Feature: allow differing numerator and denominator degree in Pade app… #76
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…rox. As suggested by @jason-s in python-control#73 This is a relatively minimal change, and should do no worse and no better than the previous implementation when numerator and denominator have equal degree.
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@slivingston I am not sure there is another online source; everyone citing Vajta seems to refer to the author's website. |
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Well, you could cite ResearchGate's copy: https://www.researchgate.net/publication/229003251_Some_remarks_on_Pade-approximations |
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Other references are: Moler, Cleve, and Charles Van Loan. "Nineteen dubious ways to compute the exponential of a matrix, twenty-five years later." SIAM review 45.1 (2003): 3-49. http://www.cs.cornell.edu/cv/researchpdf/19ways+.pdf or the original (1978) at http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.129.9283 Hanta, V., and A. Procházka. "Rational approximation of time delay." Institute of Chemical Technology in Prague. Department of computing and control engineering. Technická 5.166 (2009): 28. http://www2.humusoft.cz/www/papers/tcp09/035_hanta.pdf |
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@roryyorke The proposed changes and additions are good. In delay_test.py, you write "...ideally test to numerical limits". Could you comment how that may be achieved as future work? Thanks, @jason-s. I will add the references to the docstring of pade() after merging. |
Feature: allow differing numerator and denominator degree in Padé approximations
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@slivingston there are two possible extremes I can think of: large order (according to @jason-s 's article [1], maximum is n=21), and very large and small T (obviously with order 20 and T=1e16 result is going to overflow - not sure if there are numerical issues for more realistic but still large T). I think this PR closes #73 ? |
Intended to be simple-as-possible implementation (or at least, as-close-to-previous-as-possible).
I've added tests - couldn't find any existing ones.