A Lanczos procedure for the modal analysis of very large nonsymmetric matrices

Procedures for solving many different kinds of engineering and scientific problems often require intermediate computations on very large matrices. These intermediate computations frequently take the form of either a modal analysis of a large matrix or the solution of large systems of algebraic equations. When large systems of equations have to be solved, bounds on the spectrum of the iteration operator being used to solve these equations can be used to accelerate the convergence of the iteration procedure. Thus, in either situation certain types of modal computations are important. During the past few years practical procedures have been devised for computing eigenvalues and eigenvectors of very large, real symmetric matrices. However, very limited progress has been made on such procedures for large nonsymmetric matrices. In this paper we propose a practical procedure for the computation of some eigenvalues of very large, real nonsymmetric but diagonalizable matrices.