Generalized locally Toeplitz sequences: spectral analysis and applications to discretized partial differential equations
By Stefano Serra Capizzano. 2003
181 citations recorded by the source corpus.
Abstract Starting from the finite difference discretization of an elliptic second order PDE as −∑ i,j=1 d ∂ ∂ x i a i,j (x) ∂ ∂ x j u(x) =b(x) over a bounded domain, we introduce the notion of generalized locally Toeplitz sequence of matrices. The singular value distribution (the eigenvalue distribution in the Hermitian case) is studied and characterized for generalized locally Toeplitz sequences in terms of weighted multidimensional Szegő formulas. This extends preceding results attributed to Tilli which concern the unilevel case. The application of this theoretic analysis to the numerical solution of PDEs is finally discussed.
Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/fbadec104865b2f1b483335b5082b0d75b90c242
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In Applied Mathematics
In Computational Theory and Mathematics
In Mathematical Physics
Citations in the corpus
- Generalized locally Toeplitz sequences : Theory and applications (2017, methodology): “This proposition will be used in the next section to show that any LT sequence is a GLT sequence, and, implicitly, that the definition of GLT sequences, originally formulated in [89, 90] in terms of sLT sequences, can be equivalently formulated in terms of LT sequences.”