# Numerical Analysis and Scientific Computing Seminar

## Computation of the Lower Spectral Radius of a Set of Nonnegative Matrices

**Speaker:**
Nicola Guglielmi, U L'Aquila

**Location:**
Warren Weaver Hall 1302

**Date:**
Sept. 23, 2011, 10 a.m.

**Synopsis:**

This is a joint work with Vladimir Protasov (Moscow State University).

We address the problem of the exact computation of the lower spectral radius (in short LSR) of a set of matrices, which is one possible generalization to a set of operators of the usual spectral radius of a linear operator. In this talk we describe a method which allows to compute the LSR of a finite family of matrices exactly. We remark that so far no algorithm was available in the literature to compute the LSR exactly.

We introduce the concept of antinorm, which constitutes the basic tool of our procedure, and present a nethod for the computation of LSR of families of nonnegative matrices (which is valid, more in general, for families sharing an invariant cone).

The algorithm is easily implemented. If it terminates in finite time, then it constructs an extremal antinorm and finds the LSR exactly. A theoretical criterion for termination in finite time is also presented.

Some examples and numerical results are given to show the behavior of the method.