Computer Science NASC Seminar

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

Nicola Guglielmi, U L'Aquila

September 23, 2011 10:00AM
Warren Weaver Hall, Room 1302
251 Mercer Street
New York, NY, 10012-1110

Fall 2011 NASC Seminars Calendar


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.

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