Computers and Mathematics with Applications, ISSN 0898-1221, 06/2016, Volume 71, Issue 12, pp. 2513 - 2523

In this paper, we first establish the necessary and sufficient conditions for the existence and the explicit expressions of the Hermitian...

Hermitian [formula omitted]-(anti-)reflexive solutions | Matrix equation | Least squares solution | Hermitian {P, k +1}-(anti-)reflexive solutions | ANTI-REFLEXIVE SOLUTIONS | OPTIMAL APPROXIMATION | MATHEMATICS, APPLIED | LEAST-SQUARES SOLUTIONS | Hermitian {P, k+1}-(anti-)reflexive solutions | CONSTRAINT | Algorithms | Approximation | Computer simulation | Least squares method | Mathematical analysis | Norms | Feasibility | Mathematical models

Hermitian [formula omitted]-(anti-)reflexive solutions | Matrix equation | Least squares solution | Hermitian {P, k +1}-(anti-)reflexive solutions | ANTI-REFLEXIVE SOLUTIONS | OPTIMAL APPROXIMATION | MATHEMATICS, APPLIED | LEAST-SQUARES SOLUTIONS | Hermitian {P, k+1}-(anti-)reflexive solutions | CONSTRAINT | Algorithms | Approximation | Computer simulation | Least squares method | Mathematical analysis | Norms | Feasibility | Mathematical models

Journal Article

Zeitschrift für angewandte Mathematik und Physik, ISSN 0044-2275, 6/2018, Volume 69, Issue 3, pp. 1 - 20

In this paper we investigate the convergence behavior of the solutions to the time-dependent variational–hemivariational inequalities with respect to the data....

74M10 | Engineering | 49J45 | Mathematical Methods in Physics | 47J20 | Semipermeability problem | 49J40 | 74M15 | Mosco convergence | Theoretical and Applied Mechanics | Pseudomonotone | Variational–hemivariational inequality | MATHEMATICS, APPLIED | Variational-hemivariational inequality | REFLEXIVE BANACH-SPACES | FRICTIONAL CONTACT PROBLEMS

74M10 | Engineering | 49J45 | Mathematical Methods in Physics | 47J20 | Semipermeability problem | 49J40 | 74M15 | Mosco convergence | Theoretical and Applied Mechanics | Pseudomonotone | Variational–hemivariational inequality | MATHEMATICS, APPLIED | Variational-hemivariational inequality | REFLEXIVE BANACH-SPACES | FRICTIONAL CONTACT PROBLEMS

Journal Article

Journal of Computational and Applied Mathematics, ISSN 0377-0427, 2009, Volume 224, Issue 2, pp. 759 - 776

This paper is concerned with weighted least squares solutions to general coupled Sylvester matrix equations. Gradient based iterative algorithms are proposed...

Weighted least squares solutions | Coupled Sylvester matrix equations | Gradient based iterative algorithms | Maximal convergence rate | Weighted generalized inverses | LINEAR-SYSTEMS | MATHEMATICS, APPLIED | ITERATIVE SOLUTIONS | ALGORITHM | LYAPUNOV EQUATIONS | AXB | SYMMETRIC SOLUTION | REFLEXIVE

Weighted least squares solutions | Coupled Sylvester matrix equations | Gradient based iterative algorithms | Maximal convergence rate | Weighted generalized inverses | LINEAR-SYSTEMS | MATHEMATICS, APPLIED | ITERATIVE SOLUTIONS | ALGORITHM | LYAPUNOV EQUATIONS | AXB | SYMMETRIC SOLUTION | REFLEXIVE

Journal Article

Applied Mathematics and Computation, ISSN 0096-3003, 2011, Volume 217, Issue 22, pp. 9286 - 9296

Let H m × n denote the set of all m × n matrices over the quaternion algebra H and P ∈ H m × m , Q ∈ H n × n be involutions. We say that A ∈ H m × n is ( P,...

( P, Q)-skewsymmetric matrix | System of quaternion matrix equations | Moore–Penrose inverse | Maximal rank | ( P, Q)-symmetric matrix | Minimal rank | (P, Q)-skewsymmetric matrix | Moore-Penrose inverse | (P, Q)-symmetric matrix | MATHEMATICS, APPLIED | SINGULAR-VALUE DECOMPOSITION | APPROXIMATION | OUTPUT-FEEDBACK | REAL | REFLEXIVE | REGULARIZATION | PAIR | Algebra | Quaternions | Computation | Mathematical analysis | Images | Mathematical models | Matrices | Matrix methods

( P, Q)-skewsymmetric matrix | System of quaternion matrix equations | Moore–Penrose inverse | Maximal rank | ( P, Q)-symmetric matrix | Minimal rank | (P, Q)-skewsymmetric matrix | Moore-Penrose inverse | (P, Q)-symmetric matrix | MATHEMATICS, APPLIED | SINGULAR-VALUE DECOMPOSITION | APPROXIMATION | OUTPUT-FEEDBACK | REAL | REFLEXIVE | REGULARIZATION | PAIR | Algebra | Quaternions | Computation | Mathematical analysis | Images | Mathematical models | Matrices | Matrix methods

Journal Article

Computers and Mathematics with Applications, ISSN 0898-1221, 04/2017, Volume 73, Issue 8, pp. 1741 - 1759

Let R∈Cm×m and S∈Cn×n be nontrivial k-involutions if their minimal polynomials are both xk−1 for some k≥2, i.e., Rk−1=R−1≠±I and Sk−1=S−1≠±I. We say that...

[formula omitted]-symmetric matrix | Least squares solution | Moore–Penrose inverse | Optimal approximate solution | (R,S,μ)-symmetric matrix | (R,S,α,μ)-symmetric matrix | APPROXIMATION-PROBLEMS | MATHEMATICS, APPLIED | (R,S,mu)-symmetric matrix | (R,S,alpha,mu)-symmetric matrix | GENERALIZED REFLEXIVE MATRICES | BASIC PROPERTIES | PROCRUSTES PROBLEMS | INVERSE EIGENPROBLEMS | LEAST-SQUARES SOLUTIONS | Moore-Penrose inverse | Algorithms

[formula omitted]-symmetric matrix | Least squares solution | Moore–Penrose inverse | Optimal approximate solution | (R,S,μ)-symmetric matrix | (R,S,α,μ)-symmetric matrix | APPROXIMATION-PROBLEMS | MATHEMATICS, APPLIED | (R,S,mu)-symmetric matrix | (R,S,alpha,mu)-symmetric matrix | GENERALIZED REFLEXIVE MATRICES | BASIC PROPERTIES | PROCRUSTES PROBLEMS | INVERSE EIGENPROBLEMS | LEAST-SQUARES SOLUTIONS | Moore-Penrose inverse | Algorithms

Journal Article

Mathematical Methods in the Applied Sciences, ISSN 0170-4214, 07/2019, Volume 42, Issue 10, pp. 3527 - 3548

Analysis and design of linear periodic control systems are closely related to the periodic matrix equations. The objective of this paper is to provide four new...

periodic matrix equations | conjugate gradient normal equation residual (CGNR) method | conjugate gradient normal equation error (CGNE) method | reflexive periodic solution | least‐squares QR‐factorization (LSQR) method | Computer memory | Conjugates | Algorithms | Iterative methods | Control systems design | Matrix methods

periodic matrix equations | conjugate gradient normal equation residual (CGNR) method | conjugate gradient normal equation error (CGNE) method | reflexive periodic solution | least‐squares QR‐factorization (LSQR) method | Computer memory | Conjugates | Algorithms | Iterative methods | Control systems design | Matrix methods

Journal Article

Computers and Mathematics with Applications, ISSN 0898-1221, 06/2018, Volume 75, Issue 11, pp. 4151 - 4178

Analysis and design of linear periodic control systems are closely related to the periodic matrix equations. The conjugate direction (CD) method is a famous...

Periodic matrix equation | Conjugate direction (CD) method | Symmetric periodic solution | LINEAR-SYSTEMS | OPTIMAL APPROXIMATION | MATHEMATICS, APPLIED | LYAPUNOV EQUATIONS | SOLVE | STEPS ITERATION | FINITE ITERATIVE ALGORITHMS | REFLEXIVE SOLUTIONS | ARBITRARY MATRICES | LAPOK | SYLVESTER SYSTEMS | Control systems | Algorithms

Periodic matrix equation | Conjugate direction (CD) method | Symmetric periodic solution | LINEAR-SYSTEMS | OPTIMAL APPROXIMATION | MATHEMATICS, APPLIED | LYAPUNOV EQUATIONS | SOLVE | STEPS ITERATION | FINITE ITERATIVE ALGORITHMS | REFLEXIVE SOLUTIONS | ARBITRARY MATRICES | LAPOK | SYLVESTER SYSTEMS | Control systems | Algorithms

Journal Article

TRANSACTIONS OF THE INSTITUTE OF MEASUREMENT AND CONTROL, ISSN 0142-3312, 02/2020, Volume 42, Issue 3, pp. 503 - 517

The study of linear matrix equations is extremely important in many scientific fields such as control systems and stability analysis. In this work, we aim to...

SYSTEM | FORM | ALGORITHM | ITERATIVE METHOD | SOLVE | LINEAR MATRIX | INVERSE | CGNE algorithm | ANTI-REFLEXIVE SOLUTIONS | BCR | INSTRUMENTS & INSTRUMENTATION | CGNR algorithm | Hestenes-Stiefel | general Sylvester matrix equations | partially doubly symmetric solution | bi-conjugate residual (Bi-CR) algorithm | LEAST-SQUARES SOLUTION | AUTOMATION & CONTROL SYSTEMS | Stability analysis | Control stability | Algorithms | Decision analysis | Matrix methods

SYSTEM | FORM | ALGORITHM | ITERATIVE METHOD | SOLVE | LINEAR MATRIX | INVERSE | CGNE algorithm | ANTI-REFLEXIVE SOLUTIONS | BCR | INSTRUMENTS & INSTRUMENTATION | CGNR algorithm | Hestenes-Stiefel | general Sylvester matrix equations | partially doubly symmetric solution | bi-conjugate residual (Bi-CR) algorithm | LEAST-SQUARES SOLUTION | AUTOMATION & CONTROL SYSTEMS | Stability analysis | Control stability | Algorithms | Decision analysis | Matrix methods

Journal Article

Mathematical and Computer Modelling, ISSN 0895-7177, 2011, Volume 54, Issue 9, pp. 2117 - 2131

In this paper, we proposed an algorithm for solving the linear systems of matrix equations { ∑ i = 1 N A i ( 1 ) X i B i ( 1 ) = C ( 1 ) , ⋮ ∑ i = 1 N A i ( M...

Generalized reflexive matrix | Iterative algorithm | Linear systems of matrix equations | ANTI-REFLEXIVE SOLUTIONS | MATHEMATICS, APPLIED | AXB | Linear systems | Questions and answers | Algorithms

Generalized reflexive matrix | Iterative algorithm | Linear systems of matrix equations | ANTI-REFLEXIVE SOLUTIONS | MATHEMATICS, APPLIED | AXB | Linear systems | Questions and answers | Algorithms

Journal Article

Applied Mathematics and Computation, ISSN 0096-3003, 2008, Volume 202, Issue 2, pp. 571 - 588

The generalized coupled Sylvester matrix equations ( AY - ZB , CY - ZD ) = ( E , F ) with unknown matrices Y , Z are encountered in many systems and control...

The generalized coupled Sylvester matrix equations | Optimal approximation reflexive solution pair | Reflexive matrix | Kronecker matrix product | Generalized reflection matrix | generalized reflection matrix | SYSTEM | MATHEMATICS, APPLIED | REGULAR-RINGS | SYMMETRIC-SOLUTIONS | AXB | IDENTIFICATION | the generalized coupled Sylvester matrix equations | reflexive matrix | optimal approximation reflexive solution pair | Control systems | Algorithms

The generalized coupled Sylvester matrix equations | Optimal approximation reflexive solution pair | Reflexive matrix | Kronecker matrix product | Generalized reflection matrix | generalized reflection matrix | SYSTEM | MATHEMATICS, APPLIED | REGULAR-RINGS | SYMMETRIC-SOLUTIONS | AXB | IDENTIFICATION | the generalized coupled Sylvester matrix equations | reflexive matrix | optimal approximation reflexive solution pair | Control systems | Algorithms

Journal Article

Applied Mathematics and Computation, ISSN 0096-3003, 2008, Volume 195, Issue 2, pp. 721 - 732

An n × n quaternion matrix A is termed P-symmetric (or P-skewsymmetric) if A = PAP (or A = − PAP), where P is an n × n nontrivial quaternion involution. In...

P-symmetric matrix | Quaternion matrix | Moore–Penrose inverse | P-skewsymmetric matrix | System of matrix equations | Moore-Penrose inverse | GENERALIZED SYMMETRY | MATHEMATICS, APPLIED | REGULAR-RINGS | RANKS | system of matrix equations | AXB | SKEW SYMMETRY | ANTI-REFLEXIVE SOLUTIONS | EIGENVALUES | EIGENVECTORS | quaternion matrix | CENTROSYMMETRIC MATRICES | SYSTEMS

P-symmetric matrix | Quaternion matrix | Moore–Penrose inverse | P-skewsymmetric matrix | System of matrix equations | Moore-Penrose inverse | GENERALIZED SYMMETRY | MATHEMATICS, APPLIED | REGULAR-RINGS | RANKS | system of matrix equations | AXB | SKEW SYMMETRY | ANTI-REFLEXIVE SOLUTIONS | EIGENVALUES | EIGENVECTORS | quaternion matrix | CENTROSYMMETRIC MATRICES | SYSTEMS

Journal Article

Engineering Computations, ISSN 0264-4401, 07/2012, Volume 29, Issue 5, pp. 528 - 560

Purpose - The purpose of this paper is to find two iterative methods to solve the general coupled matrix equations over the generalized centro-symmetric and...

The general coupled matrix equations | Mathematics | Optimal approximation generalized centro-symmetric solution group | Generalized centro-symmetric solution group | Iterative methods | SYLVESTER EQUATIONS | EIGENVALUE PROBLEMS | COMMON SOLUTION | REGULAR-RINGS | LEAST-SQUARES SOLUTIONS | AXB | NONSYMMETRIC LINEAR-SYSTEMS | IDENTIFICATION | REFLEXIVE SOLUTIONS | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | ENGINEERING, MULTIDISCIPLINARY | PAIR | Studies | Operations research | Algorithms | Matrix | Principal components analysis | Libraries | Computational mathematics | Control theory | System theory | Approximation | Mathematical analysis | Norms | Iterative algorithms | Mathematical models | Matrices | Matrix methods

The general coupled matrix equations | Mathematics | Optimal approximation generalized centro-symmetric solution group | Generalized centro-symmetric solution group | Iterative methods | SYLVESTER EQUATIONS | EIGENVALUE PROBLEMS | COMMON SOLUTION | REGULAR-RINGS | LEAST-SQUARES SOLUTIONS | AXB | NONSYMMETRIC LINEAR-SYSTEMS | IDENTIFICATION | REFLEXIVE SOLUTIONS | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | ENGINEERING, MULTIDISCIPLINARY | PAIR | Studies | Operations research | Algorithms | Matrix | Principal components analysis | Libraries | Computational mathematics | Control theory | System theory | Approximation | Mathematical analysis | Norms | Iterative algorithms | Mathematical models | Matrices | Matrix methods

Journal Article

Transactions of the Institute of Measurement and Control, ISSN 0142-3312, 2018, Volume 41, Issue 4, pp. 1139 - 1148

In this paper, we present an iterative algorithm to solve a generalized coupled Sylvester - conjugate matrix equations over Hamiltonian matrices. When the...

Hamiltonian solutions | Coupled Sylvester – conjugate matrix equation | inner product | iterative algorithm | Frobenius norm | INSTRUMENTS & INSTRUMENTATION | SYMMETRIC-SOLUTIONS | REFLEXIVE | ALGORITHMS | Coupled Sylvester - conjugate matrix equation | AUTOMATION & CONTROL SYSTEMS | PAIR | Conjugates | Iterative algorithms | Matrix | Iterative methods | Roundoff error

Hamiltonian solutions | Coupled Sylvester – conjugate matrix equation | inner product | iterative algorithm | Frobenius norm | INSTRUMENTS & INSTRUMENTATION | SYMMETRIC-SOLUTIONS | REFLEXIVE | ALGORITHMS | Coupled Sylvester - conjugate matrix equation | AUTOMATION & CONTROL SYSTEMS | PAIR | Conjugates | Iterative algorithms | Matrix | Iterative methods | Roundoff error

Journal Article

Linear Algebra and Its Applications, ISSN 0024-3795, 2010, Volume 432, Issue 6, pp. 1531 - 1552

In the present paper, by extending the idea of conjugate gradient (CG) method, we construct an iterative method to solve the general coupled matrix equations ∑...

Generalized bisymmetric matrix | Least Frobenius norm solution group | Iterative method | General coupled matrix equations | Optimal approximation generalized bisymmetric solution group | OPTIMAL APPROXIMATION | MATHEMATICS, APPLIED | bisymmetric solution group | SYLVESTER EQUATIONS | REGULAR-RINGS | EFFICIENT ITERATIVE METHOD | SYMMETRIC-SOLUTIONS | LEAST-SQUARES SOLUTIONS | IDENTIFICATION | General Coupled matrix equations | REFLEXIVE SOLUTIONS | Optimal approximation generalized | SYSTEMS

Generalized bisymmetric matrix | Least Frobenius norm solution group | Iterative method | General coupled matrix equations | Optimal approximation generalized bisymmetric solution group | OPTIMAL APPROXIMATION | MATHEMATICS, APPLIED | bisymmetric solution group | SYLVESTER EQUATIONS | REGULAR-RINGS | EFFICIENT ITERATIVE METHOD | SYMMETRIC-SOLUTIONS | LEAST-SQUARES SOLUTIONS | IDENTIFICATION | General Coupled matrix equations | REFLEXIVE SOLUTIONS | Optimal approximation generalized | SYSTEMS

Journal Article

Computers and Mathematics with Applications, ISSN 0898-1221, 03/2017, Volume 73, Issue 5, pp. 747 - 764

In this study, we consider the iteration solutions of the generalized Sylvester-conjugate matrix equation: AXB+CX¯D=E by a modified conjugate gradient method....

Hamiltonian matrix | Modified conjugate gradient method | Minimum-norm solution | Generalized Sylvester-conjugate matrix equation | MATHEMATICS, APPLIED | RIGHT-HAND SIDES | APPROXIMATION | ITERATIVE METHOD | SYMMETRIC-SOLUTIONS | LEAST-SQUARES SOLUTIONS | LINEAR MATRIX | IDENTIFICATION | REFLEXIVE MATRICES | SYSTEMS | Algorithms

Hamiltonian matrix | Modified conjugate gradient method | Minimum-norm solution | Generalized Sylvester-conjugate matrix equation | MATHEMATICS, APPLIED | RIGHT-HAND SIDES | APPROXIMATION | ITERATIVE METHOD | SYMMETRIC-SOLUTIONS | LEAST-SQUARES SOLUTIONS | LINEAR MATRIX | IDENTIFICATION | REFLEXIVE MATRICES | SYSTEMS | Algorithms

Journal Article

Applied Mathematics and Computation, ISSN 0096-3003, 2009, Volume 209, Issue 2, pp. 254 - 258

An n × n complex matrix P is said to be a generalized reflection matrix if P H = P and P 2 = I . An n × n complex matrix A is said to be a ( P , Q )...

[formula omitted] generalized anti-reflexive matrix | Matrix nearness problem | [formula omitted] generalized reflexive matrix | Matrix equation | (P, Q) generalized reflexive matrix | (P, Q) generalized anti-reflexive matrix | MATHEMATICS, APPLIED | Questions and answers

[formula omitted] generalized anti-reflexive matrix | Matrix nearness problem | [formula omitted] generalized reflexive matrix | Matrix equation | (P, Q) generalized reflexive matrix | (P, Q) generalized anti-reflexive matrix | MATHEMATICS, APPLIED | Questions and answers

Journal Article

17.
Full Text
On the generalized reflexive and anti-reflexive solutions to a system of matrix equations

Linear Algebra and Its Applications, ISSN 0024-3795, 12/2012, Volume 437, Issue 11, pp. 2793 - 2812

Let P and Q be two generalized reflection matrices, i.e, P=PH, P2=I and Q=QH, Q2=I. An n×n matrix A is said to be generalized reflexive (generalized...

Generalized reflexive matrix | Iterative algorithm | Generalized anti-reflexive matrix | System of matrix equations | MATHEMATICS | MATHEMATICS, APPLIED | ITERATIVE SOLUTIONS | APPROXIMATION | SYMMETRIC-SOLUTIONS | LEAST-SQUARES SOLUTIONS | ALGORITHMS | IDENTIFICATION | Questions and answers | Algorithms | Universities and colleges

Generalized reflexive matrix | Iterative algorithm | Generalized anti-reflexive matrix | System of matrix equations | MATHEMATICS | MATHEMATICS, APPLIED | ITERATIVE SOLUTIONS | APPROXIMATION | SYMMETRIC-SOLUTIONS | LEAST-SQUARES SOLUTIONS | ALGORITHMS | IDENTIFICATION | Questions and answers | Algorithms | Universities and colleges

Journal Article

Linear and Multilinear Algebra, ISSN 0308-1087, 06/2016, Volume 64, Issue 6, pp. 1207 - 1219

In this paper, we consider the reverse order law for -inverses of matrices and we do that taking two completely different approaches. The paper is an...

generalized inverse | inverses | index theorem | 47A05 | 15A09 | reverse order law | MULTIPLE MATRIX PRODUCTS | C-ASTERISK-ALGEBRAS | RINGS | (1,2,4)-INVERSES | MATHEMATICS | REFLEXIVE GENERALIZED INVERSE | OPERATORS | Ghosts | Illustrations | Theorems | Algebra | Theorem proving | Images | Paper | Banach space

generalized inverse | inverses | index theorem | 47A05 | 15A09 | reverse order law | MULTIPLE MATRIX PRODUCTS | C-ASTERISK-ALGEBRAS | RINGS | (1,2,4)-INVERSES | MATHEMATICS | REFLEXIVE GENERALIZED INVERSE | OPERATORS | Ghosts | Illustrations | Theorems | Algebra | Theorem proving | Images | Paper | Banach space

Journal Article