A Generalization of the Conjugate-Gradient Method to Solve Complex Systems

The conjugate-gradient method has gained favour recently, notably as a procedure for solving large, preconditioned systems of algebraic equations. Preconditioning techniques have been developed for preparing the system for efficient solution by conjugate gradients. The basic conjugate-gradient metho...

Full description

Saved in:
Bibliographic Details
Published in:IMA journal of numerical analysis 1986-10, Vol.6 (4), p.447-452
Main Author: JACOBS, D. A. H
Format: Article
Language:English
Subjects:
Exact sciences and technology
Mathematics
Numerical analysis
Numerical analysis. Scientific computation
Numerical linear algebra
Sciences and techniques of general use
Citations: Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
cited_by cdi_FETCH-LOGICAL-c304t-33d529f4fc3dfbd0f6b9264cf5d1e1e4bcb62eed645accf5ac06d6b3eeeaee793
cites
container_end_page 452
container_issue 4
container_start_page 447
container_title IMA journal of numerical analysis
container_volume 6
creator JACOBS, D. A. H
description The conjugate-gradient method has gained favour recently, notably as a procedure for solving large, preconditioned systems of algebraic equations. Preconditioning techniques have been developed for preparing the system for efficient solution by conjugate gradients. The basic conjugate-gradient method was developed for symmetric, positive definite systems. In this paper a generalization to complex systems is described by developing the work of Fletcher. The methods improve on ‘symmetrization’, solving the normal equations for the asymmetric case, and expanding the complex system to a real one of twice the order. The method has already proved to be effective.
doi_str_mv 10.1093/imanum/6.4.447
format article
fullrecord <record><control><sourceid>istex_cross</sourceid><recordid>TN_cdi_crossref_primary_10_1093_imanum_6_4_447</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>ark_67375_HXZ_QGG07Z2Q_P</sourcerecordid><originalsourceid>FETCH-LOGICAL-c304t-33d529f4fc3dfbd0f6b9264cf5d1e1e4bcb62eed645accf5ac06d6b3eeeaee793</originalsourceid><addsrcrecordid>eNo9kE1LAzEQhoMoWKtXzzl43Ta7ySbdYym6VSpaqiC9hGwysVv3oySptP56t6x4Gph53oH3Qeg2JqOYZHRc1qrZ12M-YiPGxBkaxIyziHKWnKMBSUQSsUxkl-jK-y0hhHFBBuhpinNowKmq_FGhbBvcWhw2gGdts91_qgBR7pQpoQn4GcKmNTi0eNVW3yek3lVwwKujD1D7a3RhVeXh5m8O0fvD_dtsHi1e8sfZdBFpSliIKDVpkllmNTW2MMTyIks40zY1McTACl3wBMBwlirdbZUm3PCCAoACEBkdolH_V7vWewdW7lzX3R1lTOTJhOxNSC6Z7Ex0gbs-sFNeq8o61ejS_6cmZCKomHRY1GNlV-fwf1buS_IOSOX8Yy2XeU7EOlnKV_oLz05xCQ</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype></control><display><type>article</type><title>A Generalization of the Conjugate-Gradient Method to Solve Complex Systems</title><source>Oxford University Press Archive</source><creator>JACOBS, D. A. H</creator><creatorcontrib>JACOBS, D. A. H</creatorcontrib><description>The conjugate-gradient method has gained favour recently, notably as a procedure for solving large, preconditioned systems of algebraic equations. Preconditioning techniques have been developed for preparing the system for efficient solution by conjugate gradients. The basic conjugate-gradient method was developed for symmetric, positive definite systems. In this paper a generalization to complex systems is described by developing the work of Fletcher. The methods improve on ‘symmetrization’, solving the normal equations for the asymmetric case, and expanding the complex system to a real one of twice the order. The method has already proved to be effective.</description><identifier>ISSN: 0272-4979</identifier><identifier>EISSN: 1464-3642</identifier><identifier>DOI: 10.1093/imanum/6.4.447</identifier><identifier>CODEN: IJNADH</identifier><language>eng</language><publisher>Oxford: Oxford University Press</publisher><subject>Exact sciences and technology ; Mathematics ; Numerical analysis ; Numerical analysis. Scientific computation ; Numerical linear algebra ; Sciences and techniques of general use</subject><ispartof>IMA journal of numerical analysis, 1986-10, Vol.6 (4), p.447-452</ispartof><rights>1987 INIST-CNRS</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c304t-33d529f4fc3dfbd0f6b9264cf5d1e1e4bcb62eed645accf5ac06d6b3eeeaee793</citedby></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,780,784,27924,27925</link.rule.ids><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&amp;idt=8087378$$DView record in Pascal Francis$$Hfree_for_read</backlink></links><search><creatorcontrib>JACOBS, D. A. H</creatorcontrib><title>A Generalization of the Conjugate-Gradient Method to Solve Complex Systems</title><title>IMA journal of numerical analysis</title><description>The conjugate-gradient method has gained favour recently, notably as a procedure for solving large, preconditioned systems of algebraic equations. Preconditioning techniques have been developed for preparing the system for efficient solution by conjugate gradients. The basic conjugate-gradient method was developed for symmetric, positive definite systems. In this paper a generalization to complex systems is described by developing the work of Fletcher. The methods improve on ‘symmetrization’, solving the normal equations for the asymmetric case, and expanding the complex system to a real one of twice the order. The method has already proved to be effective.</description><subject>Exact sciences and technology</subject><subject>Mathematics</subject><subject>Numerical analysis</subject><subject>Numerical analysis. Scientific computation</subject><subject>Numerical linear algebra</subject><subject>Sciences and techniques of general use</subject><issn>0272-4979</issn><issn>1464-3642</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>1986</creationdate><recordtype>article</recordtype><recordid>eNo9kE1LAzEQhoMoWKtXzzl43Ta7ySbdYym6VSpaqiC9hGwysVv3oySptP56t6x4Gph53oH3Qeg2JqOYZHRc1qrZ12M-YiPGxBkaxIyziHKWnKMBSUQSsUxkl-jK-y0hhHFBBuhpinNowKmq_FGhbBvcWhw2gGdts91_qgBR7pQpoQn4GcKmNTi0eNVW3yek3lVwwKujD1D7a3RhVeXh5m8O0fvD_dtsHi1e8sfZdBFpSliIKDVpkllmNTW2MMTyIks40zY1McTACl3wBMBwlirdbZUm3PCCAoACEBkdolH_V7vWewdW7lzX3R1lTOTJhOxNSC6Z7Ex0gbs-sFNeq8o61ejS_6cmZCKomHRY1GNlV-fwf1buS_IOSOX8Yy2XeU7EOlnKV_oLz05xCQ</recordid><startdate>19861001</startdate><enddate>19861001</enddate><creator>JACOBS, D. A. H</creator><general>Oxford University Press</general><scope>BSCLL</scope><scope>IQODW</scope><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>19861001</creationdate><title>A Generalization of the Conjugate-Gradient Method to Solve Complex Systems</title><author>JACOBS, D. A. H</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c304t-33d529f4fc3dfbd0f6b9264cf5d1e1e4bcb62eed645accf5ac06d6b3eeeaee793</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>1986</creationdate><topic>Exact sciences and technology</topic><topic>Mathematics</topic><topic>Numerical analysis</topic><topic>Numerical analysis. Scientific computation</topic><topic>Numerical linear algebra</topic><topic>Sciences and techniques of general use</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>JACOBS, D. A. H</creatorcontrib><collection>Istex</collection><collection>Pascal-Francis</collection><collection>CrossRef</collection><jtitle>IMA journal of numerical analysis</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>JACOBS, D. A. H</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>A Generalization of the Conjugate-Gradient Method to Solve Complex Systems</atitle><jtitle>IMA journal of numerical analysis</jtitle><date>1986-10-01</date><risdate>1986</risdate><volume>6</volume><issue>4</issue><spage>447</spage><epage>452</epage><pages>447-452</pages><issn>0272-4979</issn><eissn>1464-3642</eissn><coden>IJNADH</coden><abstract>The conjugate-gradient method has gained favour recently, notably as a procedure for solving large, preconditioned systems of algebraic equations. Preconditioning techniques have been developed for preparing the system for efficient solution by conjugate gradients. The basic conjugate-gradient method was developed for symmetric, positive definite systems. In this paper a generalization to complex systems is described by developing the work of Fletcher. The methods improve on ‘symmetrization’, solving the normal equations for the asymmetric case, and expanding the complex system to a real one of twice the order. The method has already proved to be effective.</abstract><cop>Oxford</cop><pub>Oxford University Press</pub><doi>10.1093/imanum/6.4.447</doi><tpages>6</tpages></addata></record>
fulltext fulltext
identifier ISSN: 0272-4979
ispartof IMA journal of numerical analysis, 1986-10, Vol.6 (4), p.447-452
issn 0272-4979
1464-3642
language eng
recordid cdi_crossref_primary_10_1093_imanum_6_4_447
source Oxford University Press Archive
subjects Exact sciences and technology
Mathematics
Numerical analysis
Numerical analysis. Scientific computation
Numerical linear algebra
Sciences and techniques of general use
title A Generalization of the Conjugate-Gradient Method to Solve Complex Systems
url http://sfxeu10.hosted.exlibrisgroup.com/loughborough?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-07T05%3A06%3A03IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-istex_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=A%20Generalization%20of%20the%20Conjugate-Gradient%20Method%20to%20Solve%20Complex%20Systems&rft.jtitle=IMA%20journal%20of%20numerical%20analysis&rft.au=JACOBS,%20D.%20A.%20H&rft.date=1986-10-01&rft.volume=6&rft.issue=4&rft.spage=447&rft.epage=452&rft.pages=447-452&rft.issn=0272-4979&rft.eissn=1464-3642&rft.coden=IJNADH&rft_id=info:doi/10.1093/imanum/6.4.447&rft_dat=%3Cistex_cross%3Eark_67375_HXZ_QGG07Z2Q_P%3C/istex_cross%3E%3Cgrp_id%3Ecdi_FETCH-LOGICAL-c304t-33d529f4fc3dfbd0f6b9264cf5d1e1e4bcb62eed645accf5ac06d6b3eeeaee793%3C/grp_id%3E%3Coa%3E%3C/oa%3E%3Curl%3E%3C/url%3E&rft_id=info:oai/&rft_id=info:pmid/&rfr_iscdi=true