Conjugate gradient methods for Toeplitz systems

RH Chan, MK Ng - SIAM review, 1996 - SIAM
In this expository paper, we survey some of the latest developments in using preconditioned
conjugate gradient methods for solving Toeplitz systems. One of the main results is that the …

[图书][B] Iterative methods for Toeplitz systems

MK Ng - 2004 - books.google.com
Page 1 NUMERICAL MATHEMATICS AND SCIENTIFIC COMPUTATION Iterative Methods
for Toeplitz Systems MICHAEL K. NG OXFORD SCIENCE PUBLICATIONS Page 2 Page 3 …

On the extreme eigenvalues of Hermitian (block) Toeplitz matrices

S Serra - Linear algebra and its applications, 1998 - Elsevier
We are concerned with the behavior of the minimum (maximum) eigenvalue λ0 (n)(λn (n)) of
an (n+ 1)×(n+ 1) Hermitian Toeplitz matrix Tn (ƒ) where ƒ is an integrable real-valued …

Preconditioning technique based on sine transformation for nonlocal Helmholtz equations with fractional Laplacian

TY Li, F Chen, HW Sun, T Sun - Journal of Scientific Computing, 2023 - Springer
We propose two preconditioners based on the fast sine transformation for solving linear
systems with ill-conditioned multilevel Toeplitz structure. These matrices are generated by …

Any circulant-like preconditioner for multilevel matrices is not superlinear

SS Capizzano, E Tyrtyshnikov - SIAM Journal on Matrix Analysis and …, 2000 - SIAM
Superlinear preconditioners (those that provide a proper cluster at 1) are very important for
the cg-like methods since they make these methods converge superlinearly. As is well …

Multigrid methods for symmetric positive definite block Toeplitz matrices with nonnegative generating functions

G Fiorentino, S Serra - SIAM Journal on Scientific Computing, 1996 - SIAM
In this paper we introduce a generalized multigrid method for solving linear systems
\bfT_N,M\bfx=\bfb where T_N,M∈ℜ^NM*NM is a symmetric block Toeplitz matrix with …

[图书][B] Developments and applications of block Toeplitz iterative solvers

XQ Jin - 2003 - books.google.com
This volume contains the latest developments in the use of iterative methods to block
Toeplitz systems. These systems arise in a variety of applications in mathematics, scientific …

On the spectrum of stiffness matrices arising from isogeometric analysis

C Garoni, C Manni, F Pelosi, S Serra-Capizzano… - Numerische …, 2014 - Springer
We study the spectral properties of stiffness matrices that arise in the context of isogeometric
analysis for the numerical solution of classical second order elliptic problems. Motivated by …

On lipschitz regularization of convolutional layers using toeplitz matrix theory

A Araujo, B Negrevergne, Y Chevaleyre… - Proceedings of the AAAI …, 2021 - ojs.aaai.org
This paper tackles the problem of Lipschitz regularization of Convolutional Neural Networks.
Lipschitz regularity is now established as a key property of modern deep learning with …

A Korovkin-type theory for finite Toeplitz operators via matrix algebras

S Serra - Numerische Mathematik, 1999 - Springer
Preconditioned conjugate gradients (PCG) are widely and successfully used methods for
solving a Toeplitz linear system A_n⃗x=⃗b 59, 9, 20, 5, 34, 62, 6, 10, 28, 45, 44, 46, 49 …