A new class of parallel alternating-type iterative methods
This paper is concerned with parallel alternating-type iterative methods for solving large sparse linear systems of the form Au = b arising in the numerical solution of partial differential equations by finite difference methods. Examples of alternating-type methods include the alternating direction...
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| Veröffentlicht in: | Journal of computational and applied mathematics 1996-11, Vol.74 (1), p.331-344 |
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| creator | Young, David M. Kincaid, David R. |
| description | This paper is concerned with parallel alternating-type iterative methods for solving large sparse linear systems of the form
Au =
b
arising in the numerical solution of partial differential equations by finite difference methods. Examples of alternating-type methods include the alternating direction implicit (ADI) method and the unsymmetric SOR (USSOR) method. Each iteration of an alternating-type method involves the use of two parameters, say
ϱ and
ϱ′. We consider parallel alternating-type methods where, given an initial vector
u
(0)
, the positive integer
m, and two sets of
m parameters
“ϱ
i”
and
“ϱ′
j”
, one carries out
m
2 single iterations in parallel, each involving one pair (
ϱ
i
,
ϱ′
j
) of the parameters. It is shown that in some cases a linear combination
v
∗
of the vectors thus obtained is the same as the vector
v
∗∗
which would be obtained by a sequential process involving
m iterations based on the successive use of the parameter pairs (
ϱ
1,
ϱ′
1), (
ϱ
2,
ϱ′
2),…, (
ϱ
m
,
ϱ′
m
). Thus, the parallel procedure offers the potential of reducing the wall-clock time by a factor of
m as compared with the sequential procedure. Preliminary numerical results based on the use of a virtual parallel system of sequential computers confirm the expected reductions in the number of iterations. |
| doi_str_mv | 10.1016/0377-0427(96)00030-1 |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_miscellaneous_26280792</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><els_id>0377042796000301</els_id><sourcerecordid>26280792</sourcerecordid><originalsourceid>FETCH-LOGICAL-c410t-6108c83cfde7ff8de44227df5e1748cea36b8c95a9f7cfa7c8176497e241a2a13</originalsourceid><addsrcrecordid>eNp9kE1LAzEQhoMoWKv_wMMeRPSwmmTTfHgQSvELCl70HMbsRCPpbk22lf57d2np0dPwwjPvMA8h54zeMMrkLa2UKqng6srIa0ppRUt2QEZMK1MypfQhGe2RY3KS83cPScPEiNxNiwZ_Cxch56L1xRISxIixgNhhaqALzWfZbZZYhD73cY3FAruvts6n5MhDzHi2m2Py_vjwNnsu569PL7PpvHSC0a6UjGqnK-drVN7rGoXgXNV-gkwJ7RAq-aGdmYDxynlQTjMlhVHIBQMOrBqTy23vMrU_K8ydXYTsMEZosF1lyyXXVBneg2ILutTmnNDbZQoLSBvLqB1E2cGCHSxY04dBlB36L3b9kB1En6BxIe93-YQaqVWP3W8x7H9dB0w2u4CNwzokdJ2t2_D_nT-jFnux</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>26280792</pqid></control><display><type>article</type><title>A new class of parallel alternating-type iterative methods</title><source>Access via ScienceDirect (Elsevier)</source><source>EZB-FREE-00999 freely available EZB journals</source><creator>Young, David M. ; Kincaid, David R.</creator><creatorcontrib>Young, David M. ; Kincaid, David R.</creatorcontrib><description>This paper is concerned with parallel alternating-type iterative methods for solving large sparse linear systems of the form
Au =
b
arising in the numerical solution of partial differential equations by finite difference methods. Examples of alternating-type methods include the alternating direction implicit (ADI) method and the unsymmetric SOR (USSOR) method. Each iteration of an alternating-type method involves the use of two parameters, say
ϱ and
ϱ′. We consider parallel alternating-type methods where, given an initial vector
u
(0)
, the positive integer
m, and two sets of
m parameters
“ϱ
i”
and
“ϱ′
j”
, one carries out
m
2 single iterations in parallel, each involving one pair (
ϱ
i
,
ϱ′
j
) of the parameters. It is shown that in some cases a linear combination
v
∗
of the vectors thus obtained is the same as the vector
v
∗∗
which would be obtained by a sequential process involving
m iterations based on the successive use of the parameter pairs (
ϱ
1,
ϱ′
1), (
ϱ
2,
ϱ′
2),…, (
ϱ
m
,
ϱ′
m
). Thus, the parallel procedure offers the potential of reducing the wall-clock time by a factor of
m as compared with the sequential procedure. Preliminary numerical results based on the use of a virtual parallel system of sequential computers confirm the expected reductions in the number of iterations.</description><identifier>ISSN: 0377-0427</identifier><identifier>EISSN: 1879-1778</identifier><identifier>DOI: 10.1016/0377-0427(96)00030-1</identifier><identifier>CODEN: JCAMDI</identifier><language>eng</language><publisher>Amsterdam: Elsevier B.V</publisher><subject>Alternating direction ; Alternating-type ; Exact sciences and technology ; Implicit method ; Interactive methods ; Mathematics ; Methods of scientific computing (including symbolic computation, algebraic computation) ; Numerical analysis ; Numerical analysis. Scientific computation ; Numerical linear algebra ; Parallel computing ; Sciences and techniques of general use ; Unsymmetric successive overrelaxation method</subject><ispartof>Journal of computational and applied mathematics, 1996-11, Vol.74 (1), p.331-344</ispartof><rights>1996</rights><rights>1997 INIST-CNRS</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c410t-6108c83cfde7ff8de44227df5e1748cea36b8c95a9f7cfa7c8176497e241a2a13</citedby><cites>FETCH-LOGICAL-c410t-6108c83cfde7ff8de44227df5e1748cea36b8c95a9f7cfa7c8176497e241a2a13</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://dx.doi.org/10.1016/0377-0427(96)00030-1$$EHTML$$P50$$Gelsevier$$Hfree_for_read</linktohtml><link.rule.ids>309,310,314,780,784,789,790,3550,23930,23931,25140,27924,27925,45995</link.rule.ids><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=2509687$$DView record in Pascal Francis$$Hfree_for_read</backlink></links><search><creatorcontrib>Young, David M.</creatorcontrib><creatorcontrib>Kincaid, David R.</creatorcontrib><title>A new class of parallel alternating-type iterative methods</title><title>Journal of computational and applied mathematics</title><description>This paper is concerned with parallel alternating-type iterative methods for solving large sparse linear systems of the form
Au =
b
arising in the numerical solution of partial differential equations by finite difference methods. Examples of alternating-type methods include the alternating direction implicit (ADI) method and the unsymmetric SOR (USSOR) method. Each iteration of an alternating-type method involves the use of two parameters, say
ϱ and
ϱ′. We consider parallel alternating-type methods where, given an initial vector
u
(0)
, the positive integer
m, and two sets of
m parameters
“ϱ
i”
and
“ϱ′
j”
, one carries out
m
2 single iterations in parallel, each involving one pair (
ϱ
i
,
ϱ′
j
) of the parameters. It is shown that in some cases a linear combination
v
∗
of the vectors thus obtained is the same as the vector
v
∗∗
which would be obtained by a sequential process involving
m iterations based on the successive use of the parameter pairs (
ϱ
1,
ϱ′
1), (
ϱ
2,
ϱ′
2),…, (
ϱ
m
,
ϱ′
m
). Thus, the parallel procedure offers the potential of reducing the wall-clock time by a factor of
m as compared with the sequential procedure. Preliminary numerical results based on the use of a virtual parallel system of sequential computers confirm the expected reductions in the number of iterations.</description><subject>Alternating direction</subject><subject>Alternating-type</subject><subject>Exact sciences and technology</subject><subject>Implicit method</subject><subject>Interactive methods</subject><subject>Mathematics</subject><subject>Methods of scientific computing (including symbolic computation, algebraic computation)</subject><subject>Numerical analysis</subject><subject>Numerical analysis. Scientific computation</subject><subject>Numerical linear algebra</subject><subject>Parallel computing</subject><subject>Sciences and techniques of general use</subject><subject>Unsymmetric successive overrelaxation method</subject><issn>0377-0427</issn><issn>1879-1778</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>1996</creationdate><recordtype>article</recordtype><recordid>eNp9kE1LAzEQhoMoWKv_wMMeRPSwmmTTfHgQSvELCl70HMbsRCPpbk22lf57d2np0dPwwjPvMA8h54zeMMrkLa2UKqng6srIa0ppRUt2QEZMK1MypfQhGe2RY3KS83cPScPEiNxNiwZ_Cxch56L1xRISxIixgNhhaqALzWfZbZZYhD73cY3FAruvts6n5MhDzHi2m2Py_vjwNnsu569PL7PpvHSC0a6UjGqnK-drVN7rGoXgXNV-gkwJ7RAq-aGdmYDxynlQTjMlhVHIBQMOrBqTy23vMrU_K8ydXYTsMEZosF1lyyXXVBneg2ILutTmnNDbZQoLSBvLqB1E2cGCHSxY04dBlB36L3b9kB1En6BxIe93-YQaqVWP3W8x7H9dB0w2u4CNwzokdJ2t2_D_nT-jFnux</recordid><startdate>19961105</startdate><enddate>19961105</enddate><creator>Young, David M.</creator><creator>Kincaid, David R.</creator><general>Elsevier B.V</general><general>Elsevier</general><scope>6I.</scope><scope>AAFTH</scope><scope>IQODW</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>8FD</scope><scope>JQ2</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope></search><sort><creationdate>19961105</creationdate><title>A new class of parallel alternating-type iterative methods</title><author>Young, David M. ; Kincaid, David R.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c410t-6108c83cfde7ff8de44227df5e1748cea36b8c95a9f7cfa7c8176497e241a2a13</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>1996</creationdate><topic>Alternating direction</topic><topic>Alternating-type</topic><topic>Exact sciences and technology</topic><topic>Implicit method</topic><topic>Interactive methods</topic><topic>Mathematics</topic><topic>Methods of scientific computing (including symbolic computation, algebraic computation)</topic><topic>Numerical analysis</topic><topic>Numerical analysis. Scientific computation</topic><topic>Numerical linear algebra</topic><topic>Parallel computing</topic><topic>Sciences and techniques of general use</topic><topic>Unsymmetric successive overrelaxation method</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Young, David M.</creatorcontrib><creatorcontrib>Kincaid, David R.</creatorcontrib><collection>ScienceDirect Open Access Titles</collection><collection>Elsevier:ScienceDirect:Open Access</collection><collection>Pascal-Francis</collection><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Technology Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><jtitle>Journal of computational and applied mathematics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Young, David M.</au><au>Kincaid, David R.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>A new class of parallel alternating-type iterative methods</atitle><jtitle>Journal of computational and applied mathematics</jtitle><date>1996-11-05</date><risdate>1996</risdate><volume>74</volume><issue>1</issue><spage>331</spage><epage>344</epage><pages>331-344</pages><issn>0377-0427</issn><eissn>1879-1778</eissn><coden>JCAMDI</coden><abstract>This paper is concerned with parallel alternating-type iterative methods for solving large sparse linear systems of the form
Au =
b
arising in the numerical solution of partial differential equations by finite difference methods. Examples of alternating-type methods include the alternating direction implicit (ADI) method and the unsymmetric SOR (USSOR) method. Each iteration of an alternating-type method involves the use of two parameters, say
ϱ and
ϱ′. We consider parallel alternating-type methods where, given an initial vector
u
(0)
, the positive integer
m, and two sets of
m parameters
“ϱ
i”
and
“ϱ′
j”
, one carries out
m
2 single iterations in parallel, each involving one pair (
ϱ
i
,
ϱ′
j
) of the parameters. It is shown that in some cases a linear combination
v
∗
of the vectors thus obtained is the same as the vector
v
∗∗
which would be obtained by a sequential process involving
m iterations based on the successive use of the parameter pairs (
ϱ
1,
ϱ′
1), (
ϱ
2,
ϱ′
2),…, (
ϱ
m
,
ϱ′
m
). Thus, the parallel procedure offers the potential of reducing the wall-clock time by a factor of
m as compared with the sequential procedure. Preliminary numerical results based on the use of a virtual parallel system of sequential computers confirm the expected reductions in the number of iterations.</abstract><cop>Amsterdam</cop><pub>Elsevier B.V</pub><doi>10.1016/0377-0427(96)00030-1</doi><tpages>14</tpages><oa>free_for_read</oa></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0377-0427 |
| ispartof | Journal of computational and applied mathematics, 1996-11, Vol.74 (1), p.331-344 |
| issn | 0377-0427 1879-1778 |
| language | eng |
| recordid | cdi_proquest_miscellaneous_26280792 |
| source | Access via ScienceDirect (Elsevier); EZB-FREE-00999 freely available EZB journals |
| subjects | Alternating direction Alternating-type Exact sciences and technology Implicit method Interactive methods Mathematics Methods of scientific computing (including symbolic computation, algebraic computation) Numerical analysis Numerical analysis. Scientific computation Numerical linear algebra Parallel computing Sciences and techniques of general use Unsymmetric successive overrelaxation method |
| title | A new class of parallel alternating-type iterative methods |
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