Practical Scientific Computing

9

Computational Eigenvalue Problems

Finding the eigenvalues of a square matrix is a problem that arises in a wide variety of scientific and engineering applications. These applications include, for example, problems involving structural vibrations, energy levels in quantum systems, molecular vibrations, and analysis of systems of linear differential equations. The eigenvalue problem is a special case of the nonlinear problem, so the only way to compute eigenvalues is to use iterative methods. This chapter presents two of the most important numerical techniques for solving eigenvalue problems: the power method and the QR method. We restrict our attention to eigenvalues of real matrices, although much of the theory extends to matrices with complex ...