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- W3102012192 abstract "In this work, we perform a spectral analysis of flipped multilevel Toeplitz sequences, i.e., we study the asymptotic spectral behaviour of ${Y_{boldsymbol{n}}T_{boldsymbol{n}}(f)}_{boldsymbol{n}}$, where $T_{boldsymbol{n}}(f)$ is a real, square multilevel Toeplitz matrix generated by a function $fin L^1([-pi,pi]^d)$ and $Y_{boldsymbol{n}}$ is the exchange matrix, which has $1$s on the main anti-diagonal. In line with what we have shown for unilevel flipped Toeplitz matrix sequences, the asymptotic spectrum is determined by a $2times 2$ 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." @default.
- W3102012192 created "2020-11-23" @default.
- W3102012192 creator A5022749162 @default.
- W3102012192 creator A5062815653 @default.
- W3102012192 date "2020-11-16" @default.
- W3102012192 modified "2023-09-24" @default.
- W3102012192 title "The asymptotic spectrum of flipped multilevel Toeplitz matrices and of certain preconditionings" @default.
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- W3102012192 doi "https://doi.org/10.48550/arxiv.2011.08372" @default.
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