Forward and Backward substitution Algorithms - Computational Linear Algebra
Channel: Nick Space Cowboy
Date: 2021-12-08

In this video we review the forward substitution algorithm that was introduced in video #2 on triangular matrices. Then we develop the backward substitution algorithm from the beginning and code it up both in python and in octave. The forward and backward substitution algorithms are crucial algorithms in computational linear algebra as they allow us to quickly and easily solve linear systems that are in an upper or lower triangular form.

Github: 
https://github.com/nkphysics/Computational-Linear-Algebra-/tree/master/Unit1/3_Triangle_Algorithm
Gitlab: https://gitlab.com/n_space_cowboy/computational-linear-algebra/-/tree/master/3_Triangle_Algorithm

Contents:
0:00 | Introduction
0:54| Forward Substitution Review
1:33| Getting Upper Triangular solutions by hand
3:39| Generalizing Solutions and looking for patterns
7:28| Discussion of coding it up and finalizing
10:13| Back Substitution Python Code
13:55| Back Substitution Octave Code

If you have any questions, or comments, feel free to let me know in the comment section. 
Thank you for watching and interacting with the video on the Forward and Backward Substitution algorithms.