Spectral behavior of matrix sequences and discretized boundary value problems
By Stefano Serra Capizzano. 2001
72 citations recorded by the source corpus.
Abstract In this paper we provide theoretical tools for dealing with the spectral properties of general sequences of matrices of increasing dimension. More specifically, we give a unified treatment of notions such as distribution, equal distribution, localization, equal localization, clustering and sub-clustering. As a case study we consider the matrix sequences arising from the finite difference (FD) discretization of elliptic and semielliptic boundary value problems (BVPs). The spectral analysis is then extended to Toeplitz-based preconditioned matrix sequences with special attention to the case where the coefficients of the differential operator are not regular (belong to L 1 ) and to the case of multidimensional problems. The related clustering properties allow the establishment of some ergodic formulas for the eigenvalues of the preconditioned matrices.
Subfields: Atomic and Molecular Physics, and Optics, Computational Theory and Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/4648ab425eb8bf41d646fb7cadd4f0e32edcb13e
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In Computational Theory and Mathematics
In Mathematical Physics
Citations in the corpus
- Matrix algebra preconditioners for multilevel Toeplitz matrices are not superlinear (2002, unknown): “6 [12].”
- Linear Algebra and its Applications (2010, unknown): “That is, for zero sources, Hence (3.5) is unconditionally stable (and conservative for zero S ).”
- Generalized locally Toeplitz sequences: spectral analysis and applications to discretized partial differential equations (2003, background): “In addition in the case of the finite elements, due to the variational approach, we are allowed to consider problems where the weight A(x) has L1 entries: in this case the definition of locally Toeplitz matrices should be slightly modified by replacing “sampling” of the weight by “local integrals” (”