Newton Schulz method for solving nonlinear matrix equation Xp + AXA=Q
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...
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| Published in: | Journal of the Korean Mathematical Society pp. 1529 - 1540 |
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| Main Authors: | , , |
| Format: | Journal Article |
| Language: | English |
| Published: |
대한수학회
01-11-2018
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| Subjects: | |
| Online Access: | Get full text |
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| Summary: | 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. KCI Citation Count: 0 |
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| ISSN: | 0304-9914 2234-3008 |