NDLI: A unified theory for Krylov algorithms

Content Provider	IEEE Xplore Digital Library
Author	Gang Xie
Copyright Year	2002
Description	Author affiliation: Inst. of Comput. Applications, CAEP, China (Gang Xie)
Abstract	Large systems of linear equations arise in many different scientific applications. For example, partial differential equations discretized with the finite difference or finite element method yield a system of equations. Large systems can be solved with either sparse factorization techniques or iterative methods. These two approaches can be combined into a method that uses approximate factorization preconditioning for an iterative method. Krylov algorithms are iterative numerical methods for large unsymmetric systems of linear equations. In this paper, we set up a general theoretical framework for Krylov algorithms and so highlight their common features. We first introduce the conception of orthogonality between linear subspaces. We then formulate a unified definition for Krylov algorithms. On this basis, we study some of their common properties. This work may give useful hints on formulating new better iterative methods for unsymmetric problems.
Starting Page	71
Ending Page	75
File Size	331964
Page Count	5
File Format	PDF
ISBN	0769515126
DOI	10.1109/ICAPP.2002.1173554
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2002-10-23
Publisher Place	China
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Iterative methods Iterative algorithms Differential equations Partial differential equations Finite difference methods Finite element methods Difference equations Gradient methods Computer applications Application software
Content Type	Text
Resource Type	Article

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
5	Website/Portal (Helpdesk)	Queries regarding NDLI and its services	support@ndl.gov.in
6	Contents and Copyright Issues	Queries related to content curation and copyright issues	content@ndl.gov.in
7	National Digital Library of India Club (NDLI Club)	Queries related to NDLI Club formation, support, user awareness program, seminar/symposium, collaboration, social media, promotion, and outreach	clubsupport@ndl.gov.in
8	Digital Preservation Centre (DPC)	Assistance with digitizing and archiving copyright-free printed books	dpc@ndl.gov.in
9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in

Finite element applications of parallel adaptive integration strategies

An improved Wilkinson algorithm for solving linear equations

A New Iterative Eliiptic PDE Solver on a Distributed PC Cluster

Implicit discretization of linear partial differential equations and repetitive processes

Generating fair meshes with G/sup 1/ boundary conditions

Finite-element neural networks for solving differential equations

Acceleration of Convergence of the Finite-Element Method

SciNapse: a problem-solving environment for partial differential equations

A Common Data Management Infrastructure for Adaptive Algorithms for PDE Solutions

A unified theory for Krylov algorithms

Similar Documents

Finite element applications of parallel adaptive integration strategies

An improved Wilkinson algorithm for solving linear equations

A New Iterative Eliiptic PDE Solver on a Distributed PC Cluster

Implicit discretization of linear partial differential equations and repetitive processes

Generating fair meshes with G/sup 1/ boundary conditions

Finite-element neural networks for solving differential equations

Acceleration of Convergence of the Finite-Element Method

SciNapse: a problem-solving environment for partial differential equations

A Common Data Management Infrastructure for Adaptive Algorithms for PDE Solutions

A unified theory for Krylov algorithms