A Decreasing Sequence of Upper Bounds for the Perron Root

摘要

We construct a decreasing sequence of rectangles in such a way that all the nonzero eigenvalues of a complex matrix are contained in each rectangle, We also obtain a decreasing sequence of upper bounds for the Perron root of a nonnegative matrix with at most r + 1 nonzero eigenvalues, These upper bounds are new and readily computable. Examples are given to show that this bounds perform well.