Multiprecision algorithms for computing the matrix logarithm

Version 1.0.0.0 (12 KB) by Massimiliano Fasi
Computation of the matrix logarithm in multiprecision.
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Updated 14 Dec 2017

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This code computes the logarithm and the Frechét derivative of a square matrix with non-negative eigenvalues in multiple precision. Both functions require the Advanpix Multiprecision Computing Toolbox for MATLAB (see www.advanpix.com) to work correctly.
The submission contains two functions:
* LOGM_MP computes the matrix logarithm and its Frechét derivative by using the inverse scaling and squaring algorithm and exploiting the complex Schur decomposition of the matrix.
* LOGM_MP_FULL computes the matrix logarithm without transforming the input matrix to upper triangular form.
A detailed description of the algorithms can be found in:
M. Fasi and N. J. Higham, Multiprecision Algorithms for Computing the Matrix Logarithm. Technical Report 2017.16, Manchester Institute for Mathematical Sciences, The University of Manchester, UK, May 2017.

Cite As

Massimiliano Fasi (2024). Multiprecision algorithms for computing the matrix logarithm (https://www.mathworks.com/matlabcentral/fileexchange/63841-multiprecision-algorithms-for-computing-the-matrix-logarithm), MATLAB Central File Exchange. Retrieved .

MATLAB Release Compatibility
Created with R2017b
Compatible with any release
Platform Compatibility
Windows macOS Linux
Acknowledgements

Inspired by: The Matrix Function Toolbox

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logm_multiprecision/

Version Published Release Notes
1.0.0.0

Add a picture.

Add diagonalization for normal matrices.
Fix performance bug in ALPHA(A,K,M).