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HomeMIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018Lecture 12: Computing Eigenvalues and Singular Values
Lecture 12: Computing Eigenvalues and Singular Values
49:28
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
