Solution of Non-linear Eigenvalue Problems by the Continuation Method

The Problem of finding the roots (eigenvalues) of the equationdet A()=0, where A in an nxn matrix, is studied. There existseveral efficient local iterative methods for this problem.However, no efficient global method is available. We describethe application of the continuation method to this problem andsolve two examples by it. We conclude that the continuationmethod is a practical global strategy for locating eigenvaluesof non-linear matrices. This method is even more effective whenit is combined with an appropriate iterative scheme.