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
Backward error and condition number of a generalized Sylvester equation, with application to the stochastic Galerkin method
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DOI: 10.1016/j.laa.2020.02.018
Abstract: The governing equation of the stochastic Galerkin method can be formulated as a generalized Sylvester equation. Therefore, developing solvers for it is attracting a lot of attention from the uncertainty quantification community. In this regard… read more here.
Keywords: backward error; generalized sylvester; stochastic galerkin; equation ... See more keywords