User:Mfasi: Difference between revisions

* The project I would like to work on is ''Improve logm, sqrtm, funm''.

I would implement such functions, using known algorithms for matrix functions. In particular, I would like to start implementing the Schur-Parlett recurrence for general matrix functions, that is known to be <math>$O(n^4)$</math>, and then implementing better - specific - algorithms for the other two functions. For the matrix logarithm I do not know wether there is something better than the scaling and squaring method devised by Higham in ''Functions of Matrices: Theory and Computation'', while for the p-th root there is a recent work [http://poisson.phc.unipi.it/~maxreen/bruno/pdf/B.%20Iannazzo%20and%20C.%20Manasse%20-%20A%20Schur%20logarithmic%20algorithm%20for%20fractional%20powers%20of%20matrices%20-%20SIMAX.pdf] that has a lower asymptotical complexity (but seems rather involved, so I cannot say anything about the real performances).