Related papers: On inner iterations of Jacobi-Davidson type method…
It is needed to solve generalized eigenvalue problems (GEP) in many applications, such as the numerical simulation of vibration analysis, quantum mechanics, electronic structure, etc. The subspace iteration is a kind of widely used…
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…
For large-scale eigenvalue problems requiring many mutually orthogonal eigenvectors, traditional numerical methods suffer substantial computational and communication costs with limited parallel scalability, primarily due to explicit…
The tensor-train (TT) decomposition is widely used to compress large tensors into a more compact form by exploiting their inherent data structures. A fundamental approach for constructing the TT format is the well-known TT-SVD method, which…
We shall investigate randomized algorithms for solving large-scale linear inverse problems with general regularizations. We first present some techniques to transform inverse problems of general form into the ones of standard form, then…
The singular value decomposition (SVD) of a matrix is a powerful tool for many matrix computation problems. In this paper, we consider generalizing the standard SVD to analyze and compute the regularized solution of linear ill-posed…
We analyze sparse frame based regularization of inverse problems by means of a diagonal frame decomposition (DFD) for the forward operator, which generalizes the SVD. The DFD allows to define a non-iterative (direct) operator-adapted frame…
Matrix completion is a widely used technique for image inpainting and personalized recommender system, etc. In this work, we focus on accelerating the matrix completion using faster randomized singular value decomposition (rSVD). Firstly,…
The focus in this work is on interior-point methods for inequality-constrained quadratic programs, and particularly on the system of nonlinear equations to be solved for each value of the barrier parameter. Newton iterations give high…
This paper introduces a discretization-accurate stopping criterion of symmetric iterative methods for solving systems of algebraic equations resulting from the finite element approximation. The stopping criterion consists of the evaluations…
For a datastream, the change over a short interval is often of low rank. For high throughput information arranged in matrix format, recomputing an optimal SVD approximation after each step is typically prohibitive. Instead, incremental and…
We present a short step interior point method for solving a class of nonlinear programming problems with quadratic objective function. Convex quadratic programming problems can be reformulated as problems in this class. The method is shown…
Semidefinite programs (SDPs) are powerful theoretical tools that have been studied for over two decades, but their practical use remains limited due to computational difficulties in solving large-scale, realistic-sized problems. In this…
A one-sided Jacobi hyperbolic singular value decomposition (HSVD) algorithm, using a massively parallel graphics processing unit (GPU), is developed. The algorithm also serves as the final stage of solving a symmetric indefinite eigenvalue…
We present an improved form of the algorithm for constructing Jacobi rotations. This is simultaneously a more accurate code for finding the eigenvalues and eigenvectors of a real symmetric 2x2 matrix.
Singular equations with rank-deficient Jacobians arise frequently in algebraic computing applications. As shown in case studies in this paper, direct and intuitive modeling of algebraic problems often results in nonisolated singular…
We propose a second-order accurate method to estimate the eigenvectors of extremely large matrices thereby addressing a problem of relevance to statisticians working in the analysis of very large datasets. More specifically, we show that…
This paper proposes an efficient method for computing partial eigenvalues of large sparse matrices what can be called the inexact inverse power method (IIPM). It is similar to the inexact Rayleigh quotient method and inexact Jacobi-Davidson…
A self-learning algebraic multigrid method for dominant and minimal singular triplets and eigenpairs is described. The method consists of two multilevel phases. In the first, multiplicative phase (setup phase), tentative singular triplets…
We provide a new algorithm for the treatment of inverse problems which combines the traditional SVD inversion with an appropriate thresholding technique in a well chosen new basis. Our goal is to devise an inversion procedure which has the…