Linear Algebraic Solvers and Eigenvalue Analysis

This chapter gives an overview of the most widely used numerical methods for the solution of linear systems of equations and for eigenproblems, including direct methods and iterative methods. Iterative methods are often used in combination with the so-called preconditioning operators. We will give a brief overview of the various preconditioners that exist. For eigenproblems of the type inline image, the QR method is discussed. The QR method is expensive for larger values of inline image, and for these larger values, a number of iterative methods, including the Lanczos method, Arnoldi's method, and the Jacobi–Davidson method are shown.