Conjugate gradient methods for Toeplitz systems
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 …
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 …
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 …
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 …
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 …
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 …
\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 …
Toeplitz systems. These systems arise in a variety of applications in mathematics, scientific …
On the spectrum of stiffness matrices arising from isogeometric analysis
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 …
analysis for the numerical solution of classical second order elliptic problems. Motivated by …
On lipschitz regularization of convolutional layers using toeplitz matrix theory
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 …
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 …
solving a Toeplitz linear system A_n⃗x=⃗b 59, 9, 20, 5, 34, 62, 6, 10, 28, 45, 44, 46, 49 …