On an inversion-free algorithm for the nonlinear matrix problem Xα+A∗X−βA+B∗X−γB=I,

ABSTRACT

We perform extensive theoretical analysis on an inversion-free algorithm to obtain a maximal positive definite solution (PDS) of a general nonlinear matrix equation (NME) with suitable square matrices. We illustrate some estimations for obtaining the solution, rate of convergence and convergence analysis of the presented algorithm. To ensure its validity and usefulness, several different types of test problems, including randomly generated ones, are given. Comparisons with the existing iterative methods are done through error and computational time.

KEYWORDS:

• Convergence analysis
• iteration methods
• positive definite solution
• nonlinear matrix equation
• inversion-free

2010 MATHEMATICS SUBJECT CLASSIFICATIONS:

• 65F30
• 15A24

Acknowledgments

The authors are thankful to two anonymous referees for several comments and corrections on an earlier version of this manuscript.

Disclosure statement

The writers mention that they have no known personal relationships or competing financial interests, which could have appeared to influence the work reported in this article.

Additional information

Funding

The first and second authors are grateful to the Science and Engineering Research Board (SERB), India, for providing project funding under the scheme – CRG/2018/000615.