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User:Mfasi: Difference between revisions
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* The project I would like to work on is '''Improve logm, sqrtm, funm'''. | * 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 | I would like to implement such functions, using known algorithms for matrix functions. In particular, I would like to start implementing the Schur-Parlett recurrence that should be easy to do using the syl() function, that is known to be O(n^4), 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 [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 recent work] that has a lower asymptotical complexity (but seems rather involved, so I cannot say anything about the real performances). | ||
* [TODO] Please provide a rough estimated timeline for your work on the task. ''This should include the GSoC midterms and personal commitments like exams or vacation ("non-coding time"). Optionally include two or three milestones you expect.'' | * [TODO] Please provide a rough estimated timeline for your work on the task. ''This should include the GSoC midterms and personal commitments like exams or vacation ("non-coding time"). Optionally include two or three milestones you expect.'' | ||
[[Category: Summer of Code]] | [[Category: Summer of Code]] | ||