Methods for the Eigenvalue Analysis

Abstract

In addition to the matrix-iteration method discussed in Chapter 3, there are several other computer methods that are widely used for solving the eigenvalue problem of vibration systems. Among these methods are the Jacobi method and the QR method. In these methods, which are based on the similarity transformation, a series of transformations that convert a given matrix to a diagonal matrix which has the same eigenvalues as the original matrix are used. Not every matrix, however, is similar to a diagonal matrix, and therefore we find it appropriate to devote several sections of this chapter to discuss the similarity transformation before we briefly discuss the computer methods used for solving the eigenvalue problem of vibration systems. Several definitions will be used repeatedly throughout the development presented in this chapter. Some of these definitions are summarized below.