Newton Schulz method for solving nonlinear matrix equation Xp + A*XA=Q
- Resource Type
- Article
- Authors
- 김현민; 김영진; Jie Meng
- Source
- 대한수학회지, 55(6), pp.1529-1540 Nov, 2018
- Subject
- 수학
- Language
- English
- ISSN
- 2234-3008
0304-9914
The matrix equation $X^p + {A^*}XA=Q$ has been studied to find the positive definite solution in several researches. In this paper, we consider fixed-point iteration and Newton's method for finding the matrix $p$-th root. From these two considerations, we will use the Newton-Schulz algorithm (N.S.A). We will show the residual relation and the local convergence of the fixed-point iteration. The local convergence guarantees the convergence of N.S.A. We also show numerical experiments and easily check that the N.S. algorithm reduce the CPU-time significantly.