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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 te tA k -1 , for t>0, with A k 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 k -1 . Furthermore, considering the exponential as a Schwartz distribution, necessary and sufficient conditions for weak* convergence are presented.
MSC:
15A16Matrix exponential and similar functions of matrices
65F15Eigenvalues, eigenvectors (numerical linear algebra)
15A18Eigenvalues, singular values, and eigenvectors
46F10Operations with distributions (generalized functions)