Lecture 10: Survey of Difficulties with Ax = b

Description

The subject of this lecture is the matrix equation \(Ax = b\). Solving for \(x\) presents a number of challenges that must be addressed when doing computations with large matrices.

Summary

Large condition number \(\Vert A \Vert \ \Vert A^{-1} \Vert\)
\(A\) is ill-conditioned and small errors are amplified.
Undetermined case \(m < n\) : typical of deep learning
Penalty method regularizes a singular problem.

Related chapter in textbook: Introduction to Chapter II

Instructor: Prof. Gilbert Strang