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Perturbation analysis of the matrix equation X=Q+AH(X−C)−1A

✍ Scribed by Ji-guang Sun

Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
160 KB
Volume
372
Category
Article
ISSN
0024-3795

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✦ Synopsis

Consider the nonlinear matrix equation

where Q is an n × n Hermitian positive definite matrix, C is an mn × mn Hermitian positive semidefinite matrix, A is an mn × n matrix, and X is the m × m block diagonal matrix defined by X = diag(X, X, . . . , X), in which X is an n × n matrix. This matrix equation is connected with certain interpolation problem. In this paper, perturbation bounds and condition numbers for the maximal solution are presented, and residual bounds for an approximate solution to the maximal solution are obtained. The results are illustrated by numerical examples.

📜 SIMILAR VOLUMES

On solutions of the matrix equations X−A
On solutions of the matrix equations X−AXB=C and X−AXB=C
✍ Tongsong Jiang; Musheng Wei 📂 Article 📅 2003 🏛 Elsevier Science 🌐 English ⚖ 99 KB

This paper studies the solutions of complex matrix equations X -AXB = C and X -AXB = C, and obtains explicit solutions of the equations by the method of characteristic polynomial and a method of real representation of a complex matrix respectively.