A structure-preserving doubling algorithm for the square root of regular M-matrix

Abstract

The matrix square root is widely encountered in many fields of mathematics. In this paper, based on the properties of M-matrix and quadratic matrix equations, we study the square root of M-matrix, and prove that for a regular M-matrix there always exists a regular M-matrix as its square root. In addition, a structure-preserving doubling algorithm is proposed to compute the square root. Theoretical analysis and numerical experiments are given to show that our method is feasible and is effective under certain conditions.

Keywords

• matrix square root
• m-matrix
• iterative method
• doubling algorithm