Chapter 7 - Iterative algorithms of solution of eigenvalue problem

Abstract

Chapter 7 presents Iterative Algorithms of Solution of Eigenvalue Problem, which are better suited for large and sparse matrices. The first presented algorithm is the elementary power/subspace iteration. Then it has full presentations of two celebrated algorithms, Lanczos for symmetric matrices and Arnoldi for unsymmetric matrices. All the algorithms are complemented by an overview of iterative algorithms and plots of convergence patterns. Lastly, 3 important topics: generalized eigenvalue problem, nonlinear eigenvalue problem and Jacobi-Davidson iterations, are briefly discussed.