Lecture 12: Computing Eigenvalues and Singular Values

Description

Numerical linear algebra is the subject of this lecture and, in particular, how to compute eigenvalues and singular values. This includes discussion of the Hessenberg matrix, a square matrix that is almost (except for one extra diagonal) triangular.

Summary

\(QR\) method for eigenvalues: Reverse \(A = QR\) to \(A_1 = RQ\)
Then reverse \(A_1 = Q_1R_1\) to \(A_2 = R_1Q_1\): Include shifts
\(A\)'s become triangular with eigenvalues on the diagonal.
Krylov spaces and Krylov iterations

Related section in textbook: II.1

Instructor: Prof. Gilbert Strang