28 citations · 222 across the 42 of their papers we have counts for
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The Refined Joint Bidiagonalization Method and an Implicitly Restarted Algorithm for Large GSVD Computations
Kaixiao Fang, Zhongxiao Jia
We make a convergence analysis on the joint bidiagonalization (JBD) method that computes several extreme generalized singular value decomposition (GSVD) components of a regular mat…
A Numerical Analysis of Sketched Linear Squares Problems and Stopping Criteria for Iterative Solvers
Zhongxiao Jia, Xinyuan Wan
Randomized subspace embedding methods have had a great impact on the solution of a linear least squares (LS) problem by reducing its row dimension, leading to a randomized or sketc…
A Chebyshev--Jackson series based block SS--RR algorithm for computing partial eigenpairs of real symmetric matrices
Zhongxiao Jia, Tianhang Liu
This paper considers eigenpair computations of large symmetric matrices with the desired eigenvalues lying in a given interval using the contour integral-based block SS--RR method,…
An Implicitly Restarted Joint Bidiagonalization Algorithm for Large GSVD Computations
Kaixiao Fang, Zhongxiao Jia
The joint bidiagonalization (JBD) process of a regular matrix pair is mathematically equivalent to two simultaneous Lanczos bidiagonalization processes of the upper and l…
A CJ-FEAST GSVDsolver for computing a partial GSVD of a large matrix pair with the generalized singular values in a given interval
Zhongxiao Jia, Kailiang Zhang
We propose a CJ-FEAST GSVDsolver to compute a partial generalized singular value decomposition (GSVD) of a large matrix pair with the generalized singular values in a given…
An augmented matrix-based CJ-FEAST SVDsolver for computing a partial singular value decomposition with the singular values in a given interval
Zhongxiao Jia, Kailiang Zhang
The cross-product matrix-based CJ-FEAST SVDsolver proposed previously by the authors is shown to compute the left singular vector possibly much less accurately than the right singu…
A skew-symmetric Lanczos bidiagonalization method for computing several largest eigenpairs of a large skew-symmetric matrix
Jinzhi Huang, Zhongxiao Jia
The spectral decomposition of a real skew-symmetric matrix can be mathematically transformed into a specific structured singular value decomposition (SVD) of . Based on such…
An analysis of the Rayleigh-Ritz and refined Rayleigh-Ritz methods for regular nonlinear eigenvalue problems
Zhongxiao Jia, Qingqing Zheng
We establish a general convergence theory of the Rayleigh--Ritz method and the refined Rayleigh--Ritz method for computing some simple eigenpair of a given analytic…
Two harmonic Jacobi--Davidson methods for computing a partial generalized singular value decomposition of a large matrix pair
Jinzhi Huang, Zhongxiao Jia
Two harmonic extraction based Jacobi--Davidson (JD) type algorithms are proposed to compute a partial generalized singular value decomposition (GSVD) of a large regular matrix pair…
A FEAST SVDsolver based on Chebyshev--Jackson series for computing partial singular triplets of large matrices
Zhongxiao Jia, Kailiang Zhang
The FEAST eigensolver is extended to the computation of the singular triplets of a large matrix with the singular values in a given interval. The resulting FEAST SVDsolver is s…
A comparison of eigenvalue-based algorithms and the generalized Lanczos trust-region algorithm for Solving the trust-region subproblem
Zhongxiao Jia, Fa Wang
Solving the trust-region subproblem (TRS) plays a key role in numerical optimization and many other applications. Based on a fundamental result that the solution of TRS of size …
A cross-product free Jacobi-Davidson type method for computing a partial generalized singular value decomposition (GSVD) of a large matrix pair
Jinzhi Huang, Zhongxiao Jia
A Cross-Product Free (CPF) Jacobi-Davidson (JD) type method is proposed to compute a partial generalized singular value decomposition (GSVD) of a large regular matrix pair .…
Theoretical and Computable Optimal Subspace Expansions for Matrix Eigenvalue Problems
Zhongxiao Jia
Consider the optimal subspace expansion problem for the matrix eigenvalue problem : Which vector in the current subspace , after multiplied by , provides…
The Krylov Subspaces, Low Rank Approximations and Ritz Values of LSQR for Linear Discrete Ill-Posed Problems: the Multiple Singular Value Case
Zhongxiao Jia
For the large-scale linear discrete ill-posed problem or with contaminated by white noise, the Golub-Kahan bidiagonalization based LSQR method and its mat…
The joint bidiagonalization process with partial reorthogonalization
Zhongxiao Jia, Haibo Li
The joint bidiagonalization(JBD) process is a useful algorithm for the computation of the generalized singular value decomposition(GSVD) of a matrix pair. However, it always suffer…
The joint bidiagonalization method for large GSVD computations in finite precision
Zhongxiao Jia, Haibo Li
The joint bidiagonalization (JBD) method has been used to compute some extreme generalized singular values and vectors of a large regular matrix pair , where we propose th…
The convergence of the Generalized Lanczos Trust-Region Method for the Trust-Region Subproblem
Zhongxiao Jia, Fa Wang
Solving the trust-region subproblem (TRS) plays a key role in numerical optimization and many other applications. The generalized Lanczos trust-region (GLTR) method is a well-known…
On choices of formulations of computing the generalized singular value decomposition of a large matrix pair
Jinzhi Huang, Zhongxiao Jia
For the computation of the generalized singular value decomposition (GSVD) of a large matrix pair of full column rank, the GSVD is commonly formulated as two mathematically…
Regularization Properties of the Krylov Iterative Solvers CGME and LSMR For Linear Discrete Ill-Posed Problems with an Application to Truncated Randomized SVDs
Zhongxiao Jia
For the large-scale linear discrete ill-posed problem or with contaminated by Gaussian white noise, there are four commonly used Krylov solvers: LSQR and…
The Low Rank Approximations and Ritz Values in LSQR For Linear Discrete Ill-Posed Problems
Zhongxiao Jia
LSQR and its mathematically equivalent CGLS have been popularly used over the decades for large-scale linear discrete ill-posed problems, where the iteration number plays the r…
A Joint Bidiagonalization Based Algorithm for Large Scale Linear Discrete Ill-posed Problems in General-Form Regularization
Zhongxiao Jia, Yanfei Yang
Based on the joint bidiagonalization process of a large matrix pair , we propose and develop an iterative regularization algorithm for the large scale linear discrete ill-…
Approximation Accuracy of the Krylov Subspaces for Linear Discrete Ill-Posed Problems
Zhongxiao Jia
For the large-scale linear discrete ill-posed problem or with contaminated by Gaussian white noise, the Lanczos bidiagonalization based Krylov solver LSQR…
On inner iterations of Jacobi-Davidson type methods for large SVD computations
Jinzhi Huang, Zhongxiao Jia
We make a convergence analysis of the harmonic and refined harmonic extraction versions of Jacobi-Davidson SVD (JDSVD) type methods for computing one or more interior singular trip…
Modified Truncated Randomized Singular Value Decomposition (MTRSVD) Algorithms for Large Scale Discrete Ill-posed Problems with General-Form Regularization
Zhongxiao Jia, Yanfei Yang
In this paper, we propose new randomization based algorithms for large scale linear discrete ill-posed problems with general-form regularization: subject to ${\min}…