Matrix interpretations are a new kind of algebraic interpretations with interesting capabilities for proving termination of rewriting systems. Roughly speaking, a matrix interpretation for a !-ary symbol " is a linear expression #1$1+⋅ ⋅ ⋅+#!$!+#0 where the #1, . . . , #! are matrices of '×' natural numbers and the variables $1, . . . , $! (and also #0) represent '-tuples of natural numbers. In...

Computing the roots of a scalar polynomial, or the eigenvalues of a matrix polynomial, expressed in the Chebyshev basis {Tk(x)} is a fundamental problem that arises in many applications. In this work, we analyze the backward stability of the polynomial rootfinding problem solved with colleague matrices. In other words, given a scalar polynomial p(x) or a matrix polynomial P (x) expressed in the...

We investigate how to factorize a multivariate polynomial matrix into the product of two matrices. There are two major parts. The first is a factorization theorem, which asserts that a multivariate polynomial matrix whose lower order minors satisfy certain conditions admits a matrix factorization. Our theory is a generalization to the previous results given by Lin et.al [16] and Liu et.al [17]....