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A study of Schröder’s method for the matrix pth root using power series expansions
- Source :
- Numerical Algorithms. 83:265-279
- Publication Year :
- 2019
- Publisher :
- Springer Science and Business Media LLC, 2019.
-
Abstract
- When A is a matrix with all eigenvalues in the disk |z - 1| < 1, the principal pth root of A can be computed by Schroder’s method, among many other methods. In this paper, we present a further study of Schroder’s method for the matrix pth root, through an examination of power series expansions of some scalar functions. Specifically, we obtain a new and informative error estimate for the matrix sequence generated by the Schroder’s method, a monotonic convergence result when A is a nonsingular M-matrix, and a structure preserving result when A is a nonsingular M-matrix or a real nonsingular H-matrix with positive diagonal entries. We also explain how a convergence region larger than the disk |z - 1| < 1 can be obtained for Schroder’s method.
- Subjects :
- Power series
Pure mathematics
Applied Mathematics
Numerical analysis
Diagonal
Monotonic function
010103 numerical & computational mathematics
01 natural sciences
law.invention
010101 applied mathematics
Invertible matrix
law
0101 mathematics
Series expansion
Eigenvalues and eigenvectors
M-matrix
Mathematics
Subjects
Details
- ISSN :
- 15729265 and 10171398
- Volume :
- 83
- Database :
- OpenAIRE
- Journal :
- Numerical Algorithms
- Accession number :
- edsair.doi...........7ea2f9fcc9419487d9d9308e992f0e57