JournalJOURNAL OF THE KOREAN MATHEMATICAL SOCIETY (0394-9914), 55(6), 1529 ~ 1540
Enrollment typeSCI
publication date 20181101
The matrix equation Xp+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.
