TY - JOUR
T1 - A Padé approximation method for square roots of symmetric positive definite matrices
AU - Lu, Ya Yan
PY - 1998/7
Y1 - 1998/7
N2 - 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 √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.
AB - 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 √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.
KW - Matrix square root
KW - Padé approximation
KW - Prime fraction form
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U2 - 10.1137/S089547989731631X
DO - 10.1137/S089547989731631X
M3 - 21_Publication in refereed journal
VL - 19
SP - 833
EP - 845
JO - SIAM Journal on Matrix Analysis and Applications
JF - SIAM Journal on Matrix Analysis and Applications
SN - 0895-4798
IS - 3
ER -