Numerical recipes in FORTRAN (2nd ed.): the art of scientific computing
Numerical recipes in FORTRAN (2nd ed.): the art of scientific computing
A Schur--Fréchet Algorithm for Computing the Logarithm and Exponential of a Matrix
SIAM Journal on Matrix Analysis and Applications
Conditioning and Padé Approximation of the Logarithm of a Matrix
SIAM Journal on Matrix Analysis and Applications
Accuracy and Stability of Numerical Algorithms
Accuracy and Stability of Numerical Algorithms
Functions of Matrices: Theory and Computation (Other Titles in Applied Mathematics)
Functions of Matrices: Theory and Computation (Other Titles in Applied Mathematics)
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A new approach for computing an expression of the form $a^{1/2^k}-1$ is presented that avoids the danger of subtractive cancellation in floating point arithmetic, where a is a complex number not belonging to the closed negative real axis and k is a nonnegative integer. We also derive a condition number for the problem. The algorithm therefore allows highly accurate numerical calculation of log(a) using Briggs' method.