Double iterative algorithm for solving different constrained solutions of multivariate quadratic matrix equations

Constrained solutions are required in some practical problems. This paper studies the problem of different constrained solutions for a class of multivariate quadratic matrix equations, which has rarely been studied before. First, the quadratic matrix equations are transformed into linear matrix equa...

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Veröffentlicht in:	AIMS mathematics Jg. 7; H. 2; S. 1845 - 1855
1. Verfasser:	Zhu, Shousheng
Format:	Journal Article
Sprache:	Englisch
Veröffentlicht:	AIMS Press 01.01.2022
Schlagworte:	different constrained solutions modified conjugate gradient method multivariate quadratic matrix equations newton's method
ISSN:	2473-6988, 2473-6988
Online-Zugang:	Volltext
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Beschreibung
Zusammenfassung:	Constrained solutions are required in some practical problems. This paper studies the problem of different constrained solutions for a class of multivariate quadratic matrix equations, which has rarely been studied before. First, the quadratic matrix equations are transformed into linear matrix equations by Newton's method. Second, the different constrained solutions of the linear matrix equations are solved by the modified conjugate gradient method, and then the different constrained solutions of the multivariate quadratic matrix equations are obtained. Finally, the convergence of the algorithm is proved. The algorithm can be well performed on the computers, and the effectiveness of the method is verified by numerical examples.
ISSN:	2473-6988 2473-6988
DOI:	10.3934/math.2022106