ABSTRACT
The calculation of eigenvalues and eigenvectors is a problem that plays an important part in a large number of applications, both theoretical and practical. They touch most areas in science, engineering, and economics. In this chapter, the authors describe the power method and introduce a new method called the quadratic method for computing the eigenvalues and eigenvectors of a symmetric matrix A. There are many techniques for approximating the eigenpairs of a matrix. The most popular ones are the QR and QL algorithms. Eigenvalue problems arise in many branches of applied mathematics, and, in particular, in the solutions of differential equations such as problems in the fields of elasticity and vibration. Systems of ordinary differential equations, modeling physical or biological problems, typically contain parameters, which in a given situation must be assigned definite numerical values.
