
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