A PADE-APPROXIMATION METHOD FOR SQUARE ROOTS OF SYMMETRICAL POSITIVE-DEFINITE MATRICES

Authors
Citation
Yy. Lu, A PADE-APPROXIMATION METHOD FOR SQUARE ROOTS OF SYMMETRICAL POSITIVE-DEFINITE MATRICES, SIAM journal on matrix analysis and applications (Print), 19(3), 1998, pp. 833-845
Citations number
14
Categorie Soggetti
Mathematics,Mathematics
ISSN journal
08954798
Volume
19
Issue
3
Year of publication
1998
Pages
833 - 845
Database
ISI
SICI code
0895-4798(1998)19:3<833:APMFSR>2.0.ZU;2-D
Abstract
A numerical method for computing the square root of a symmetric positi ve definite matrix is developed in this paper. It is based on the Pade approximation of root 1 + x in the prime fraction form. A precise ana lysis allows us to determine the minimum number of terms required in t he Pade approximation for a given error tolerance. Theoretical studies and numerical experiments indicate that the method is more efficient than the standard method based on the spectral decomposition, unless t he condition number is very large.