Analysis and computation of a quadratic matrix polynomial with Schur-products and applications to the Barboy-Tenne model.

摘要

Quadratic matrix polynomials of the form Y2+tau∘ Y = B+tau∘C, where Y, tau, B, and C are real, symmetric 3x3 matrices and the dot ∘ denotes the Schur product, arise in the Barboy-Tenne equations of statistical mechanics [1]. In this paper we discuss the number of solutions for Y, and devise and implement algorithms solving equations of this form. We will focus our attention on solving the equations in two specific cases and discuss the existence of a solution in the general case.