Complex monodromy and the topology of real algebraic sets

A relation between the Euler characteristics of the Milnorfibres of a real analytic function is derived from a simple identity involvingcomplex monodromy and complex conjugation. A corollary is the result of Costeand Kurdyka that the Euler characteristic of the local link of an irreduciblealgebraic subset of a real algebraic set is generically constant modulo 4. Asimilar relation for iterated Milnor fibres of ordered sets of functions isused to define topological invariants of ordered collections of algebraicsubsets.     

A Simultaneous Iteration Method for the Unsymmetric Eigenvalue Problem

This paper describes a method of obtaining all or a dominantsubset of the eigenvalues and corresponding left and right-handeigenvectors of unsymmetric matrices by simultaneous iteration.The method differs from Bauer's biiteration in that re-orientationof the trial vectors is achieved at each iteration by performingan "interaction analysis".