Computing a matrix function for exponential integrators
Journal of Computational and Applied Mathematics
The complexity of Boolean matrix root computation
Theoretical Computer Science - Special papers from: COCOON 2003
Journal of Computational and Applied Mathematics
The complexity of Boolean matrix root computation
COCOON'03 Proceedings of the 9th annual international conference on Computing and combinatorics
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A numerical method for computing the square root of a symmetric positive definite matrix is developed in this paper. It is based on the Padé approximation of $\sqrt{1+x}$ in the prime fraction form. A precise analysis allows us to determine the minimum number of terms required in the Padé 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 the condition number is very large.