NUMERICAL ANALYSIS OF MATRIX FUNCTIONS
http://www.maths.manchester.ac.uk/~higham/NAMF

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A Schur Algorithm for Computing Matrix pth Roots
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.7.9650

A SCHUR–PARLETT ALGORITHM FOR COMPUTING MATRIX FUNCTIONS
http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.7.6150&rep=rep1&type=pdf

Updating the Singular Value Decomposition 
http://www.sciencedirect.com/science/article/pii/S0377042704000172

Computing the matrix cosine  
http://www.maths.manchester.ac.uk/~higham/narep/narep411.pdf

Computing f(A)b for Matrix Functions f
http://www.maths.manchester.ac.uk/~higham/narep/narep436.pdf

Computing the Polar Decomposition and the Matrix Sign Decomposition in Matrix Groups
http://eprints.ma.man.ac.uk/49/

Structured Conditioning of Matrix Functions
http://www.math.technion.ac.il/iic/ela/ela-articles/11.html

Final Report
http://www.maths.manchester.ac.uk/~higham/NAMF/finrep.pdf

A short introduction to the general topic by Higham et Lijing
Matrix Functions a short course
http://eprints.ma.man.ac.uk/2067/01/covered/MIMS_ep2013_73.pdf