Approximating Functions in a Metric Space
Approximations are common in many areas of mathematics from Taylor series to machine learning.
In this video, we will define what is meant by a best approximation and prove that a best approximation exists in a metric space.
Chapters
0:00 - Examples of Approximation
0:46 - Best Aproximations (definition)
2:32 - Existence proof
7:18 - Summary
The product links below are Amazon affiliate links. If you buy certain products on Amazon soon after clicking them, I may receive a commission. The price is the same for you, but it does help to support the channel :-)
The Approximation Theory series is based on the book "Approximation Theory and Methods" by M.J.D. Powell:
https://amzn.to/4fd13aM
Errata and Clarifications:
A compact subset of a metric space is closed and bounded but a closed and bounded subset of a metric space is not always compact. Please consider the closed versus open set section as illustrative only as the proof strictly requires compactness.
This video was made using:
Animation - Apple Keynote
Editing - DaVinci Resolve
Mic - Shure SM58 https://amzn.to/3gNC801
Supporting the Channel.
If you would like to support me in making free mathematics tutorials then you can make a small donation over at
https://www.buymeacoffee.com/DrWillWood
Thank you so much, I hope you find the content useful.
Watch video Approximating Functions in a Metric Space online without registration, duration hours minute second in high quality. This video was added by user Dr. Will Wood 13 February 2021, don't forget to share it with your friends and acquaintances, it has been viewed on our site 56,452 once and liked it 1.9 thousand people.