Old and new convergence proofs for multigrid methods
H Yserentant - Acta numerica, 1993 - cambridge.org
Multigrid methods are the fastest known methods for the solution of the large systems of
equations arising from the discretization of partial differential equations. For self-adjoint and …
equations arising from the discretization of partial differential equations. For self-adjoint and …
Frequency principle: Fourier analysis sheds light on deep neural networks
We study the training process of Deep Neural Networks (DNNs) from the Fourier analysis
perspective. We demonstrate a very universal Frequency Principle (F-Principle)---DNNs …
perspective. We demonstrate a very universal Frequency Principle (F-Principle)---DNNs …
The analysis of multigrid methods
JH Bramble, X Zhang - Handbook of numerical analysis, 2000 - Elsevier
Publisher Summary This chapter discusses the analysis of multigrid methods. It explains
briefly the classical iterative methods for linear systems. This includes the estimate for the …
briefly the classical iterative methods for linear systems. This includes the estimate for the …
[图书][B] The mathematical theory of finite element methods
SC Brenner - 2008 - Springer
Untitled Page 1 Page 2 15 Texts in Applied Mathematics Editors JE Marsden L. Sirovich SS
Antman Advisors G. Iooss P. Holmes D. Barkley M. Dellnitz P. Newton Page 3 Texts in Applied …
Antman Advisors G. Iooss P. Holmes D. Barkley M. Dellnitz P. Newton Page 3 Texts in Applied …
Algebraic multigrid methods
J Xu, L Zikatanov - Acta Numerica, 2017 - cambridge.org
This paper provides an overview of AMG methods for solving large-scale systems of
equations, such as those from discretizations of partial differential equations. AMG is often …
equations, such as those from discretizations of partial differential equations. AMG is often …
[图书][B] Domain decomposition methods-algorithms and theory
A Toselli, O Widlund - 2006 - books.google.com
This book offers a comprehensive presentation of some of the most successful and popular
domain decomposition preconditioners for finite and spectral element approximations of …
domain decomposition preconditioners for finite and spectral element approximations of …
[图书][B] Finite elements and fast iterative solvers: with applications in incompressible fluid dynamics
H Elman, D Silvester, A Wathen - 2014 - books.google.com
This book is a description of why and how to do Scientific Computing for fundamental
models of fluid flow. It contains introduction, motivation, analysis, and algorithms and is …
models of fluid flow. It contains introduction, motivation, analysis, and algorithms and is …
[图书][B] Finite elements: Theory, fast solvers, and applications in solid mechanics
D Braess - 2001 - books.google.com
" This definitive introduction to finite element methods has been updated thoroughly for this
third edition, which features important new material for both research and application of the …
third edition, which features important new material for both research and application of the …
[图书][B] Iterative solution of large sparse systems of equations
W Hackbusch - 1994 - Springer
The numerical treatment of partial differential equations splits into two different parts. The
first part are the discretisation methods and their analysis. This led to the author's …
first part are the discretisation methods and their analysis. This led to the author's …
Iterative methods by space decomposition and subspace correction
J Xu - SIAM review, 1992 - SIAM
The main purpose of this paper is to give a systematic introduction to a number of iterative
methods for symmetric positive definite problems. Based on results and ideas from various …
methods for symmetric positive definite problems. Based on results and ideas from various …