Best Approximate Solution of Matrix Equation AXB+CYD=E
From MaRDI portal
Publication:5470485
DOI10.1137/040615791zbMath1096.15004OpenAlexW2023686904MaRDI QIDQ5470485
Yuan Lei, Zhong Zhi Bai, An-Ping Liao
Publication date: 31 May 2006
Published in: SIAM Journal on Matrix Analysis and Applications (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1137/040615791
matrix equationgeneralized singular value decompositionbest approximate solutionleast-squares solutioncanonical correlation decomposition
Numerical solutions to overdetermined systems, pseudoinverses (65F20) Ill-posedness and regularization problems in numerical linear algebra (65F22) Matrix equations and identities (15A24)
Related Items
The iterative algorithm for solving a class of generalized coupled Sylvester-transpose equations over centrosymmetric or anti-centrosymmetric matrix ⋮ Application of the alternating direction method for an inverse monic quadratic eigenvalue problem ⋮ A preconditioned nested splitting conjugate gradient iterative method for the large sparse generalized Sylvester equation ⋮ On solutions of the matrix equation \(AX=B\) with respect to semi-tensor product ⋮ A minimal residual algorithm for the inconsistent matrix equation \(AXB = C\) over symmetric matrices ⋮ Nested splitting conjugate gradient method for matrix equation \(AXB=C\) and preconditioning ⋮ Symmetric solutions of the coupled generalized Sylvester matrix equations via BCR algorithm ⋮ The least squares anti-bisymmetric solution and the optimal approximation solution for Sylvester equation ⋮ Determinantal representations of general and (skew-)Hermitian solutions to the generalized Sylvester-type quaternion matrix equation ⋮ On the Kaczmarz methods based on relaxed greedy selection for solving matrix equation \(A X B = C\) ⋮ An iterative method for the symmetric and skew symmetric solutions of a linear matrix equation \(AXB+CYD=E\) ⋮ Alternating direction method for generalized Sylvester matrix equation \(AXB + CYD = E\) ⋮ On Symmetric and Skew-Symmetric Solutions to a Procrustes Problem ⋮ Generalized conjugate direction algorithm for solving the general coupled matrix equations over symmetric matrices ⋮ An iterative algorithm for the least Frobenius norm Hermitian and generalized skew Hamiltonian solutions of the generalized coupled Sylvester-conjugate matrix equations ⋮ A matrix CRS iterative method for solving a class of coupled Sylvester-transpose matrix equations ⋮ The MGPBiCG method for solving the generalized coupled Sylvester-conjugate matrix equations ⋮ Least-squares symmetric and skew-symmetric solutions of the generalized Sylvester matrix equation \(\sum_{i = 1}^s A_i X B_i + \sum_{j = 1}^t C_j Y D_j = E\) ⋮ Numerical algorithms for solving the least squares symmetric problem of matrix equation AXB + CXD = E ⋮ A note on the solvability for generalized Sylvester equations ⋮ The least-squares solution with the least norm to a system of tensor equations over the quaternion algebra ⋮ The least squares problem of the matrix equation \(A_1X_1B^T_1+A_2X_2B^T_2=T\) ⋮ The reflexive least squares solutions of the matrix equation \(A_1X_1B_1+A_2X_2B_2+\cdots +A_lX_lB_l=C\) with a submatrix constraint ⋮ Least squares η-bi-Hermitian problems of the quaternion matrix equation (AXB,CXD) = (E,F) ⋮ An efficient algorithm for the submatrix constraint of the matrix equationA1X1B1+A2X2B2+···+AlXlBl=C ⋮ On Hermitian solutions of the split quaternion matrix equation \(AXB+CXD=E\) ⋮ Submatrix constrained least-squares inverse problem for symmetric matrices from the design of vibrating structures ⋮ The solution of a generalized Sylvester quaternion matrix equation and its application ⋮ On the minimum-norm least squares solution of the complex generalized coupled Sylvester matrix equations ⋮ Optimal matrix pencil approximation problem in structural dynamic model updating ⋮ Direct methods onη‐Hermitian solutions of the split quaternion matrix equation (AXB,CXD)=(E,F) ⋮ Alternating direction method for structure-persevering finite element model updating problem ⋮ Further results on Moore-Penrose inverses of tensors with application to tensor nearness problems ⋮ On the least squares generalized Hamiltonian solution of generalized coupled Sylvester-conjugate matrix equations ⋮ Factorization of Generalized Theta Functions Revisited ⋮ Preconditioned Positive-Definite and Skew-Hermitian Splitting Iteration Methods for Continuous Sylvester Equations AX + XB = C ⋮ Two kinds of condition numbers for the quadratic matrix equation ⋮ Matrix equation \(AXB=E\) with \(PX=sXP\) constraint ⋮ A generalization of the Hermitian and skew-Hermitian splitting iteration method for solving Sylvester equations ⋮ A system of matrix equations with five variables ⋮ Gradient-based iterative algorithms for generalized coupled Sylvester-conjugate matrix equations ⋮ The inverse eigenvalue problem of structured matrices from the design of Hopfield neural networks ⋮ A system of generalized Sylvester quaternion matrix equations and its applications ⋮ The accelerated gradient based iterative algorithm for solving a class of generalized Sylvester-transpose matrix equation ⋮ Weighted steepest descent method for solving matrix equations ⋮ Least squares solutions of the matrix equation \(AXB+CYD=E\) with the least norm for symmetric arrowhead matrices ⋮ Cramer's rules for Sylvester quaternion matrix equation and its special cases ⋮ Lopsided DSS iteration method for solving complex Sylvester matrix equation ⋮ An iterative algorithm for generalized Hamiltonian solution of a class of generalized coupled Sylvester-conjugate matrix equations ⋮ Iterative methods for solving linear matrix equation and linear matrix system ⋮ The matrix pencil nearness problem in structural dynamic model updating ⋮ The matrix nearness problem associated with the quaternion matrix equation \(AXA^H+BYB^H=C\) ⋮ Analytical best approximate Hermitian and generalized skew-Hamiltonian solution of matrix equation \(AXA^{\mathrm{H}}+CYC^{\mathrm{H}}=F\) ⋮ An iterative algorithm for the least Frobenius norm least squares solution of a class of generalized coupled Sylvester-transpose linear matrix equations ⋮ General Solutions for a Class of Inverse Quadratic Eigenvalue Problems ⋮ Inverse problems for \((R,S)\)-symmetric matrices in structural dynamic model updating ⋮ The right–left preconditioning technique for the solution of the large matrix equationAXB = C ⋮ A generalized modified Hermitian and skew-Hermitian splitting (GMHSS) method for solving complex Sylvester matrix equation ⋮ A note on the iterative solutions of general coupled matrix equation ⋮ Cramer's rule for the general solution to a restricted system of quaternion matrix equations ⋮ Least squares Hermitian solution of the complex matrix equation \(AXB+CXD=E\) with the least norm ⋮ L-structured quaternion matrices and quaternion linear matrix equations ⋮ Reducible solution to a quaternion tensor equation ⋮ The least square solution with the least norm to a system of quaternion matrix equations ⋮ Perturbation analysis for the matrix least squares problem \(A X B = C\) ⋮ Ranks of submatrices in (skew-)Hermitian solutions to a quaternion matrix equation ⋮ A computational framework of gradient flows for general linear matrix equations ⋮ Two-sided coupled generalized Sylvester matrix equations solving using a simultaneous decomposition for fifteen matrices ⋮ Structured condition number for multiple right-hand side linear systems with parameterized quasiseparable coefficient matrix ⋮ On Hermitian solutions of the reduced biquaternion matrix equation (AXB,CXD) = (E,G) ⋮ Special least squares solutions of the reduced biquaternion matrix equation \(AX=B\) with applications ⋮ Least-squares solution with the minimum-norm for the matrix equation \(A^T XB + B^T X^T A = D\) and its applications ⋮ The double-step scale splitting method for solving complex Sylvester matrix equation ⋮ A system of real quaternion matrix equations with applications ⋮ The submatrix constraint problem of matrix equation \(AXB+CYD=E\) ⋮ Least-squares problem for the quaternion matrix equationAXB+CYD=Eover different constrained matrices ⋮ Computing symmetric solutions of general Sylvester matrix equations via Lanczos version of biconjugate residual algorithm ⋮ Cramer's rule for a system of quaternion matrix equations with applications ⋮ Nonnegative definite and re-nonnegative definite solutions to a system of matrix equations with statistical applications ⋮ The symmetric solution of the matrix equation \(AXB=D\) on subspace ⋮ Matrix form of the CGS method for solving general coupled matrix equations ⋮ A System of Matrix Equations over the Quaternion Algebra with Applications ⋮ On preconditioned normal and skew-Hermitian splitting iteration method for continuous Sylvester equations AX + XB = C*
This page was built for publication: Best Approximate Solution of Matrix Equation AXB+CYD=E