Geometry of Matrix Polynomial Spaces
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DOI: 10.1007/s10208-019-09423-1
Abstract: We study how small perturbations of general matrix polynomials may change their elementary divisors and minimal indices by constructing the closure hierarchy (stratification) graphs of matrix polynomials’ orbits and bundles. To solve this problem, we… read more here.
Keywords: fiedler; geometry; matrix polynomials; matrix polynomial ... See more keywords
Condition Numbers and Backward Error of a Matrix Polynomial Equation Arising in Stochastic Models
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DOI: 10.1007/s10915-018-0641-x
Abstract: We consider a matrix polynomial equation (MPE) $$A_nX^n+A_{n-1}X^{n-1}+\cdots +A_0=0$$AnXn+An-1Xn-1+⋯+A0=0, where $$A_n, A_{n-1},\ldots , A_0 \in \mathbb {R}^{m\times m}$$An,An-1,…,A0∈Rm×m are the coefficient matrices, and $$X\in \mathbb {R}^{m\times m}$$X∈Rm×m is the unknown matrix. A sufficient condition for… read more here.
Keywords: polynomial equation; matrix polynomial; condition numbers; backward error ... See more keywords