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Abstract
In this work, we perform a spectral analysis of flipped multilevel Toeplitz sequences, i.e., we study the asymptotic spectral behavior of $\{Y_{{n}} T_{{n}} (f)\}_{{n}}$, where $T_{{n}}(f)$ is a real, square multilevel Toeplitz matrix generated by a function $f\in L^1([-\pi,\pi]^d)$ and $Y_n$ is the exchange matrix, which has 1's on the main antidiagonal. In line with what we have shown for unilevel flipped Toeplitz matrix sequences, the asymptotic spectrum is determined by a 2 x 2 matrix-valued function whose eigenvalues are $\pm |f|$. Furthermore, we characterize the eigenvalue distribution of certain preconditioned flipped multilevel Toeplitz sequences with an analysis that covers both multilevel Toeplitz and circulant preconditioners. Finally, all our findings are illustrated by several numerical experiments.
Original language | English |
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Pages (from-to) | 1319-1336 |
Number of pages | 18 |
Journal | SIAM Journal on Matrix Analysis and Applications |
Volume | 42 |
Issue number | 3 |
DOIs | |
Publication status | Published - 26 Aug 2021 |
Keywords
- multilevel Toeplitz matrices
- spectral symbol
- GLT theory
- preconditioning
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Dive into the research topics of 'The asymptotic spectrum of flipped multilevel Toeplitz matrices and of certain preconditionings'. Together they form a unique fingerprint.Projects
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Effective preconditioners for linear systems in fractional diffusion
Pestana, J. (Principal Investigator)
EPSRC (Engineering and Physical Sciences Research Council)
19/01/18 → 19/06/20
Project: Research