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Eigenvalue conditions for convergence of singularly perturbed matrix exponential functions. (English) Zbl 1227.15010
This paper deals with the convergence of sequences of matrix exponential functions \(t\rightarrow e^{tA^{-1}_{k}}\), for \(t>0\), with \(A_k\rightarrow A\), \(A_k\) being nonsingular and \(A\) being nilpotent. The convergence of the sequences is investigating in the pointwise and almost uniform senses, with the results obtained in terms of the eigenvalues of \(A^{-1}_{k}\). Furthermore, considering the exponential as a Schwartz distribution, necessary and sufficient conditions for weak* convergence are presented.

15A16 Matrix exponential and similar functions of matrices
65F15 Numerical computation of eigenvalues and eigenvectors of matrices
15A18 Eigenvalues, singular values, and eigenvectors
46F10 Operations with distributions and generalized functions
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