Lecture 11: Minimizing ‖x‖ Subject to Ax = b

Description

In this lecture, Professor Strang revisits the ways to solve least squares problems. In particular, he focuses on the Gram-Schmidt process that finds orthogonal vectors.

Summary

Picture the shortest \(x\) in \(\ell^1\) and \(\ell^2\) and \(\ell^\infty\) norms
The \(\ell^1\) norm gives a sparse solution \(x\).
Details of Gram-Schmidt orthogonalization and \(A = QR\)
Orthogonal vectors in \(Q\) from independent vectors in \(A\)

Related section in textbook: I.11

Instructor: Prof. Gilbert Strang