A New sqrtm for Matlab (1999)
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author = {For Matlab and N. J. Higham and Nicholas J. Higham},
title = {A New sqrtm for Matlab},
year = {1999}
}
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Abstract:
Matlab's function sqrtm computes a square root of a matrix. We propose a replacement for the sqrtm in Matlab 5.2 that is more accurate and returns useful information about the stability and conditioning of the problem. Key words. matrix square root, Matlab, Schur decomposition, condition number, stability AMS subject classifications. 65F30 1 Introduction Matlab has included since at least version 3 a function sqrtm for computing a square root of a matrix. The function works by reducing the matrix to Schur form and then applying a recurrence of Parlett for computing a general function of a triangular matrix. An error estimate is computed and if it is too large then an attempt is made to improve the accuracy of the computed square root. The function sqrtm in versions of Matlab up to version 5.2 can be much less accurate than is warranted by the condition of the problem. We propose a replacement for sqrtm that is more accurate and returns useful information about the stability and con...
Citations
| 2102 | Topics in Matrix Analysis – Horn, Johnson - 1991 |
| 104 | Matrix Computations, Third Edition – Golub - 1996 |
| 49 | The Test Matrix Toolbox for Matlab (Version 3.0 – Higham - 1995 |
| 24 | Newton’s method for the matrix square root – Higham - 1986 |
| 23 | Computing real square roots of a real matrix – Higham - 1987 |
| 15 | A Schur Method for the Square Root of a Matrix – Bjorck, Hammarling - 1983 |
| 12 | A recurrence among the elements of functions of triangular matrices – Parlett - 1976 |
