ON THE CONVERGENCE OF THE GAVER–STEHFEST ALGORITHM
The Gaver–Stehfest algorithm for numerical inversion of Laplace transform was developed in the late 1960s. Due to its simplicity and good performance it is becoming increasingly more popular in such diverse areas as geophysics, operations research and economics, financial and actuarial mathematics,...
Gespeichert in:
| Veröffentlicht in: | SIAM journal on numerical analysis 2013-01, Vol.51 (6), p.2984-2998 |
|---|---|
| 1. Verfasser: | |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | 2998 |
|---|---|
| container_issue | 6 |
| container_start_page | 2984 |
| container_title | SIAM journal on numerical analysis |
| container_volume | 51 |
| creator | KUZNETSOV, A. |
| description | The Gaver–Stehfest algorithm for numerical inversion of Laplace transform was developed in the late 1960s. Due to its simplicity and good performance it is becoming increasingly more popular in such diverse areas as geophysics, operations research and economics, financial and actuarial mathematics, computational physics, and chemistry. Despite the large number of applications and numerical studies, this method has never been rigorously investigated. In particular, it is not known whether the Gaver–Stehfest approximations converge or what the rate of convergence is. In this paper we answer the first of these two questions: We prove that the Gaver–Stehfest approximations converge for functions of bounded variation and functions satisfying an analogue of Dini criterion. |
| doi_str_mv | 10.1137/13091974x |
| format | Article |
| fullrecord | <record><control><sourceid>jstor_proqu</sourceid><recordid>TN_cdi_proquest_miscellaneous_1475531739</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><jstor_id>24511528</jstor_id><sourcerecordid>24511528</sourcerecordid><originalsourceid>FETCH-LOGICAL-c453t-ddad728f786d50f4a2212c3d69f8ab918d4a5c4a46f5b03e8af24c406836d0933</originalsourceid><addsrcrecordid>eNpd0M9Kw0AQBvBFFKzVgw8gBLzoIbqzf7K7xxK2SaE20EbxFrZJFlraRndb0Jvv4Bv6JK5WPXga5uPHMHwInQO-AaDiFihWoAR7OUA9wIrHAgQ-RD2MaRIDI-oYnXi_xGGXQHuIFZOozHWUFpMHPc30JNVRMfyOskFIPt7eZ6XOh3pWRoNxVkxHZX53io6sWfn27Gf20f1Ql2kej4tslA7Gcc043cZNYxpBpBUyaTi2zBACpKZNoqw0cwWyYYbXzLDE8jmmrTSWsJrhRNKkwYrSPrra331y3fOu9dtqvfB1u1qZTdvtfAVMcE5BUBXo5T-67HZuE74LiikgVEoc1PVe1a7z3rW2enKLtXGvFeDqq7_qt7_HYC_2dum3nfuDhHEATiT9BMvzZWY</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>1449123880</pqid></control><display><type>article</type><title>ON THE CONVERGENCE OF THE GAVER–STEHFEST ALGORITHM</title><source>SIAM Journals Online</source><source>Jstor Complete Legacy</source><source>JSTOR Mathematics & Statistics</source><creator>KUZNETSOV, A.</creator><creatorcontrib>KUZNETSOV, A.</creatorcontrib><description>The Gaver–Stehfest algorithm for numerical inversion of Laplace transform was developed in the late 1960s. Due to its simplicity and good performance it is becoming increasingly more popular in such diverse areas as geophysics, operations research and economics, financial and actuarial mathematics, computational physics, and chemistry. Despite the large number of applications and numerical studies, this method has never been rigorously investigated. In particular, it is not known whether the Gaver–Stehfest approximations converge or what the rate of convergence is. In this paper we answer the first of these two questions: We prove that the Gaver–Stehfest approximations converge for functions of bounded variation and functions satisfying an analogue of Dini criterion.</description><identifier>ISSN: 0036-1429</identifier><identifier>EISSN: 1095-7170</identifier><identifier>DOI: 10.1137/13091974x</identifier><language>eng</language><publisher>Philadelphia: Society for Industrial and Applied Mathematics</publisher><subject>Algorithms ; Applied mathematics ; Approximation ; Geophysics ; Laplace transforms ; Mathematical functions ; Neighborhoods ; Random variables</subject><ispartof>SIAM journal on numerical analysis, 2013-01, Vol.51 (6), p.2984-2998</ispartof><rights>Copyright ©2014 Society for Industrial and Applied Mathematics</rights><rights>2013, Society for Industrial and Applied Mathematics</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c453t-ddad728f786d50f4a2212c3d69f8ab918d4a5c4a46f5b03e8af24c406836d0933</citedby><cites>FETCH-LOGICAL-c453t-ddad728f786d50f4a2212c3d69f8ab918d4a5c4a46f5b03e8af24c406836d0933</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://www.jstor.org/stable/pdf/24511528$$EPDF$$P50$$Gjstor$$H</linktopdf><linktohtml>$$Uhttps://www.jstor.org/stable/24511528$$EHTML$$P50$$Gjstor$$H</linktohtml><link.rule.ids>314,776,780,799,828,3171,27901,27902,57992,57996,58225,58229</link.rule.ids></links><search><creatorcontrib>KUZNETSOV, A.</creatorcontrib><title>ON THE CONVERGENCE OF THE GAVER–STEHFEST ALGORITHM</title><title>SIAM journal on numerical analysis</title><description>The Gaver–Stehfest algorithm for numerical inversion of Laplace transform was developed in the late 1960s. Due to its simplicity and good performance it is becoming increasingly more popular in such diverse areas as geophysics, operations research and economics, financial and actuarial mathematics, computational physics, and chemistry. Despite the large number of applications and numerical studies, this method has never been rigorously investigated. In particular, it is not known whether the Gaver–Stehfest approximations converge or what the rate of convergence is. In this paper we answer the first of these two questions: We prove that the Gaver–Stehfest approximations converge for functions of bounded variation and functions satisfying an analogue of Dini criterion.</description><subject>Algorithms</subject><subject>Applied mathematics</subject><subject>Approximation</subject><subject>Geophysics</subject><subject>Laplace transforms</subject><subject>Mathematical functions</subject><subject>Neighborhoods</subject><subject>Random variables</subject><issn>0036-1429</issn><issn>1095-7170</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2013</creationdate><recordtype>article</recordtype><sourceid>8G5</sourceid><sourceid>BENPR</sourceid><sourceid>GUQSH</sourceid><sourceid>M2O</sourceid><recordid>eNpd0M9Kw0AQBvBFFKzVgw8gBLzoIbqzf7K7xxK2SaE20EbxFrZJFlraRndb0Jvv4Bv6JK5WPXga5uPHMHwInQO-AaDiFihWoAR7OUA9wIrHAgQ-RD2MaRIDI-oYnXi_xGGXQHuIFZOozHWUFpMHPc30JNVRMfyOskFIPt7eZ6XOh3pWRoNxVkxHZX53io6sWfn27Gf20f1Ql2kej4tslA7Gcc043cZNYxpBpBUyaTi2zBACpKZNoqw0cwWyYYbXzLDE8jmmrTSWsJrhRNKkwYrSPrra331y3fOu9dtqvfB1u1qZTdvtfAVMcE5BUBXo5T-67HZuE74LiikgVEoc1PVe1a7z3rW2enKLtXGvFeDqq7_qt7_HYC_2dum3nfuDhHEATiT9BMvzZWY</recordid><startdate>20130101</startdate><enddate>20130101</enddate><creator>KUZNETSOV, A.</creator><general>Society for Industrial and Applied Mathematics</general><scope>AAYXX</scope><scope>CITATION</scope><scope>3V.</scope><scope>7WY</scope><scope>7WZ</scope><scope>7X2</scope><scope>7XB</scope><scope>87Z</scope><scope>88A</scope><scope>88F</scope><scope>88I</scope><scope>88K</scope><scope>8AL</scope><scope>8FE</scope><scope>8FG</scope><scope>8FH</scope><scope>8FK</scope><scope>8FL</scope><scope>8G5</scope><scope>ABJCF</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>ARAPS</scope><scope>ATCPS</scope><scope>AZQEC</scope><scope>BBNVY</scope><scope>BENPR</scope><scope>BEZIV</scope><scope>BGLVJ</scope><scope>BHPHI</scope><scope>CCPQU</scope><scope>D1I</scope><scope>DWQXO</scope><scope>FRNLG</scope><scope>F~G</scope><scope>GNUQQ</scope><scope>GUQSH</scope><scope>HCIFZ</scope><scope>JQ2</scope><scope>K60</scope><scope>K6~</scope><scope>K7-</scope><scope>KB.</scope><scope>L.-</scope><scope>L6V</scope><scope>LK8</scope><scope>M0C</scope><scope>M0K</scope><scope>M0N</scope><scope>M1Q</scope><scope>M2O</scope><scope>M2P</scope><scope>M2T</scope><scope>M7P</scope><scope>M7S</scope><scope>MBDVC</scope><scope>P5Z</scope><scope>P62</scope><scope>PATMY</scope><scope>PDBOC</scope><scope>PQBIZ</scope><scope>PQBZA</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PTHSS</scope><scope>PYCSY</scope><scope>Q9U</scope><scope>7SC</scope><scope>7U5</scope><scope>8FD</scope><scope>H8D</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope></search><sort><creationdate>20130101</creationdate><title>ON THE CONVERGENCE OF THE GAVER–STEHFEST ALGORITHM</title><author>KUZNETSOV, A.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c453t-ddad728f786d50f4a2212c3d69f8ab918d4a5c4a46f5b03e8af24c406836d0933</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2013</creationdate><topic>Algorithms</topic><topic>Applied mathematics</topic><topic>Approximation</topic><topic>Geophysics</topic><topic>Laplace transforms</topic><topic>Mathematical functions</topic><topic>Neighborhoods</topic><topic>Random variables</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>KUZNETSOV, A.</creatorcontrib><collection>CrossRef</collection><collection>ProQuest Central (Corporate)</collection><collection>ABI/INFORM Collection</collection><collection>ABI/INFORM Global (PDF only)</collection><collection>Agricultural Science Collection</collection><collection>ProQuest Central (purchase pre-March 2016)</collection><collection>ABI/INFORM Global (Alumni Edition)</collection><collection>Biology Database (Alumni Edition)</collection><collection>Military Database (Alumni Edition)</collection><collection>Science Database (Alumni Edition)</collection><collection>Telecommunications (Alumni Edition)</collection><collection>Computing Database (Alumni Edition)</collection><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>ProQuest Natural Science Collection</collection><collection>ProQuest Central (Alumni) (purchase pre-March 2016)</collection><collection>ABI/INFORM Collection (Alumni Edition)</collection><collection>Research Library (Alumni Edition)</collection><collection>Materials Science & Engineering Collection</collection><collection>ProQuest Central (Alumni Edition)</collection><collection>ProQuest Central UK/Ireland</collection><collection>Advanced Technologies & Aerospace Collection</collection><collection>Agricultural & Environmental Science Collection</collection><collection>ProQuest Central Essentials</collection><collection>Biological Science Collection</collection><collection>ProQuest Central</collection><collection>Business Premium Collection</collection><collection>Technology Collection</collection><collection>Natural Science Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Materials Science Collection</collection><collection>ProQuest Central Korea</collection><collection>Business Premium Collection (Alumni)</collection><collection>ABI/INFORM Global (Corporate)</collection><collection>ProQuest Central Student</collection><collection>Research Library Prep</collection><collection>SciTech Premium Collection</collection><collection>ProQuest Computer Science Collection</collection><collection>ProQuest Business Collection (Alumni Edition)</collection><collection>ProQuest Business Collection</collection><collection>Computer Science Database</collection><collection>Materials Science Database</collection><collection>ABI/INFORM Professional Advanced</collection><collection>ProQuest Engineering Collection</collection><collection>ProQuest Biological Science Collection</collection><collection>ABI/INFORM Global</collection><collection>Agricultural Science Database</collection><collection>Computing Database</collection><collection>Military Database</collection><collection>Research Library</collection><collection>Science Database</collection><collection>Telecommunications Database</collection><collection>Biological Science Database</collection><collection>Engineering Database</collection><collection>Research Library (Corporate)</collection><collection>Advanced Technologies & Aerospace Database</collection><collection>ProQuest Advanced Technologies & Aerospace Collection</collection><collection>Environmental Science Database</collection><collection>Materials Science Collection</collection><collection>ProQuest One Business</collection><collection>ProQuest One Business (Alumni)</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>Engineering Collection</collection><collection>Environmental Science Collection</collection><collection>ProQuest Central Basic</collection><collection>Computer and Information Systems Abstracts</collection><collection>Solid State and Superconductivity Abstracts</collection><collection>Technology Research Database</collection><collection>Aerospace Database</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>SIAM journal on numerical analysis</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>KUZNETSOV, A.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>ON THE CONVERGENCE OF THE GAVER–STEHFEST ALGORITHM</atitle><jtitle>SIAM journal on numerical analysis</jtitle><date>2013-01-01</date><risdate>2013</risdate><volume>51</volume><issue>6</issue><spage>2984</spage><epage>2998</epage><pages>2984-2998</pages><issn>0036-1429</issn><eissn>1095-7170</eissn><abstract>The Gaver–Stehfest algorithm for numerical inversion of Laplace transform was developed in the late 1960s. Due to its simplicity and good performance it is becoming increasingly more popular in such diverse areas as geophysics, operations research and economics, financial and actuarial mathematics, computational physics, and chemistry. Despite the large number of applications and numerical studies, this method has never been rigorously investigated. In particular, it is not known whether the Gaver–Stehfest approximations converge or what the rate of convergence is. In this paper we answer the first of these two questions: We prove that the Gaver–Stehfest approximations converge for functions of bounded variation and functions satisfying an analogue of Dini criterion.</abstract><cop>Philadelphia</cop><pub>Society for Industrial and Applied Mathematics</pub><doi>10.1137/13091974x</doi><tpages>15</tpages><oa>free_for_read</oa></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0036-1429 |
| ispartof | SIAM journal on numerical analysis, 2013-01, Vol.51 (6), p.2984-2998 |
| issn | 0036-1429 1095-7170 |
| language | eng |
| recordid | cdi_proquest_miscellaneous_1475531739 |
| source | SIAM Journals Online; Jstor Complete Legacy; JSTOR Mathematics & Statistics |
| subjects | Algorithms Applied mathematics Approximation Geophysics Laplace transforms Mathematical functions Neighborhoods Random variables |
| title | ON THE CONVERGENCE OF THE GAVER–STEHFEST ALGORITHM |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-02-02T04%3A06%3A40IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-jstor_proqu&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=ON%20THE%20CONVERGENCE%20OF%20THE%20GAVER%E2%80%93STEHFEST%20ALGORITHM&rft.jtitle=SIAM%20journal%20on%20numerical%20analysis&rft.au=KUZNETSOV,%20A.&rft.date=2013-01-01&rft.volume=51&rft.issue=6&rft.spage=2984&rft.epage=2998&rft.pages=2984-2998&rft.issn=0036-1429&rft.eissn=1095-7170&rft_id=info:doi/10.1137/13091974x&rft_dat=%3Cjstor_proqu%3E24511528%3C/jstor_proqu%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=1449123880&rft_id=info:pmid/&rft_jstor_id=24511528&rfr_iscdi=true |