Diagonalization Techniques: Jacobi Method

This lecture covers the Jacobi method and other diagonalization techniques, including similarity transformation, Givens rotation, classical and cyclic Jacobi algorithms, QR decomposition, power methods, and parallel implementation. It discusses the iterative methods, norm of residual, and power iteration to find eigenvalues. The Jacobi algorithm for symmetric matrices, similarity transformation properties, and elementary matrix transformations are explained. Practical examples of the Jacobi method and QR decomposition are provided, along with the construction of Jacobi rotation matrices. The lecture concludes with a two-step algorithm for diagonalization, emphasizing the importance of parallel implementation.