On the Iterative Methods for the Solution of Three Types of Nonlinear Matrix Equations

Ivan G. Ivanov () and Hongli Yang
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Ivan G. Ivanov: Faculty of Economics and Business Administration, Sofia University “St.Kl.Ohridski”, 1000 Sofia, Bulgaria
Hongli Yang: College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China

Mathematics, 2023, vol. 11, issue 21, 1-14

Abstract: In this paper, we investigate the iterative methods for the solution of different types of nonlinear matrix equations. More specifically, we consider iterative methods for the minimal nonnegative solution of a set of Riccati equations, a nonnegative solution of a quadratic matrix equation, and the maximal positive definite solution of the equation X + A ∗ X − 1 A = Q . We study the recent iterative methods for computing the solution to the above specific type of equations and propose more effective modifications of these iterative methods. In addition, we make comments and comparisons of the existing methods and show the effectiveness of our methods by illustration examples.

Keywords: Riccati equation; nonlinear matrix equation; M-matrix; minimal nonnegative solution (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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