What is...Padé approximation?
Goal.
I would like to tell you a bit about my favorite theorems, ideas or concepts in mathematics and why I like them so much.
This time.
What is...Padé approximation? Or: Better than Taylor.
Disclaimer.
Nobody is perfect, and I might have said something silly. If there is any doubt, then please check the references.
Slides.
http://www.dtubbenhauer.com/youtube.html
TeX files for the presentation.
https://github.com/dtubbenhauer/My-Te...
Thumbnail.
Picture created using Mathematica’s plot https://reference.wolfram.com/languag...
Main discussion.
https://en.wikipedia.org/wiki/Pad%C3%...
https://mathworld.wolfram.com/PadeApp...
https://www.cfm.brown.edu/people/dobr...
http://www.scholarpedia.org/article/P...
https://www.colorado.edu/amath/sites/...
https://en.wikipedia.org/wiki/Pad%C3%...
https://mathoverflow.net/questions/12...
https://www.johndcook.com/blog/2021/0...
Background material.
https://en.wikipedia.org/wiki/Categor...
https://en.wikipedia.org/wiki/Taylor_...
https://en.wikipedia.org/wiki/Taylor%...
https://en.wikipedia.org/wiki/Polynomial
https://en.wikipedia.org/wiki/Rationa...
https://en.wikipedia.org/wiki/Power_s...
https://en.wikipedia.org/wiki/Formal_...
Computer talk.
https://demonstrations.wolfram.com/Pa...
https://demonstrations.wolfram.com/Ac...
https://demonstrations.wolfram.com/Mu...
https://ask.sagemath.org/question/327...
https://reference.wolfram.com/languag...
Pictures used.
https://en.wikipedia.org/wiki/Linear_...
https://en.wikipedia.org/wiki/Cubic_f...
https://en.wikipedia.org/wiki/Rationa...
https://en.wikipedia.org/wiki/Tangent...
https://en.wikipedia.org/wiki/Taylor_...
Picture created using https://demonstrations.wolfram.com/Pa...
Pictures from https://en.wikipedia.org/wiki/Pad%C3%...
https://www.johndcook.com/exppadeplot...
YouTube and co.
• Padé Approximants
• Why Padé Approximations Are Great! | ...
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#numericalanalysis
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