Linear Algebra - Least Squares Approximation - 09 - Fitting data to more general functions example
Channel: Arthur Parzygnat
Date: 2023-01-31

We go through an example to illustrate how least squares works for more general functions. In this case, we have a linear combination of the functions x goes to x (the identity) and x goes to the square-root of x. Although the numbers aren't so nice at first, the end result is, and it illustrates how the technique works in one example. I therefore skipped some moments where I try to work out the awful arithmetic. 

This is part of a series of lectures on special topics in linear algebra https://www.youtube.com/playlist?list=PLSx1kJDjrLRSS4Aio9WfQlNnH6X6pC_8t. It is assumed the viewer has taken (or is well into) a course in linear algebra. Some topics may also require additional background. Topics covered include linear regression and data analysis, ordinary linear differential equations, differential operators, function spaces, category-theoretic aspects of linear algebra, support vector machines (machine learning), Hamming's error-correcting codes, stochastic maps and Markov chains, tensor products, finite-dimensional C*-algebras, algebraic probability theory, completely positive maps, aspects of quantum information theory, and more.

The next video on Special Topics in Linear Algebra is on Fitting data to the Michaelis--Menten equation (an example from biochemistry): https://youtu.be/tIHuBk8l83w

The previous video on Special Topics in Linear Algebra is on the inverse of A transpose times A: https://youtu.be/H6YUIl5NwjI

An earlier video on fitting data to more general functions: https://youtu.be/w_pqFOfLiP0

These videos were created during the 2019 Spring semester at the UConn CETL Lightboard Room.