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
Condition numbers of matrices with given spectrum
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DOI: 10.1007/s13324-019-00328-4
Abstract: This note surveys recent strategies to estimate the condition number $$CN(T)=\Vert T\Vert \cdot \Vert T^{-1}\Vert $$CN(T)=‖T‖·‖T-1‖ of complex $$n\times n$$n×n matrices T with given spectrum. More precisely, we present a proof of the fact that… read more here.
Keywords: vert; given spectrum; numbers matrices; condition numbers ... See more keywords