<?xml version="1.0" encoding="utf-8"?>
<TEI xmlns="http://www.tei-c.org/ns/1.0" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns:hal="http://hal.archives-ouvertes.fr/" xmlns:gml="http://www.opengis.net/gml/3.3/" xmlns:gmlce="http://www.opengis.net/gml/3.3/ce" version="1.1" xsi:schemaLocation="http://www.tei-c.org/ns/1.0 http://api.archives-ouvertes.fr/documents/aofr-sword.xsd">
  <teiHeader>
    <fileDesc>
      <titleStmt>
        <title>HAL TEI export of hal-00276477</title>
      </titleStmt>
      <publicationStmt>
        <distributor>CCSD</distributor>
        <availability status="restricted">
          <licence target="https://creativecommons.org/publicdomain/zero/1.0/">CC0 1.0 - Universal</licence>
        </availability>
        <date when="2026-05-18T12:05:33+02:00"/>
      </publicationStmt>
      <sourceDesc>
        <p part="N">HAL API Platform</p>
      </sourceDesc>
    </fileDesc>
  </teiHeader>
  <text>
    <body>
      <listBibl>
        <biblFull>
          <titleStmt>
            <title xml:lang="en">Fast Computation of Moore-Penrose Inverse Matrices</title>
            <author role="aut">
              <persName>
                <forename type="first">Pierre</forename>
                <surname>Courrieu</surname>
              </persName>
              <email type="md5">d700b29c6778bf35260eda29409409c4</email>
              <email type="domain">univ-amu.fr</email>
              <idno type="idhal" notation="string">pierre-courrieu</idno>
              <idno type="idhal" notation="numeric">174505</idno>
              <idno type="halauthorid" notation="string">5917-174505</idno>
              <idno type="ORCID">https://orcid.org/0000-0002-7219-0910</idno>
              <idno type="GOOGLE SCHOLAR">https://scholar.google.fr/citations?hl=fr&amp;user=rsJ7g58AAAAJ</idno>
              <idno type="IDREF">https://www.idref.fr/196081947</idno>
              <affiliation ref="#struct-849"/>
            </author>
            <editor role="depositor">
              <persName>
                <forename>Pierre</forename>
                <surname>Courrieu</surname>
              </persName>
              <email type="md5">11841cbdbe24628c7c92628142802629</email>
              <email type="domain">univ-amu.fr.invalid</email>
            </editor>
          </titleStmt>
          <editionStmt>
            <edition n="v1" type="current">
              <date type="whenSubmitted">2008-04-29 18:50:00</date>
              <date type="whenWritten">2005-05-24</date>
              <date type="whenModified">2024-10-15 03:24:12</date>
              <date type="whenReleased">2008-04-30 14:25:01</date>
              <date type="whenProduced">2005</date>
              <date type="whenEndEmbargoed">2008-04-29</date>
              <ref type="file" target="https://hal.science/hal-00276477v1/document">
                <date notBefore="2008-04-29"/>
              </ref>
              <ref type="file" subtype="greenPublisher" n="1" target="https://hal.science/hal-00276477v1/file/Courrieu05b.pdf" id="file-276477-367771">
                <date notBefore="2008-04-29"/>
              </ref>
              <ref type="externalLink" target="http://arxiv.org/pdf/0804.4809"/>
            </edition>
            <respStmt>
              <resp>contributor</resp>
              <name key="128109">
                <persName>
                  <forename>Pierre</forename>
                  <surname>Courrieu</surname>
                </persName>
                <email type="md5">11841cbdbe24628c7c92628142802629</email>
                <email type="domain">univ-amu.fr.invalid</email>
              </name>
            </respStmt>
          </editionStmt>
          <publicationStmt>
            <distributor>CCSD</distributor>
            <idno type="halId">hal-00276477</idno>
            <idno type="halUri">https://hal.science/hal-00276477</idno>
            <idno type="halBibtex">courrieu:hal-00276477</idno>
            <idno type="halRefHtml">&lt;i&gt;Neural Information Processing - Letters and Reviews&lt;/i&gt;, 2005, 8 (2), pp.25-29</idno>
            <idno type="halRef">Neural Information Processing - Letters and Reviews, 2005, 8 (2), pp.25-29</idno>
            <availability status="restricted">
              <licence target="https://about.hal.science/hal-authorisation-v1/">HAL Authorization<ref corresp="#file-276477-367771"/></licence>
            </availability>
          </publicationStmt>
          <seriesStmt>
            <idno type="stamp" n="CNRS">CNRS - Centre national de la recherche scientifique</idno>
            <idno type="stamp" n="UNIV-AMU">Aix Marseille Université</idno>
            <idno type="stamp" n="LPC">Laboratoire de psychologie cognitive</idno>
            <idno type="stamp" n="CRPN">Centre de Recherche en Psychologie et Neurosciences</idno>
          </seriesStmt>
          <notesStmt>
            <note type="commentary">Number of pages: 5. Typo page 26 line 3: one must read W=G^+F (instead of W=G^+W, which does not make sense!)</note>
            <note type="audience" n="2">International</note>
            <note type="popular" n="0">No</note>
            <note type="peer" n="1">Yes</note>
          </notesStmt>
          <sourceDesc>
            <biblStruct>
              <analytic>
                <title xml:lang="en">Fast Computation of Moore-Penrose Inverse Matrices</title>
                <author role="aut">
                  <persName>
                    <forename type="first">Pierre</forename>
                    <surname>Courrieu</surname>
                  </persName>
                  <email type="md5">d700b29c6778bf35260eda29409409c4</email>
                  <email type="domain">univ-amu.fr</email>
                  <idno type="idhal" notation="string">pierre-courrieu</idno>
                  <idno type="idhal" notation="numeric">174505</idno>
                  <idno type="halauthorid" notation="string">5917-174505</idno>
                  <idno type="ORCID">https://orcid.org/0000-0002-7219-0910</idno>
                  <idno type="GOOGLE SCHOLAR">https://scholar.google.fr/citations?hl=fr&amp;user=rsJ7g58AAAAJ</idno>
                  <idno type="IDREF">https://www.idref.fr/196081947</idno>
                  <affiliation ref="#struct-849"/>
                </author>
              </analytic>
              <monogr>
                <idno type="halJournalId" status="VALID">47150</idno>
                <idno type="issn">1738-2572</idno>
                <title level="j">Neural Information Processing - Letters and Reviews</title>
                <imprint>
                  <publisher>KAIST Press</publisher>
                  <biblScope unit="volume">8</biblScope>
                  <biblScope unit="issue">2</biblScope>
                  <biblScope unit="pp">25-29</biblScope>
                  <date type="datePub">2005</date>
                </imprint>
              </monogr>
              <idno type="arxiv">0804.4809</idno>
            </biblStruct>
          </sourceDesc>
          <profileDesc>
            <langUsage>
              <language ident="en">English</language>
            </langUsage>
            <textClass>
              <keywords scheme="author">
                <term xml:lang="en">Rank Deficient Least Square Systems</term>
                <term xml:lang="en">Moore-Penrose Inverse</term>
                <term xml:lang="en">Pseudoinverse</term>
                <term xml:lang="en">Generalized Inverse</term>
                <term xml:lang="en">Neural Learning</term>
                <term xml:lang="en">Minimum-norm Synaptic Weight Vectors</term>
                <term xml:lang="en">Regularization</term>
              </keywords>
              <classCode scheme="halDomain" n="info.info-ne">Computer Science [cs]/Neural and Evolutionary Computing [cs.NE]</classCode>
              <classCode scheme="halTypology" n="ART">Journal articles</classCode>
              <classCode scheme="halOldTypology" n="ART">Journal articles</classCode>
              <classCode scheme="halTreeTypology" n="ART">Journal articles</classCode>
            </textClass>
            <abstract xml:lang="en">
              <p>Many neural learning algorithms require to solve large least square systems in order to obtain synaptic weights. Moore-Penrose inverse matrices allow for solving such systems, even with rank deficiency, and they provide minimum-norm vectors of synaptic weights, which contribute to the regularization of the input-output mapping. It is thus of interest to develop fast and accurate algorithms for computing Moore-Penrose inverse matrices. In this paper, an algorithm based on a full rank Cholesky factorization is proposed. The resulting pseudoinverse matrices are similar to those provided by other algorithms. However the computation time is substantially shorter, particularly for large systems.</p>
            </abstract>
          </profileDesc>
        </biblFull>
      </listBibl>
    </body>
    <back>
      <listOrg type="structures">
        <org type="laboratory" xml:id="struct-849" status="OLD">
          <idno type="IdRef">157855511</idno>
          <idno type="RNSR">201220328Y</idno>
          <idno type="ROR">https://ror.org/01rf5x574</idno>
          <orgName>Laboratoire de psychologie cognitive</orgName>
          <orgName type="acronym">LPC</orgName>
          <date type="start">2000-01-01</date>
          <date type="end">2024-01-01</date>
          <desc>
            <address>
              <addrLine>Pôle 3 C, Case D 3 place Victor Hugo 13331 Marseille Cedex 3</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://lpc.univ-amu.fr/</ref>
          </desc>
          <listRelation>
            <relation name="UMR7290 /  UMR6146 / FRE2071" active="#struct-198056" type="direct"/>
            <relation name="UMR7290 /  UMR6146 / FRE2071" active="#struct-441569" type="direct"/>
          </listRelation>
        </org>
        <org type="institution" xml:id="struct-198056" status="VALID">
          <idno type="IdRef">15863621X</idno>
          <idno type="ISNI">0000 0001 2176 4817</idno>
          <idno type="ROR">https://ror.org/035xkbk20</idno>
          <orgName>Aix Marseille Université</orgName>
          <orgName type="acronym">AMU</orgName>
          <date type="start">2012-01-01</date>
          <desc>
            <address>
              <addrLine>Aix-Marseille UniversitéJardins du Pharo58 Boulevard Charles Livon13284 Marseille cedex 7</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.univ-amu.fr/</ref>
          </desc>
        </org>
        <org type="regroupinstitution" xml:id="struct-441569" status="VALID">
          <idno type="IdRef">02636817X</idno>
          <idno type="ISNI">0000000122597504</idno>
          <idno type="ROR">https://ror.org/02feahw73</idno>
          <orgName>Centre National de la Recherche Scientifique</orgName>
          <orgName type="acronym">CNRS</orgName>
          <date type="start">1939-10-19</date>
          <desc>
            <address>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.cnrs.fr/</ref>
          </desc>
        </org>
      </listOrg>
    </back>
  </text>
</TEI>