Projects per year
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 matrixvalued 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 

Pages (fromto)  13191336 
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
Projects
 1 Finished

Effective preconditioners for linear systems in fractional diffusion
EPSRC (Engineering and Physical Sciences Research Council)
19/01/18 → 19/06/20
Project: Research