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ON THE NEWTON METHOD FOR THE MATRIX PTH ROOT.
- Source :
-
SIAM Journal on Matrix Analysis & Applications . 2006, Vol. 28 Issue 2, p503-523. 21p. 1 Chart, 4 Graphs. - Publication Year :
- 2006
-
Abstract
- Stable versions of Newton's iteration for computing the principal matrix pth root A1/P of an n x n matrix A are provided. In the case in which X0 is the identity matrix, it is proved that the method converges for any matrix A having eigenvalues with modulus less than 1 and with positive real parts. Based on these results we provide a general algorithm for computing the principal pth root of any matrix A having no nonpositive real eigenvalues. The algorithm has quadratic convergence, is stable in a neighborhood of the solution, and has a cost of O(n3 log p) operations per step. Numerical experiments and comparisons are performed. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 08954798
- Volume :
- 28
- Issue :
- 2
- Database :
- Academic Search Index
- Journal :
- SIAM Journal on Matrix Analysis & Applications
- Publication Type :
- Academic Journal
- Accession number :
- 21489542
- Full Text :
- https://doi.org/10.1137/050624790