A Short Introduction to Numerical Linear Algebra — Part 2
Contents
- Intro
- More on the SVD
- Conditioning
- References
Intro
The following is a continuation of the previous story ‘A Short Introduction to Numerical Linear Algebra — Part 1’. If you haven’t read it yet, then you may find it useful to read before. You can find it below.
This post will continue some of the introduction to the Singular Value Decomposition and conditioning.
More on the SVD
If you’ve followed along to this point then you’ve probably seen you can rewrite a matrix as a product of several other matrices. There are tons of other matrix decompositions that are different than the SVD and each has different pros and cons. Typically the way linear algebra is taught you’re shown some stuff about Gaussian Elimination but not so much on the actual solving of the systems of equations. There are several benefits of using the SVD but one of them is it provides a direct computational way of solving systems of equations, particularly ill-conditioned ones.
