	Shaoqiang Feng Zhongxiao Jia
+ PDF Chat	The convergence of harmonic Ritz values, harmonic Ritz vectors and refined harmonic Ritz vectors	2004	Zhongxiao Jia
+	An analogue of the results of Saad and Stewart for harmonic Ritz vectors	2004	Guizhi Chen Zhongxiao Jia
+	Some theoretical comparisons of refined Ritz vectors and Ritz vectors	2004	Zhongxiao Jia
+	A refined shift-and-invert arnoldi algorithm for large unsymmetric generalized eigenproblems	2002	Zhongxiao Jia Yong Zhang
+	The refined harmonic Arnoldi method and an implicitly restarted refined algorithm for computing interior eigenpairs of large matrices	2002	Zhongxiao Jia
+	Some Problems in Large Scale Non-Hermitian Matrix Computations	2002	Zhongxiao Jia
+	The Convergence of Harmonic Ritz Values, Harmonic Ritz Vectors and Refined Harmonic Ritz Vectors	2001	Zhongxiao Jia
+	A Refined Shift-and-Invert Arnoldi Algorithm for Large Unsymmetric Generalized Eigenproblems	2001	Zhongxiao Jia
+	Using Cross-Product Matrices to Compute the Svd	2001	Zhongxiao Jia
+ PDF Chat	An analysis of the Rayleigh--Ritz method for approximating eigenspaces	2000	Zhongxiao Jia G. W. Stewart
+	Some recursions on Arnoldi's method and IOM for large non-Hermitian linear systems	2000	Zhongxiao Jia
+	A refined subspace iteration algorithm for large sparse eigenproblems	2000	Zhongxiao Jia
+	A FEW RESULTS ON ARNOLDI'S METHOD AND IOM FOR LARGE NON-HERMITIAN LINEAR SYSTEMS	2000	Zhongxiao Jia
+	Polynomial characterizations of the approximate eigenvectors by the refined Arnoldi method and an implicitly restarted refined Arnoldi algorithm	1999	Zhongxiao Jia
+	On IGMRES: An incomplete generalized minimal residual method for large unsymmetric linear systems	1998	Zhongxiao Jia
+	A variation on the block Arnoldi method for large unsymmetric matrix eigenproblems	1998	Zhongxiao Jia
+	The convergence of Krylov subspace methods for large unsymmetric linear systems	1998	Zhongxiao Jia
+	A refined iterative algorithm based on the block arnoldi process for large unsymmetric eigenproblems	1998	Zhongxiao Jia
+	Refined iterative algorithms based on Arnoldi's process for large unsymmetric eigenproblems	1997	Zhongxiao Jia
+	On IOM(q): The Incomplete Orthogonalization Method for Large Unsymmetric Linear Systems	1996	Zhongxiao Jia
+	A block incomplete orthogonalization method for large nonsymmetric eigenproblems	1995	Zhongxiao Jia
+	The Convergence of Generalized Lanczos Methods for Large Unsymmetric Eigenproblems	1995	Zhongxiao Jia

Common Coauthors

Coauthor	Papers Together
Jinzhi Huang	8
Yuquan Sun	6
Wen‐Wei Lin	5
Yi Huang	5
Cen Li	4
Wenjie Kang	4
Kailiang Zhang	4
Haibo Li	3
Bingyu Li	3
Congying Duan	3
Qian Zhang	3
Ching-Sung Liu	2
Guizhi Chen	2
Yanfei Yang	2
Datian Niu	2
Jinzhi Huang	2
Hui Lv	1
Eric King‐wah Chu	1
Kailiang Zhang	1
Qian Zhang	1
Tsung‐Ming Huang	1
Tiexiang Li	1
Shaoqiang Feng	1
Wang Fa	1
Ching-Sung Liu	1
Yong Zhang	1
Hung‐Yuan Fan	1
Zhen Wang	1
Qingqing Zheng	1
Fa Wang	1
Fa Wang	1
Yi Huang	1
Qing‐Wen Wang	1
G. W. Stewart	1

Commonly Cited References

Action	Title	Year	Authors	# of times referenced
+	The Symmetric Eigenvalue Problem	1998	Beresford Ν. Parlett	35
+	The Convergence of Generalized Lanczos Methods for Large Unsymmetric Eigenproblems	1995	Zhongxiao Jia	29
+ PDF Chat	An analysis of the Rayleigh--Ritz method for approximating eigenspaces	2000	Zhongxiao Jia G. W. Stewart	29
+	Refined iterative algorithms based on Arnoldi's process for large unsymmetric eigenproblems	1997	Zhongxiao Jia	27
+	Computational methods for large eigenvalue problems	2002	H VANDERVORST	27
+	Numerical methods for least squares problems	1996	Åke Björck	23
+	Templates for the Solution of Algebraic Eigenvalue Problems: A Practical Guide	1987	James Demmel Jack Dongarra Axel Ruhe Henk van der Vorst Zhaojun Bai	22
+	A Jacobi–Davidson Iteration Method for Linear Eigenvalue Problems	1996	Gérard L. G. Sleijpen H.A. van der Vorst	21
+ PDF Chat	LSQR: An Algorithm for Sparse Linear Equations and Sparse Least Squares	1982	Christopher C. Paige Michael A. Saunders	19
+	Rank-Deficient and Discrete Ill-Posed Problems: Numerical Aspects of Linear Inversion	1987	Per Christian Hansen	18
+	The refined harmonic Arnoldi method and an implicitly restarted refined algorithm for computing interior eigenpairs of large matrices	2002	Zhongxiao Jia	17
+	Numerical Methods for Least Squares Problems	1996	Åke Björck	16
+	Polynomial characterizations of the approximate eigenvectors by the refined Arnoldi method and an implicitly restarted refined Arnoldi algorithm	1999	Zhongxiao Jia	16
+	A refined subspace iteration algorithm for large sparse eigenproblems	2000	Zhongxiao Jia	16
+ PDF Chat	A Refined Harmonic Lanczos Bidiagonalization Method and an Implicitly Restarted Algorithm for Computing the Smallest Singular Triplets of Large Matrices	2010	Zhongxiao Jia Datian Niu	15
+ PDF Chat	The principle of minimized iterations in the solution of the matrix eigenvalue problem	1951	Walter E. Arnoldi	15
+	Regularization Tools version 4.0 for Matlab 7.3	2007	Per Christian Hansen	14
+	Using cross-product matrices to compute the SVD	2006	Zhongxiao Jia	13
+	Rank-Deficient and Discrete Ill-Posed Problems	1998	Per Christian Hansen	12
+	None	2001	Martin Hanke	12
+ PDF Chat	The convergence of harmonic Ritz values, harmonic Ritz vectors and refined harmonic Ritz vectors	2004	Zhongxiao Jia	12
+	A Test Matrix Collection for Non-Hermitian Eigenvalue Problems	1997	A. Bai David Day Jack Dongarra	12
+	Some theoretical comparisons of refined Ritz vectors and Ritz vectors	2004	Zhongxiao Jia	12
+	Numerical Methods for Large Eigenvalue Problems	2011	Yousef Saad	12
+	A refined iterative algorithm based on the block arnoldi process for large unsymmetric eigenproblems	1998	Zhongxiao Jia	12
+	Conjugate Gradient Type Methods for Ill-Posed Problems	2017	Martin Hanke	12
+ PDF Chat	Inner iterations in the shift-invert residual Arnoldi method and the Jacobi-Davidson method	2014	Zhongxiao Jia Cen Li	11
+	Regularization of Inverse Problems	1996	Heinz W. Engl Martin Hanke Andreas B. Neubauer	11
+ PDF Chat	Harmonic and Refined Extraction Methods for the Singular Value Problem, with Applications in Least Squares Problems	2004	Michiel E. Hochstenbach	10
+	Inexact inverse iteration for symmetric matrices	2006	Jörg Berns-Müller Ivan G. Graham A. Spence	10
+ PDF Chat	Iterative regularization with minimum-residual methods	2007	Tine K. Jensen Per Christian Hansen	9
+ PDF Chat	A Bidiagonalization-Regularization Procedure for Large Scale Discretizations of Ill-Posed Problems	1981	Dianne P. O’Leary John A. Simmons	9
+	Approximate solutions and eigenvalue bounds from Krylov subspaces	1995	Chris Paige Beresford Ν. Parlett H.A. van der Vorst	9
+	Harmonic projection methods for large non-symmetric eigenvalue problems	1998	Ronald B. Morgan Min Zeng	9
+ PDF Chat	Choosing Regularization Parameters in Iterative Methods for Ill-Posed Problems	2001	Misha E. Kilmer Dianne P. O’Leary	9
+	Statistical and Computational Inverse Problems	2005	Jari P. Kaipio Erkki Somersalo	8
+	Inheritance of the discrete Picard condition in Krylov subspace methods	2015	Silvia Gazzola Paolo Novati	8
+	The regularizing effect of the Golub-Kahan iterative bidiagonalization and revealing the noise level in the data	2009	Iveta Hnětýnková Martin Plešinger Zdeněk Strakoš	8
+ PDF Chat	Chebyshev acceleration techniques for solving nonsymmetric eigenvalue problems	1984	Yousef Saad	8
+ PDF Chat	Inexact Inverse Subspace Iteration with Preconditioning Applied to Non-Hermitian Eigenvalue Problems	2009	Mickaël Robbé Miloud Sadkane A. Spence	8
+	Implicitly Restarted GMRES and Arnoldi Methods for Nonsymmetric Systems of Equations	2000	Ronald B. Morgan	8
+	On Krylov projection methods and Tikhonov regularization	2015	Silvia Gazzola Paolo Novati Maria Rosaria Russo	8
+ PDF Chat	Inexact Inverse Iteration with Variable Shift for Nonsymmetric Generalized Eigenvalue Problems	2006	Jörg Berns‐Müller A. Spence	8
+ PDF Chat	Controlling Inner Iterations in the Jacobi–Davidson Method	2009	Michiel E. Hochstenbach Yvan Notay	8
+ PDF Chat	Some results on the regularization of LSQR for large-scale discrete ill-posed problems	2016	Yi Huang Zhongxiao Jia	8
+ PDF Chat	A Sparse Approximate Inverse Preconditioner for Nonsymmetric Linear Systems	1998	Michele Benzi Miroslav Tůma	7
+	An inexact inverse iteration for large sparse eigenvalue problems	1997	Yu-Ling Lai Kun-Yi Lin Wen‐Wei Lin	7
+	An Introduction to the Mathematical Theory of Inverse Problems	2021	Andreas Kirsch	7
+	Towards a Generalized Singular Value Decomposition	1981	Christopher C. Paige Michael A. Saunders	7
+	An iteration method for the solution of the eigenvalue problem of linear differential and integral operators	1950	Cornelius Lanczos	7