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Linear and Multilinear Algebra, ISSN 0308-1087, 01/2020, Volume 68, Issue 1, pp. 133 - 151
Our aim is to establish relations between the Drazin inverses of the pesudo-block matrix and the block matrix , where . Based on the relations, we give... 
Drazin inverse | pesudo-block decomposition | 15A30 | 15A09 | pesudo-block matrix | 65F20 | Ren-Cang Li
Journal Article
SIAM Journal on Matrix Analysis and Applications, ISSN 0895-4798, 2013, Volume 34, Issue 2, pp. 392 - 416
In Part I of this paper we presented minimization principles and related theoretical results for the linear response eigenvalue problem. Here we develop best... 
Eigenvalue | Random phase approximation | Quantum linear response | Eigenvector | Minimization principle | MATHEMATICS, APPLIED | STATES | minimization principle | REDUCTION | ALGORITHM | quantum linear response | random phase approximation | EQUATION | eigenvalue | RANDOM-PHASE-APPROXIMATION | eigenvector | Conjugates | Approximation | Computation | Eigenvalues | Minimization | Subspaces | Optimization | Convergence
Journal Article
SIAM Journal on Matrix Analysis and Applications, ISSN 0895-4798, 2012, Volume 33, Issue 4, pp. 1075 - 1100
We present two theoretical results for the linear response eigenvalue problem. The first result is a minimization principle for the sum of the smallest... 
Eigenvalue | Random phase approximation | Quantum linear response | Eigenvector | Minimization principle | MATHEMATICS, APPLIED | STATES | minimization principle | MATRICES | PERTURBATION | quantum linear response | random phase approximation | PENCILS | eigenvalue | RANDOM-PHASE-APPROXIMATION | eigenvector
Journal Article
Numerische Mathematik, ISSN 0029-599X, 3/2017, Volume 135, Issue 3, pp. 733 - 767
Journal Article
Linear Algebra and Its Applications, ISSN 0024-3795, 11/2019, Volume 581, pp. 163 - 197
Journal Article
Linear Algebra and Its Applications, ISSN 0024-3795, 05/2017, Volume 520, pp. 191 - 214
In this paper, we present an efficient ΓQR algorithm for solving the linear response eigenvalue problem Hx=λx, where H is Π−-symmetric with respect to... 
Γ-orthogonality | [formula omitted]-matrix | Structure preserving | Linear response eigenvalue problem | ΓQR algorithm | matrix
Journal Article
Journal of Computational and Applied Mathematics, ISSN 0377-0427, 2009, Volume 233, Issue 4, pp. 1035 - 1045
This paper is concerned with the numerical solution of large scale Sylvester equations A X − X B = C , Lyapunov equations as a special case in particular... 
Factored ADI method | Galerkin projection | Sylvester equation | MATHEMATICS, APPLIED | NUMERICAL-SOLUTION | RANK SMITH METHOD | KRYLOV-SUBSPACE METHODS | LYAPUNOV EQUATIONS | IDENTIFICATION
Journal Article
Linear Algebra and Its Applications, ISSN 0024-3795, 12/2019, Volume 583, pp. 1 - 45
A highly accurate doubling algorithm to solve the most fundamental quadratic matrix equation in the quasi-birth-and-death (qbd) process is developed. It... 
Entrywise relative accuracy | Nonnegative solution | Doubling algorithm | Quasi-birth-and-death process | SF1 | EIGENVALUE | ITERATION | MATHEMATICS, APPLIED | LOGARITHMIC REDUCTION ALGORITHM | CONVERGENCE ANALYSIS | MATHEMATICS | NUMERICAL-SOLUTION | CYCLIC REDUCTION | M/G/1 | Quadratic equations | Algorithms | Riccati equation | Convergence
Journal Article
Journal of Computational and Applied Mathematics, ISSN 0377-0427, 08/2013, Volume 247, Issue 1, pp. 17 - 33
Two different Lanczos-type methods for the linear response eigenvalue problem are analyzed. The first one is a natural extension of the classical Lanczos... 
Lanczos-type method | Eigenvalue | Eigenvector | Linear response eigenvalue problem | Convergence analysis | RATES | MATHEMATICS, APPLIED | STATES | RANDOM-PHASE-APPROXIMATION
Journal Article
Journal Article
SIAM Journal on Optimization, ISSN 1052-6234, 2017, Volume 27, Issue 3, pp. 2110 - 2142
The so-called trust-region subproblem gets its name in the trust-region method in optimization and also plays a vital role in various other applications.... 
Conjugate gradient method | Stopping criterion | Trust-region method | Lanczos method | Trust-region subproblem | Convergence | trust-region method | MATHEMATICS, APPLIED | convergence | stopping criterion | CONJUGATE-GRADIENT METHOD | OPTIMIZATION | SUBPROBLEMS | conjugate gradient method | trust-region subproblem
Journal Article
Numerical Linear Algebra with Applications, ISSN 1070-5325, 05/2015, Volume 22, Issue 3, pp. 393 - 409
Journal Article
SIAM Journal on Matrix Analysis and Applications, ISSN 0895-4798, 2012, Volume 33, Issue 1, pp. 170 - 194
A new doubling algorithm-the alternating-directional doubling algorithm (ADDA)-is developed for computing the unique minimal nonnegative solution of an... 
Minimal nonnegative solution | M-matrix | Bilinear transformation | Doubling algorithm | Matrix Riccati equation | MATHEMATICS, APPLIED | CONVERGENCE ANALYSIS | matrix Riccati equation | minimal nonnegative solution | bilinear transformation | ITERATIVE SOLUTION | SPECTRUM | doubling algorithm | DICHOTOMY
Journal Article
SIAM Journal on Matrix Analysis and Applications, ISSN 0895-4798, 2014, Volume 35, Issue 2, pp. 765 - 782
Journal Article
SIAM Journal on Matrix Analysis and Applications, ISSN 0895-4798, 2007, Volume 29, Issue 4, pp. 1218 - 1241
The most widely used approach for solving the polynomial eigenvalue problem P(lambda)x = (Sigma(m)(i=0) lambda(i) A(i))x = 0 in n x n matrices A(i) is to... 
Palindromic | Eigenvector | Companion form | Backward error | Alternating | Matrix pencil | Quadratic eigenvalue problem | Scaling | Matrix polynomial | Linearization | companion form | MATHEMATICS, APPLIED | scaling | alternating | MATRIX POLYNOMIALS | matrix polynomial | backward error | matrix pencil | quadratic eigenvalue problem | palindromic | eigenvector | linearization
Journal Article
Journal of Scientific Computing, ISSN 0885-7474, 6/2019, Volume 79, Issue 3, pp. 1608 - 1629
An efficient numerical method for solving a symmetric positive definite second-order cone linear complementarity problem (SOCLCP) is proposed. The method is... 
Computational Mathematics and Numerical Analysis | 65K05 | 65P99 | GUS | Theoretical, Mathematical and Computational Physics | Globally uniquely solvable property | SOCLCP | Mathematics | Linear complementarity problem | Second-order cone | Algorithms | 65F99 | 90C33 | 65F30 | Mathematical and Computational Engineering | 65F15 | MATHEMATICS, APPLIED
Journal Article
IEEE Transactions on Computers, ISSN 0018-9340, 08/2009, Volume 58, Issue 8, pp. 1139 - 1145
Journal Article
Frontiers of Mathematics in China, ISSN 1673-3452, 12/2018, Volume 13, Issue 6, pp. 1397 - 1426
A detailed structured backward error analysis for four kinds of palindromic polynomial eigenvalue problems (PPEPs) $$P(\lambda ) \equiv (\sum\limits_{\ell =... 
eigentriplet | error bound | Palindromic polynomial eigenvalue problem (PPEP) | Mathematics, general | 65F15 | Mathematics | 65G99 | structured backward error | MATHEMATICS | Eigenvalues | Polynomials | Error analysis | Perturbation methods | Upper bounds | Eigen values
Journal Article
Journal of Computational and Applied Mathematics, ISSN 0377-0427, 08/2016, Volume 302, pp. 285 - 300
A suggestive indicator is proposed for predicting whether a given (complex or real) square matrix A is or is not a generalized diagonally dominant matrix... 
SCI | M-matrix | H-matrix | Generalized diagonally dominant matrix | GDDM | Self-corrective iteration | MATHEMATICS, APPLIED | CRITERION | Analysis | Algorithms | Computer science | Matrices (mathematics) | Mathematical analysis | Collection | Iterative methods | Indicators | Strikes | Extreme values
Journal Article
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