ZEROS OF DETERMINANTS OF λ-MATRICES

Abstract. Jim Wilkinson discovered that the computation of zeros of polynomials is ill condi-tioned when the polynomial is given by its coefficients. For many problems we need to compute zeros of polynomials, but we do not necessarily need to represent the polynomial with its coefficients. We develop algorithms that avoid the coefficients. They turn out to be stable, however, the drawback is often heavily increased computational effort. Modern processors on the other hand are mostly idle and wait for crunching numbers so it may pay to accept more computations in order to increase stability and also to exploit parallelism. We apply the method for nonlinear eigenvalue problems