A low-complexity algorithm to search for Legendre pairs

Authors: Sirani M. Perera, Ilias S. Kotsireas

Source: Linear Algebra and its Applications. 721:149-171

Subject Terms: Eigenvalues, singular values, and eigenvectors, fast Fourier transforms, matrix equations, Legendre pairs, sparse and orthogonal factors, Numerical methods for matrix equations, Matrix equations and identities, structured matrices, matrix analysis, complexity and performance of algorithms, Boolean and Hadamard matrices, Numerical methods for discrete and fast Fourier transforms, Combinatorial aspects of matrices (incidence, Hadamard, etc.)

File Description: application/xml

Access URL: https://zbmath.org/8057084
https://doi.org/10.1016/j.laa.2025.01.010

An inexact Matrix-Newton method for solving NEPv: An inexact matrix-Newton method for solving NEPv

Authors: Tom Werner

Source: Linear Algebra and its Applications. 721:366-398

Subject Terms: Nonlinear spectral theory, nonlinear eigenvalue problems, global GMRES, Numerical Analysis (math.NA), 01 natural sciences, Implicit function theorems, global Newton methods on manifolds, Newton's method, Numerical methods for matrix equations, matrix function, nonlinear eigenvalue problem, FOS: Mathematics, Spectral theory, eigenvalue problems on manifolds, Mathematics - Numerical Analysis, 0101 mathematics, self-consistent-field iteration

File Description: application/xml

Access URL: http://arxiv.org/abs/2311.09670
https://zbmath.org/8057093
https://doi.org/10.1016/j.laa.2024.11.003

Randomized Iterative Methods for Generalized Absolute Value Equations: Solvability and Error Bounds: Randomized iterative methods for generalized absolute value equations: solvability and error bounds

Authors: Jiaxin Xie, Hou-Duo Qi, Deren Han

Source: SIAM Journal on Optimization. 35:1731-1760

Subject Terms: Iterative numerical methods for linear systems, convergence rate, Numerical methods for matrix equations, error bound, Matrix equations and identities, stochastic methods, FOS: Mathematics, absolute value equations, Mathematics - Numerical Analysis, Numerical Analysis (math.NA), solvability, Kaczmarz method

File Description: application/xml

Access URL: http://arxiv.org/abs/2405.04091

Numerical Solutions for Stochastic Continuous-Time Algebraic Riccati Equations: Numerical solutions for stochastic continuous-time algebraic Riccati equations

Authors: Tsung-Ming Huang, Yueh-Cheng Kuo, Ren-Cang Li, Wen-Wei Lin

Source: SIAM Journal on Matrix Analysis and Applications. 46:1675-1700

Subject Terms: matrix Riccati equation, 05 social sciences, Matrix equations and identities, doubling algorithm, 01 natural sciences, 0506 political science, Newton's method, Optimization and Control (math.OC), Numerical methods for matrix equations, stochastic state-dependent linear control, FOS: Mathematics, fixed-point iteration, 0101 mathematics, Mathematics - Optimization and Control

File Description: application/xml

Access URL: http://arxiv.org/abs/2401.11774
https://zbmath.org/8071661
https://doi.org/10.1137/24m1635156

Discrete gradient-zeroing neural network algorithm for solving future Sylvester equation aided with left–right four-step rule as well as robot arm inverse kinematics: Discrete gradient-zeroing neural network algorithm for solving future Sylvester equation aided with left-right four-step rule as well as robot arm inverse kinematics

Authors: Pengfei Guo, Yunong Zhang, Zheng-an Yao

Source: Mathematics and Computers in Simulation. 233:475-501

Subject Terms: temporal-variant Sylvester equation, left and right four-step rule, future Sylvester equation, Numerical methods for matrix equations, robot arm inverse kinematics, Matrix equations and identities, discrete gradient-zeroing neural network, Kinematics of mechanisms and robots, Artificial neural networks and deep learning

File Description: application/xml

Gradient descent-based parameter-free methods for solving coupled matrix equations and studying an application in dynamical systems

Authors: Akbar Shirilord, Mehdi Dehghan

Source: Applied Numerical Mathematics. 212:29-59

Subject Terms: Numerical optimization and variational techniques, iterative method, Numerical methods for matrix equations, Matrix equations and identities, time-varying linear system, discrete-time antilinear systems, coupled matrix equation, parameter-free method, dynamical systems, hierarchical identification principle, gradient descent method, momentum technique, control theory

File Description: application/xml

Access URL: https://zbmath.org/8018677
https://doi.org/10.1016/j.apnum.2025.01.011

Preconditioned Low-Rank Riemannian Optimization for Symmetric Positive Definite Linear Matrix Equations: Preconditioned low-rank Riemannian optimization for symmetric positive definite linear matrix equations

Authors: Ivan Bioli, Daniel Kressner, Leonardo Robol

Source: SIAM Journal on Scientific Computing. 47:A1091-A1116

Subject Terms: Numerical optimization and variational techniques, Numerical methods for low-rank matrix approximation, matrix compression, Numerical Analysis (math.NA), Riemannian optimization, Nonconvex programming, global optimization, low-rank, Numerical methods for matrix equations, 65F45, 65F55, 65F08, 65K10, 90C26, linear matrix equations, large scale, FOS: Mathematics, metric preconditioning, Preconditioners for iterative methods, Mathematics - Numerical Analysis

File Description: application/xml

Access URL: http://arxiv.org/abs/2408.16416

A hybrid Newton’s method for solving tensor square root problem: A hybrid Newton's method for solving tensor square root problem

Authors: Lixia Liu, Yongjuan Gao, Xuefeng Duan, Chunfeng Wang, Sanyang Liu

Source: Journal of Applied Mathematics and Computing. 71:4875-4895

Subject Terms: Numerical solution of nonlinear eigenvalue and eigenvector problems, global convergence, Newton's method, Einstein product, Numerical methods for matrix equations, Numerical computation of solutions to systems of equations, local quadratic convergence, tensor square root

File Description: application/xml

Efficient computation of Wiener-Hopf factorization of Markov-modulated Brownian motion

Authors: Changli Liu, Jungong Xue

Source: Mathematics of Computation. 94:2367-2408

Subject Terms: Markov-modulated Brownian motion, Factorization theory (including Wiener-Hopf and spectral factorizations) of linear operators, Numerical methods for matrix equations, Matrix equations and identities, doubling algorithm, Brownian motion, M-matrix, algebraic Riccati equation

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A general alternating-direction implicit Newton method for solving continuous-time algebraic Riccati equation

Authors: Kai Jiang, Shifeng Li, Juan Zhang

Source: Applied Numerical Mathematics. 207:642-656

Subject Terms: general alternating-direction implicit method, Numerical optimization and variational techniques, Newton method, Numerical methods for matrix equations, Matrix equations and identities, Newton-type methods, complex algebraic Riccati equation, convergence analysis

File Description: application/xml

Access URL: https://zbmath.org/7952209
https://doi.org/10.1016/j.apnum.2024.09.029

Solving Matrix Polynomial Equations: Solving matrix polynomial equations

Authors: Nedashkovskyy, M.

Source: Cybernetics and Systems Analysis. 61:596-611

Subject Terms: Numerical methods for matrix equations, Matrix equations and identities, matrix polynomial equations, branched continued fractions with matrix elements, convergence to solution

File Description: application/xml

ITERATIVE ALGORITHMS FOR THE GENERALIZED DISCRETE-TIME PERIODIC SYLVESTER TRANSPOSE MATRIX EQUATIONS WITH APPLICATION IN THE PERIODIC STATE OBSERVER DESIGN OF LINEAR SYSTEMS: Iterative algorithms for the generalized discrete-time periodic Sylvester transpose matrix equations with application in the periodic state observer design of linear systems

Authors: Qi, Rui, Song, Caiqin

Source: Journal of Applied Analysis & Computation. 15:286-315

Subject Terms: iterative algorithm, iterative solutions, convergence performance, Numerical methods for matrix equations, Matrix equations and identities, generalized discrete-time periodic Sylvester transpose matrix equations

File Description: application/xml

Solving the generalized Sylvester equation with a novel fast extended neurodynamics

Authors: Gerontitis, Dimitrios, Tzekis, Panagiotis

Source: Numerical Algebra, Control and Optimization. 15:619-644

Subject Terms: zeroing neural network, linear algebra, Numerical methods for matrix equations, Matrix equations and identities, Lyapunov candidate, activation function, predefined convergence, control theory

File Description: application/xml

Truncated LSQR for matrix least squares problems

Authors: Piccinini, Lorenzo, Simoncini, Valeria

Source: Computational Optimization and Applications. 91:905-932

Subject Terms: Kronecker products, rank truncation, Dictionary learning, Large matrices, Matrix least squares, Rank truncation, Numerical methods for matrix equations, Numerical methods for low-rank matrix approximation, matrix compression, matrix least squares, dictionary learning, Factorization of matrices, large matrices

File Description: application/xml; application/pdf

Access URL: https://zbmath.org/8054646
https://doi.org/10.1007/s10589-024-00629-w
https://link.springer.com/article/10.1007/s10589-024-00629-w
https://hdl.handle.net/11585/1009753
https://doi.org/10.1007/s10589-024-00629-w

Hermitian solution to constraint system of generalized Sylvester quaternion matrix equations

Authors: Abdur Rehman, Ivan Kyrchei

Source: Arabian Journal of Mathematics. 13:595-610

Subject Terms: Applications of generalized inverses, Numerical methods for matrix equations, Sylvester quaternion matrix equations, Matrix equations and identities, Theory of matrix inversion and generalized inverses, quaternion Moore-Penrose inverse

File Description: application/xml

Access URL: https://zbmath.org/7969977
https://doi.org/10.1007/s40065-024-00477-w

On certain classes of nonlinear matrix equations: theory, applications, and numerical solution

Authors: Beatrice Meini

Source: Bollettino dell'Unione Matematica Italiana. 18:293-309

Subject Terms: nonlinear matrix equation, Nonlinear matrix equation, Polynomial matrix equation, Algebraic Riccati equation, Iterative method, iterative method, Numerical methods for matrix equations, Matrix equations and identities, algebraic Riccati equation, polynomial matrix equation

File Description: application/xml

Low-Rank Plus Diagonal Approximations for Riccati-Like Matrix Differential Equations: Low-rank plus diagonal approximations for Riccati-like matrix differential equations

Authors: Bonnabel, Silvère, Lambert, Marc, Bach, Francis

Contributors: Lambert, Marc, Centre de Robotique (CAOR), Mines Paris - PSL (École nationale supérieure des mines de Paris), Université Paris Sciences et Lettres (PSL)-Université Paris Sciences et Lettres (PSL), Délégation générale de l'armement (DGA), Ministère de la Défense, Statistical Machine Learning and Parsimony (SIERRA), Département d'informatique - ENS-PSL (DI-ENS), École normale supérieure - Paris (ENS-PSL), Université Paris Sciences et Lettres (PSL)-Université Paris Sciences et Lettres (PSL)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS-PSL), Université Paris Sciences et Lettres (PSL)-Université Paris Sciences et Lettres (PSL)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Centre National de la Recherche Scientifique (CNRS)-Centre Inria de Paris, Institut National de Recherche en Informatique et en Automatique (Inria), Laboratoire d'informatique de l'école normale supérieure (LIENS), Université Paris Sciences et Lettres (PSL)-Université Paris Sciences et Lettres (PSL)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS), ANR-19-P3IA-0001,PRAIRIE,PaRis Artificial Intelligence Research InstitutE(2019), European Project: 724063,ERC-2016-COG,SEQUOIA(2017)

Source: SIAM Journal on Matrix Analysis and Applications. 45:1669-1688

Subject Terms: [INFO.INFO-AI] Computer Science [cs]/Artificial Intelligence [cs.AI], low-rank approximation, matrix manifolds, Gaussian variational inference, high dimension, Numerical methods for low-rank matrix approximation, matrix compression, Numerical Analysis (math.NA), Low-rank approximation, High dimension, [INFO.INFO-AI]Computer Science [cs]/Artificial Intelligence [cs.AI], Riccati equation, matrix differential equation, [INFO.INFO-AU]Computer Science [cs]/Automatic Control Engineering, Matrix differential equation, Numerical methods for matrix equations, FOS: Mathematics, Kalman filter, Mathematics - Numerical Analysis, Matrix manifolds, [INFO.INFO-AU] Computer Science [cs]/Automatic Control Engineering

File Description: application/xml; application/pdf

Access URL: http://arxiv.org/abs/2407.03373
https://zbmath.org/7931224
https://doi.org/10.1137/23m1587610
https://inria.hal.science/hal-04621158v1
https://inria.hal.science/hal-04621158v1/document
https://doi.org/10.1137/23m1587610

Finding Complex-Valued Solutions of Brent Equations Using Nonlinear Least Squares: Finding complex-valued solutions of Brent equations using nonlinear least squares

Authors: Kaporin, I. E.

Source: Computational Mathematics and Mathematical Physics. 64:1881-1891

Subject Terms: nonlinear least squares problem, Numerical linear algebra, Multilinear algebra, tensor calculus, Numerical methods for matrix equations, Matrix equations and identities, fast matrix multiplication, Brent equations, Strassen algorithm

File Description: application/xml

Access URL: https://zbmath.org/7942540
https://doi.org/10.1134/s0965542524701021

QMGI algorithm for solving quaternion equation and its application in color image encryption

Authors: Xinying Li, Caiqin Song, Hongjun Liu

Source: Numerical Algorithms. 99:1429-1462

Subject Terms: pure imaginary solution, Numerical aspects of computer graphics, image analysis, and computational geometry, quaternion modified gradient based algorithm, Numerical methods for matrix equations, Matrix equations and identities, real representation, least squares solution

File Description: application/xml

Access URL: https://zbmath.org/8060150
https://doi.org/10.1007/s11075-024-01920-x

Four extremal solutions of discrete-time algebraic Riccati equations: existence theorems and computation

Authors: Chiang, Chun-Yueh, Fan, Hung-Yuan

Source: Japan Journal of Industrial and Applied Mathematics. 41:1593-1627

Subject Terms: extremal solutions, Matrix and operator functional equations, Linear systems in control theory, antistabilizing solution, Numerical methods for matrix equations, Matrix equations and identities, accelerated fixed-point iteration, discrete-time algebraic Riccati equation, semigroup property, stabilizing solution, Linear optimal control problems

File Description: application/xml

Access URL: https://zbmath.org/7922759
https://doi.org/10.1007/s13160-024-00663-5