102
edits
Mfasi
Joined 28 February 2014
→Your task
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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 for general matrix functions, that is known to be <math>O</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). | 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). | ||
* 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.'' | * 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]] | ||