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

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

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

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

The doubling algorithms are very efficient iterative methods for computing the unique minimal nonnegative solution to an M-matrix algebraic Riccati equation...

Mathematical Methods in Physics | 15A24 | Numerical Analysis | Theoretical, Mathematical and Computational Physics | 65F30 | Appl.Mathematics/Computational Methods of Engineering | Mathematics, general | Mathematics | 65H10 | Numerical and Computational Physics, Simulation | MATHEMATICS, APPLIED | WIENER-HOPF FACTORIZATION | ITERATIVE SOLUTION | Algorithms

Mathematical Methods in Physics | 15A24 | Numerical Analysis | Theoretical, Mathematical and Computational Physics | 65F30 | Appl.Mathematics/Computational Methods of Engineering | Mathematics, general | Mathematics | 65H10 | Numerical and Computational Physics, Simulation | MATHEMATICS, APPLIED | WIENER-HOPF FACTORIZATION | ITERATIVE SOLUTION | Algorithms

Journal Article

Linear Algebra and Its Applications, ISSN 0024-3795, 11/2019, Volume 581, pp. 163 - 197

The matrix joint block-diagonalization problem (jbdp) of a given matrix set A={Ai}i=1m is about finding a nonsingular matrix W such that all WTAiW are...

Modulus of non-divisibility | Modulus of uniqueness | Perturbation analysis | Matrix joint block-diagonalization | MICA | MATHEMATICS, APPLIED | EXPLOITING GROUP SYMMETRY | RANK | UNIQUENESS | MATHEMATICS | CANONICAL POLYADIC DECOMPOSITION | SEPARATION | HIGHER-ORDER TENSOR | Perturbation theory | Error analysis | Perturbation methods | Theory | Independent component analysis | Uniqueness | Mica

Modulus of non-divisibility | Modulus of uniqueness | Perturbation analysis | Matrix joint block-diagonalization | MICA | MATHEMATICS, APPLIED | EXPLOITING GROUP SYMMETRY | RANK | UNIQUENESS | MATHEMATICS | CANONICAL POLYADIC DECOMPOSITION | SEPARATION | HIGHER-ORDER TENSOR | Perturbation theory | Error analysis | Perturbation methods | Theory | Independent component analysis | Uniqueness | Mica

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

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

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

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

9.
Full Text
Convergence analysis of Lanczos-type methods for the linear response eigenvalue problem

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

Lanczos-type method | Eigenvalue | Eigenvector | Linear response eigenvalue problem | Convergence analysis | RATES | MATHEMATICS, APPLIED | STATES | RANDOM-PHASE-APPROXIMATION

Journal Article

Advances in Computational Mathematics, ISSN 1019-7168, 10/2016, Volume 42, Issue 5, pp. 1103 - 1128

We present a Chebyshev-Davidson method to compute a few smallest positive eigenvalues and corresponding eigenvectors of linear response eigenvalue problems....

Visualization | Computational Mathematics and Numerical Analysis | Linear response | Mathematical and Computational Biology | Chebyshev polynomial | Upper bound estimator | Mathematics | Computational Science and Engineering | 15A18 | Convergence rate | 65F15 | Mathematical Modeling and Industrial Mathematics | Davidson type method | Eigenvalue/eigenvector | MATHEMATICS, APPLIED | DENSITY-FUNCTIONAL THEORY | MINIMIZATION PRINCIPLES | EQUATION | Eigenvalues | Chebyshev approximation | Convergence (Mathematics) | Research | Mathematical research

Visualization | Computational Mathematics and Numerical Analysis | Linear response | Mathematical and Computational Biology | Chebyshev polynomial | Upper bound estimator | Mathematics | Computational Science and Engineering | 15A18 | Convergence rate | 65F15 | Mathematical Modeling and Industrial Mathematics | Davidson type method | Eigenvalue/eigenvector | MATHEMATICS, APPLIED | DENSITY-FUNCTIONAL THEORY | MINIMIZATION PRINCIPLES | EQUATION | Eigenvalues | Chebyshev approximation | Convergence (Mathematics) | Research | Mathematical research

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

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

SummaryRecently, Guo and Lin [SIAM J. Matrix Anal. Appl., 31 (2010), 2784–2801] proposed an efficient numerical method to solve the palindromic quadratic...

vibration analysis of high speed train | palindromic quadratic eigenvalue problem | solvent approach | doubling algorithm | nonlinear matrix equation | Palindromic quadratic eigenvalue problem | Solvent approach | Doubling algorithm | Nonlinear matrix equation | Vibration analysis of high speed train | MATHEMATICS | MATHEMATICS, APPLIED | MATRIX EQUATION | Analysis | Algorithms | Matrix | Vibration analysis | Mathematical analysis | Linear algebra | Eigenvalues | Blocking | Nonlinearity | Mathematical models | Iterative methods

vibration analysis of high speed train | palindromic quadratic eigenvalue problem | solvent approach | doubling algorithm | nonlinear matrix equation | Palindromic quadratic eigenvalue problem | Solvent approach | Doubling algorithm | Nonlinear matrix equation | Vibration analysis of high speed train | MATHEMATICS | MATHEMATICS, APPLIED | MATRIX EQUATION | Analysis | Algorithms | Matrix | Vibration analysis | Mathematical analysis | Linear algebra | Eigenvalues | Blocking | Nonlinearity | Mathematical models | Iterative methods

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

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

Large scale eigenvalue computation is about approximating certain invariant subspaces associated with the interesting part of the spectrum, and the interesting...

Error bounds | Rayleigh-Ritz approximation | Canonical angles | Deflating subspace | Eigenvalue approximation | Linear response eigenvalue problem | MATHEMATICS, APPLIED | error bounds | canonical angles | deflating subspace | EQUATIONS | MINIMIZATION PRINCIPLES | eigenvalue approximation | linear response eigenvalue problem | MATRICES | PRODUCT | SUBSPACES | COMPUTATION | Errors | Approximation | Upper bounds | Computation | Mathematical analysis | Eigenvalues | Subspaces | Invariants

Error bounds | Rayleigh-Ritz approximation | Canonical angles | Deflating subspace | Eigenvalue approximation | Linear response eigenvalue problem | MATHEMATICS, APPLIED | error bounds | canonical angles | deflating subspace | EQUATIONS | MINIMIZATION PRINCIPLES | eigenvalue approximation | linear response eigenvalue problem | MATRICES | PRODUCT | SUBSPACES | COMPUTATION | Errors | Approximation | Upper bounds | Computation | Mathematical analysis | Eigenvalues | Subspaces | Invariants

Journal Article

Numerical Linear Algebra with Applications, ISSN 1070-5325, 03/2016, Volume 23, Issue 2, pp. 291 - 313

Summary Among numerous iterative methods for solving the minimal nonnegative solution of an M‐matrix algebraic Riccati equation, the structure‐preserving...

minimal nonnegative solution | critical case | M‐matrix algebraic Riccati equation | M‐matrix | two‐phase structure‐preserving doubling algorithm | Minimal nonnegative solution | M-matrix | Critical case | M-matrix algebraic Riccati equation | Two-phase structure-preserving doubling algorithm | two-phase structure-preserving doubling algorithm | MATHEMATICS | MATHEMATICS, APPLIED | WIENER-HOPF FACTORIZATION | ITERATIVE SOLUTION | Analysis | Algorithms | Algebra | Approximation | Mathematical models | Riccati equation | Iterative methods | Convergence | Stands

minimal nonnegative solution | critical case | M‐matrix algebraic Riccati equation | M‐matrix | two‐phase structure‐preserving doubling algorithm | Minimal nonnegative solution | M-matrix | Critical case | M-matrix algebraic Riccati equation | Two-phase structure-preserving doubling algorithm | two-phase structure-preserving doubling algorithm | MATHEMATICS | MATHEMATICS, APPLIED | WIENER-HOPF FACTORIZATION | ITERATIVE SOLUTION | Analysis | Algorithms | Algebra | Approximation | Mathematical models | Riccati equation | Iterative methods | Convergence | Stands

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

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

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

The Cody and Waite argument reduction technique works perfectly for reasonably large arguments, but as the input grows, there are no bits left to approximate...

Algorithm design and analysis | Accuracy | Coq | formal proof | Polynomials | Hardware | Libraries | Computational efficiency | Argument reduction | fma | Approximation methods | Formal proof | Fma | COMPUTER SCIENCE, HARDWARE & ARCHITECTURE | ENGINEERING, ELECTRICAL & ELECTRONIC | Computer programming | Usage | Trigonometry | Analysis | Floating-point arithmetic | Reduction | Algorithms | Approximation | Computation | Proving | Recall | Checkers | Mathematical Software | Computer Arithmetic | Performance | Computer Science

Algorithm design and analysis | Accuracy | Coq | formal proof | Polynomials | Hardware | Libraries | Computational efficiency | Argument reduction | fma | Approximation methods | Formal proof | Fma | COMPUTER SCIENCE, HARDWARE & ARCHITECTURE | ENGINEERING, ELECTRICAL & ELECTRONIC | Computer programming | Usage | Trigonometry | Analysis | Floating-point arithmetic | Reduction | Algorithms | Approximation | Computation | Proving | Recall | Checkers | Mathematical Software | Computer Arithmetic | Performance | Computer Science

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

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

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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