Quadratic matrix polynomials of the form Y^2 +τ ◦Y = B +τ ◦C , where Y , τ , B, and C are real, symmetric 3x3 matrices and the dot ◦ denotes the Schur product, arise in the Barboy-Tenne equations of statistical mechanics . 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.
Library of Congress Subject Headings
Polynomials; Matrices; Schur multiplier
Lahnovych, Carrie, "Analysis and computation of a quadratic matrix polynomial with Schur-products and applications to the Barboy-Tenne model" (2010). Thesis. Rochester Institute of Technology. Accessed from
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