Matrix Logarithm with Frechet Derivatives and Condition Number

Computing the matrix logarithm in real/complex arithmetic with derivatives and condition numbers.
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Actualizado 5 Nov 2012

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Computes the log(A) for any square matrix A with non-negative eigenvalues using the inverse scaling and squaring algorithm. When A is real this algorithm uses only real arithmetic. It is also possible to compute the Frechet derivative of log(A) in any direction E and cond(log, A) to give some idea of the accuracy.

This code can be called in the following ways:
X = logm_frechet(A)
L = logm_frechet(A,E)
[X, cond] = logm_frechet(A)
[X, L] = logm_frechet(A,E)
[X, L, cond] = logm_frechet(A,E)
where X is log(A), L is the Frechet derivative and cond is the condition number.

Function LOGM_FRECHET_TEST.M runs a simple test of the codes.

More detail on the algorithm can be found in:
A. H. Al-Mohy, N. J. Higham and S. D. Relton. Computing the Frechet Derivative of the Matrix Logarithm and Estimating the Condition Number, MIMS Eprint 2012.72, Manchester Institute for Mathematical Sciences, The University of Manchester, UK, July 2012.
http://eprints.ma.man.ac.uk/1852/

Citar como

Samuel Relton (2024). Matrix Logarithm with Frechet Derivatives and Condition Number (https://www.mathworks.com/matlabcentral/fileexchange/38894-matrix-logarithm-with-frechet-derivatives-and-condition-number), MATLAB Central File Exchange. Recuperado .

Compatibilidad con la versión de MATLAB
Se creó con R2012b
Compatible con cualquier versión
Compatibilidad con las plataformas
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Más información sobre Dimensionality Reduction and Feature Extraction en Help Center y MATLAB Answers.
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Inspiración para: Condition Numbers Comparison

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1.0.0.0