Perturbation analysis of a quadratic matrix equation associated with an<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si38.gif" display="inline" overflow="scroll"><mml:mi>M</mml:mi></mml:math>-matrix

Liu, Landong

doi:10.1016/j.cam.2013.10.011

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2020

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“…Liu [32] studied the perturbation bound of the M-matrix solution for the equation Q(X) = X 2 − EX − F = 0. In this paper, we symbolized the maximal solution of Eq.…”

Section: Introductionmentioning

confidence: 99%

On the perturbation analysis of the maximal solution for the matrix equation $$ X-\overset{m}{\sum \limits_{i=1}}{A}_i^{\ast}\kern0.1em {X}^{-1}\kern0.1em {A}_i+\sum \limits_{j=1}^n{B}_j^{\ast}\kern0.1em {X}^{-1}\kern0.1em {B}_j=I $$

Ramadan

El-Shazly

2020

J Egypt Math Soc

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In this paper, we study the perturbation estimate of the maximal solution for the matrix equation X− X i¼1 m A Ã i X −1 A i þ X n j¼1 B Ã j X −1 B j ¼ I using the differentiation of matrices. We derive the differential bound for this maximal solution. Moreover, we present a perturbation estimate and an error bound for this maximal solution. Finally, a numerical example is given to clarify the reliability of our obtained results.

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“…Liu [32] studied the perturbation bound of the M-matrix solution for the equation Q(X) = X 2 − EX − F = 0. In this paper, we symbolized the maximal solution of Eq.…”

Section: Introductionmentioning

confidence: 99%

On the perturbation analysis of the maximal solution for the matrix equation $$ X-\overset{m}{\sum \limits_{i=1}}{A}_i^{\ast}\kern0.1em {X}^{-1}\kern0.1em {A}_i+\sum \limits_{j=1}^n{B}_j^{\ast}\kern0.1em {X}^{-1}\kern0.1em {B}_j=I $$

Ramadan

El-Shazly

2020

J Egypt Math Soc

View full text Add to dashboard Cite

show abstract

Perturbation analysis of a quadratic matrix equation associated with anM-matrix

Cited by 1 publication

References 19 publications

On the perturbation analysis of the maximal solution for the matrix equation $$ X-\overset{m}{\sum \limits_{i=1}}{A}_i^{\ast}\kern0.1em {X}^{-1}\kern0.1em {A}_i+\sum \limits_{j=1}^n{B}_j^{\ast}\kern0.1em {X}^{-1}\kern0.1em {B}_j=I $$

On the perturbation analysis of the maximal solution for the matrix equation $$ X-\overset{m}{\sum \limits_{i=1}}{A}_i^{\ast}\kern0.1em {X}^{-1}\kern0.1em {A}_i+\sum \limits_{j=1}^n{B}_j^{\ast}\kern0.1em {X}^{-1}\kern0.1em {B}_j=I $$

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