Pseudospectra, stability radii and their relationship with backward error for structured nonlinear eigenvlaue problems
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DOI: 10.1002/mma.9976
Abstract: This paper discusses pseudospectra and stability radii for structured nonlinear matrix functions, such as Hermitian, skew‐Hermitian, H‐even, H‐odd, complex symmetric, and complex skew‐symmetric. To compute pseudospectra and stability radii, eigenvalue backward error is required. Hence,… read more here.
Keywords: stability radii; backward error; error; pseudospectra stability ... 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
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