Solving eigenvalue problems by implicit decomposition

This paper presents three innovative methods for solving eigenvalue problems for differential equations based upon the techniques of implicit decomposition developed by Luo and Friedman. An eigenvalue problem can be written as an approximate algebraic system of the form K]{X} + λM]{X} = 0 by employing finite elements. These methods provide robust techniques to compute the real eigenpair, λ and {X}, where K] and M] can be asymmetric, indefinite, and even singular.