In this video we discuss some numerical methods for computing eigenvalues.
Particularly we cover the QR algorithm, the QR algorithm with shifts, Power Method, Inverse Iteration, and Rayleigh iteration. Before this though we briefly cover the concepts of matrix similarity, the Schur decomposition, and the Rayleigh Quotient.
Github link to code notes and references: github.com/nkphysics/Computat...
List of references (including some awesome other KZfaq videos):
• 12. Computing Eigenval...
pythonnumericalmethods.studen...
sci.utah.edu/~akil/docs/cours...
sci.utah.edu/~akil/docs/cours...
en.wikipedia.org/wiki/Eigenva...
web.math.ucsb.edu/~padraic/uc...
• Harvard AM205 video 5....
johnfoster.pge.utexas.edu/num...
• QR Decomposition - Lin...
Timestamps:
00:00 - Introduction
00:45 - Preface
02:28 - Matrix Similarity
04:19 - Schur Decomposition
09:09 - Demonstrating similar matrices share the same eigenvalues
11:20 - Rayleigh Quotient
16:03 - QR Algorithm
22:42 - QR Algorithm with shifts
37:08 - Power Method
40:51 - Inverse & Rayleigh Iteration methods