Least-squares solution for inverse eigenpair problem of nonnegative definite matrices

Xie, Dongxiu

doi:10.1016/s0898-1221(00)00235-2

Cited by 12 publications

(8 citation statements)

References 10 publications

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“…Some results of the matrix inverse problem for bi-symmetric matrices have been obtained by using the Moore-Penrose generalized inverse and the singular value decomposition (SVD) [19][20][21][22]. In addition, the matrix inverse problem for bi-symmetric matrices with a submatrix constraint has been discussed in [23] and the solvability conditions as well as its general solution have been derived by using the generalized singular value decomposition (GSVD).…”

Section: Introductionmentioning

confidence: 99%

Least‐squares solutions of matrix inverse problem for bi‐symmetric matrices with a submatrix constraint

Liao

Yuan

2007

Numerical Linear Algebra App

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SUMMARYAn n × n real matrix A = (a i j ) n × n is called bi-symmetric matrix if A is both symmetric and per-symmetric, that is, a i j = a ji and a i j = a n+1− j,n+1−i (i, j = 1, 2, . . . , n). This paper is mainly concerned with finding the least-squares bi-symmetric solutions of matrix inverse problem AX = B with a submatrix constraint, where X and B are given matrices of suitable sizes. Moreover, in the corresponding solution set, the analytical expression of the optimal approximation solution to a given matrix A * is derived. A direct method for finding the optimal approximation solution is described in detail, and three numerical examples are provided to show the validity of our algorithm.

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Section: Introductionmentioning

confidence: 99%

Least‐squares solutions of matrix inverse problem for bi‐symmetric matrices with a submatrix constraint

Liao

Yuan

2007

Numerical Linear Algebra App

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“…Let H q be a BS solution of equation (10). Then for any starting BS matrix H q0 , we have From Newton's method and the above theorem, we easily prove the following main theorem.…”

Section: An Iterative Methods For Finding the Bs Solution Of Equationmentioning

confidence: 92%

“…Let H q be a symmetric solution of equation (10). Then for any starting symmetric matrix H q0 , we have…”

Section: An Iterative Methods For Solving (10)mentioning

confidence: 99%

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Newton's Method for Symmetric and Bisymmetric Solvents of the Nonlinear Matrix Equations

Han¹,

Kim²

2013

Journal of the Korean Mathematical Society

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Abstract. One of the interesting nonlinear matrix equations is the quadratic matrix equation defined bywhere X is a n × n unknown real matrix, and A, B and C are n × n given matrices with real elements. Another one is the matrix polynomialNewton's method is used to find the symmetric and bisymmetric solvents of the nonlinear matrix equations Q(X) and P (X). The method does not depend on the singularity of the Fréchet derivative. Finally, we give some numerical examples.

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“…. , n), in R n×n , a new inner product is defined as follows: , then K is a closed convex cone and the following result holds; the proof is similar to that of Lemma 2.7 in [21] (see also [24] …”

Section: ) For Anymentioning

confidence: 99%

Least Squares Solution of BXA^T=T over Symmetric, Skew-Symmetric, and Positive Semidefinite X

Deng¹,

Hu²,

Zhang³

2003

SIAM J. Matrix Anal. & Appl.

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Abstract. An efficient method based on the quotient singular value decomposition (QSVD) is used to solve the constrained least squares problem min T − BXA T F over symmetric, skewsymmetric, and positive semidefinite (maybe asymmetrical) X. The general expression of the solution is given and some necessary and sufficient conditions are derived about the solvability of the matrix equation BXA T = T . In each case, an algorithm is given for the unique solution when B and A are of full column rank.

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Least-squares solution for inverse eigenpair problem of nonnegative definite matrices

Cited by 12 publications

References 10 publications

Least‐squares solutions of matrix inverse problem for bi‐symmetric matrices with a submatrix constraint

Least‐squares solutions of matrix inverse problem for bi‐symmetric matrices with a submatrix constraint

Newton's Method for Symmetric and Bisymmetric Solvents of the Nonlinear Matrix Equations

Least Squares Solution of BXA^T=T over Symmetric, Skew-Symmetric, and Positive Semidefinite X

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Least-squares solution for inverse eigenpair problem of nonnegative definite matrices

Cited by 12 publications

References 10 publications

Least‐squares solutions of matrix inverse problem for bi‐symmetric matrices with a submatrix constraint

Least‐squares solutions of matrix inverse problem for bi‐symmetric matrices with a submatrix constraint

Newton's Method for Symmetric and Bisymmetric Solvents of the Nonlinear Matrix Equations

Least Squares Solution of BXAT=T over Symmetric, Skew-Symmetric, and Positive Semidefinite X

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Least Squares Solution of BXA^T=T over Symmetric, Skew-Symmetric, and Positive Semidefinite X