Indeed. I love Padé approximants -- they're very underused. Another really fun trick for approximations of expensive functions are turning them into Chebsyshev functions, like Nick Trefethen's chebfun package. You can trivially differentiate, integrate and compute chebfun approximations of really horrible special functions (e.g. DE solutions) with fantastic accuracy. Criminally underused.
No, I haven't -- thank you very much for sharing. I've only ever used them, e.g. for spectral decomposition in magnetic resonance in a medical setting (1) with the fast Padé transformation, which has a wonderfully deep relationship with the DEs describing magnetic resonance (2).
Thanks also for the lecture - I'll enjoy. Nick Trefethen is such a good speaker. He taught me in a graduate course in numerical methods -- honestly, I'd watch those lectures on a loop again.
Comments
Indeed. I love Padé approximants -- they're very underused. Another really fun trick for approximations of expensive functions are turning them into Chebsyshev functions, like Nick Trefethen's chebfun package. You can trivially differentiate, integrate and compute chebfun approximations of really horrible special functions (e.g. DE solutions) with fantastic accuracy. Criminally underused.
If you like Padé approximants, have you been following Trefethen & al.’s recent work on the "AAA" algorithm etc.? https://arxiv.org/pdf/1612.00337.pdf https://arxiv.org/pdf/1705.10132.pdf
See also the lecture https://www.youtube.com/watch?v=S1upJPMIFfg
No, I haven't -- thank you very much for sharing. I've only ever used them, e.g. for spectral decomposition in magnetic resonance in a medical setting (1) with the fast Padé transformation, which has a wonderfully deep relationship with the DEs describing magnetic resonance (2).
Thanks also for the lecture - I'll enjoy. Nick Trefethen is such a good speaker. He taught me in a graduate course in numerical methods -- honestly, I'd watch those lectures on a loop again.
(1) https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5179227/
(2) https://iopscience.iop.org/article/10.1088/0031-9155/51/5/00...