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http://dx.doi.org/10.4134/JKMS.j170809

NEWTON SCHULZ METHOD FOR SOLVING NONLINEAR MATRIX EQUATION Xp + A⁎XA = Q  

Kim, Hyun-Min (Department of Mathematics Pusan National University)
Kim, Young-jin (Innovation Center for Industrial Mathematics National Institute for Mathematical Sciences)
Meng, Jie (Department of Mathematics Pusan National University)
Publication Information
Journal of the Korean Mathematical Society / v.55, no.6, 2018 , pp. 1529-1540 More about this Journal
Abstract
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.
Keywords
fixed-point iteration; Newton's method; Newton-Schulz algorithm; local convergence;
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Times Cited By KSCI : 1  (Citation Analysis)
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