Zhongxiao Jia
YOU?
Author Swipe
View article: A Chebyshev--Jackson series based block SS--RR algorithm for computing partial eigenpairs of real symmetric matrices
A Chebyshev--Jackson series based block SS--RR algorithm for computing partial eigenpairs of real symmetric matrices Open
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, a Rayleigh--Ritz projection onto a certain subspace genera…
View article: Inhibition of Lactate Accumulation via USP38‐Mediated MCT1 Deubiquitination Activates AKT/mTOR Signaling to Mitigate PM2.5‐Induced Lung Injury
Inhibition of Lactate Accumulation via USP38‐Mediated MCT1 Deubiquitination Activates AKT/mTOR Signaling to Mitigate PM2.5‐Induced Lung Injury Open
Background Lactate, traditionally viewed as a glycolysis byproduct, has emerged as an important mediator influencing immunity, inflammation, and tissue damage. While PM2.5 exposure is known to cause various metabolic disturbances, the role…
View article: An Implicitly Restarted Joint Bidiagonalization Algorithm for Large GSVD Computations
An Implicitly Restarted Joint Bidiagonalization Algorithm for Large GSVD Computations Open
The joint bidiagonalization (JBD) process of a regular matrix pair $\{A,L\}$ is mathematically equivalent to two simultaneous Lanczos bidiagonalization processes of the upper and lower parts of the Q-factor of QR factorization of the stack…
View article: The General Solution to a System of Tensor Equations over the Split Quaternion Algebra with Applications
The General Solution to a System of Tensor Equations over the Split Quaternion Algebra with Applications Open
This paper presents a systematic investigation into the solvability and the general solution of a tensor equation system within the split quaternion algebra framework. As an extension of classical quaternions with distinctive pseudo-Euclid…
View article: The General Solution to a System of Tensor Equations over the Split Quaternion Algebra with Applications
The General Solution to a System of Tensor Equations over the Split Quaternion Algebra with Applications Open
In this paper, considering a general solution to a system of tensor equations within the framework of the split quaternion algebra, we establish the necessary and sufficient conditions for the existence of the general solution. Furthermore…
View article: Preconditioning correction equations in Jacobi--Davidson type methods for computing partial singular value decompositions of large matrices
Preconditioning correction equations in Jacobi--Davidson type methods for computing partial singular value decompositions of large matrices Open
In a Jacobi--Davidson (JD) type method for singular value decomposition (SVD) problems, called JDSVD, a large symmetric and generally indefinite correction equation is solved iteratively at each outer iteration, which constitutes the inner…
View article: A CJ-FEAST GSVDsolver for computing a partial GSVD of a large matrix pair with the generalized singular values in a given interval
A CJ-FEAST GSVDsolver for computing a partial GSVD of a large matrix pair with the generalized singular values in a given interval Open
We propose a CJ-FEAST GSVDsolver to compute a partial generalized singular value decomposition (GSVD) of a large matrix pair $(A,B)$ with the generalized singular values in a given interval. The solver is a highly nontrivial extension of t…
View article: Refined and refined harmonic Jacobi--Davidson methods for computing several GSVD components of a large regular matrix pair
Refined and refined harmonic Jacobi--Davidson methods for computing several GSVD components of a large regular matrix pair Open
Three refined and refined harmonic extraction-based Jacobi--Davidson (JD) type methods are proposed, and their thick-restart algorithms with deflation and purgation are developed to compute several generalized singular value decomposition …
View article: An augmented matrix-based CJ-FEAST SVDsolver for computing a partial singular value decomposition with the singular values in a given interval
An augmented matrix-based CJ-FEAST SVDsolver for computing a partial singular value decomposition with the singular values in a given interval Open
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 singular vector and may be numerically backward unstable when a …
View article: A skew-symmetric Lanczos bidiagonalization method for computing several largest eigenpairs of a large skew-symmetric matrix
A skew-symmetric Lanczos bidiagonalization method for computing several largest eigenpairs of a large skew-symmetric matrix Open
The spectral decomposition of a real skew-symmetric matrix $A$ can be mathematically transformed into a specific structured singular value decomposition (SVD) of $A$. Based on such equivalence, a skew-symmetric Lanczos bidiagonalization (S…
View article: An analysis of the Rayleigh-Ritz and refined Rayleigh-Ritz methods for regular nonlinear eigenvalue problems
An analysis of the Rayleigh-Ritz and refined Rayleigh-Ritz methods for regular nonlinear eigenvalue problems Open
We establish a general convergence theory of the Rayleigh--Ritz method and the refined Rayleigh--Ritz method for computing some simple eigenpair $(λ_{*},x_{*})$ of a given analytic regular nonlinear eigenvalue problem (NEP). In terms of th…
View article: Two Harmonic Jacobi–Davidson Methods for Computing a Partial Generalized Singular Value Decomposition of a Large Matrix Pair
Two Harmonic Jacobi–Davidson Methods for Computing a Partial Generalized Singular Value Decomposition of a Large Matrix Pair Open
View article: Theoretical and Computable Optimal Subspace Expansions for Matrix Eigenvalue Problems
Theoretical and Computable Optimal Subspace Expansions for Matrix Eigenvalue Problems Open
Consider the optimal subspace expansion problem for the matrix eigenvalue problem $Ax=\lambda x$: Which vector $w$ in the current subspace $\mathcal{V}$, after multiplied by $A$, provides an optimal subspace expansion for approximating a d…
View article: A FEAST SVDsolver based on Chebyshev--Jackson series for computing partial singular triplets of large matrices
A FEAST SVDsolver based on Chebyshev--Jackson series for computing partial singular triplets of large matrices Open
The FEAST eigensolver is extended to the computation of the singular triplets of a large matrix $A$ with the singular values in a given interval. The resulting FEAST SVDsolver is subspace iteration applied to an approximate spectral projec…
View article: A comparison of eigenvalue-based algorithms and the generalized Lanczos trust-region algorithm for Solving the trust-region subproblem
A comparison of eigenvalue-based algorithms and the generalized Lanczos trust-region algorithm for Solving the trust-region subproblem Open
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 $n$ is mathematically equivalent to finding the rightmost eige…
View article: The joint bidiagonalization process with partial reorthogonalization
The joint bidiagonalization process with partial reorthogonalization Open
View article: A joint bidiagonalization based iterative algorithm for large scale general-form Tikhonov regularization
A joint bidiagonalization based iterative algorithm for large scale general-form Tikhonov regularization Open
View article: 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*
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* Open
For the large-scale linear discrete ill-posed problem min‖ Ax − b ‖ or Ax = b with b contaminated by white noise, the Golub–Kahan bidiagonalization based LSQR method and its mathematically equivalent CGLS, the conjugate gradient (CG) metho…
View article: A cross-product free Jacobi-Davidson type method for computing a partial generalized singular value decomposition (GSVD) of a large matrix pair
A cross-product free Jacobi-Davidson type method for computing a partial generalized singular value decomposition (GSVD) of a large matrix pair Open
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 $(A,B)$. It implicitly solves the mathematically equivalent general…
View article: Theoretical and Computable Optimal Subspace Expansions for Matrix Eigenvalue Problems
Theoretical and Computable Optimal Subspace Expansions for Matrix Eigenvalue Problems Open
Consider the optimal subspace expansion problem for the matrix eigenvalue problem $Ax=λx$: Which vector $w$ in the current subspace $\mathcal{V}$, after multiplied by $A$, provides an optimal subspace expansion for approximating a desired …
View article: Optimal Subspace Expansion for Matrix Eigenvalue Problems.
Optimal Subspace Expansion for Matrix Eigenvalue Problems. Open
In this paper, we consider the optimal subspace expansion problem for the matrix eigenvalue problem $Ax=\lambda x$: {\em Which vector $w$ in the current subspace $\mathcal{V}$, after multiplied by $A$, provides an optimal subspace expansio…
View article: The Krylov Subspaces, Low Rank Approximations and Ritz Values of LSQR for Linear Discrete Ill-Posed Problems: the Multiple Singular Value Case
The Krylov Subspaces, Low Rank Approximations and Ritz Values of LSQR for Linear Discrete Ill-Posed Problems: the Multiple Singular Value Case Open
For the large-scale linear discrete ill-posed problem $\min\|Ax-b\|$ or $Ax=b$ with $b$ contaminated by white noise, the Golub-Kahan bidiagonalization based LSQR method and its mathematically equivalent CGLS, the Conjugate Gradient (CG) me…
View article: Regularization properties of Krylov iterative solvers CGME and LSMR for linear discrete ill-posed problems with an application to truncated randomized SVDs
Regularization properties of Krylov iterative solvers CGME and LSMR for linear discrete ill-posed problems with an application to truncated randomized SVDs Open
View article: Approximation accuracy of the Krylov subspaces for linear discrete ill-posed problems
Approximation accuracy of the Krylov subspaces for linear discrete ill-posed problems Open
View article: The low rank approximations and Ritz values in LSQR for linear discrete ill-posed problem*
The low rank approximations and Ritz values in LSQR for linear discrete ill-posed problem* Open
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 k plays the role of the regularization parameter. It has been long known t…
View article: The joint bidiagonalization method for large GSVD computations in finite precision
The joint bidiagonalization method for large GSVD computations in finite precision Open
The joint bidiagonalization (JBD) method has been used to compute some extreme generalized singular values and vectors of a large regular matrix pair $\{A,L\}$, where we propose three approaches to compute approximate generalized singular …
View article: The convergence of the Generalized Lanczos Trust-Region Method for the Trust-Region Subproblem
The convergence of the Generalized Lanczos Trust-Region Method for the Trust-Region Subproblem Open
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 Lanczos type approach for solving a large-scale TRS. The m…
View article: On inner iterations of Jacobi-Davidson type methods for large SVD computations
On inner iterations of Jacobi-Davidson type methods for large SVD computations Open
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 triplets of a large matrix $A$. At each outer iteration of thes…
View article: The regularization theory of the Krylov iterative solvers LSQR and CGLS for linear discrete ill-posed problems, part I: the simple singular value case
The regularization theory of the Krylov iterative solvers LSQR and CGLS for linear discrete ill-posed problems, part I: the simple singular value case Open
For the large-scale linear discrete ill-posed problem $\min\|Ax-b\|$ or $Ax=b$ with $b$ contaminated by a white noise, the Lanczos bidiagonalization based LSQR method and its mathematically equivalent Conjugate Gradient (CG) method for $A^…
View article: The Regularization Theory of the Krylov Iterative Solvers LSQR, CGLS, LSMR and CGME For Linear Discrete Ill-Posed Problems
The Regularization Theory of the Krylov Iterative Solvers LSQR, CGLS, LSMR and CGME For Linear Discrete Ill-Posed Problems Open
For the large-scale linear discrete ill-posed problem $\min\|Ax-b\|$ or $Ax=b$ with $b$ contaminated by a white noise, Lanczos bidiagonalization based LSQR and its mathematically equivalent CGLS are most commonly used. They have intrinsic …