Diagonalization Techniques: Jacobi Method

This lecture on computational physics covers the Jacobi method and other diagonalization techniques, such as Givens rotation and QR decomposition. It explains how to find eigenvalues using power methods and the Rayleigh quotient. The Jacobi algorithm is detailed, along with similarity transformations and elementary matrix transformations. The lecture also discusses the norm of residuals, iterative methods, and the parallel implementation of the Jacobi method. Practical examples and algorithms for classical and cyclic Jacobi methods are presented, emphasizing the importance of QR decomposition in reducing matrices to tridiagonal form. The lecture concludes with a two-step algorithm for diagonalization, highlighting the efficiency of modern computational techniques.