MultiZ: A Library for Computation of High-order Derivatives Using Multicomplex or Multidual Numbers

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dc.citation.journalTitleACM TRANSACTIONS ON MATHEMATICAL SOFTWARE
dc.contributor.authorAguirre-Mesa A.M.
dc.contributor.authorGarcia M.J.
dc.contributor.authorMillwater H.
dc.contributor.researchgroupMecánica Aplicadaspa
dc.date.accessioned2021-04-16T20:10:43Z
dc.date.available2021-04-16T20:10:43Z
dc.date.issued2020-01-01
dc.description.abstractMulticomplex and multidual numbers are two generalizations of complex numbers with multiple imaginary axes, useful for numerical computation of derivatives with machine precision. The similarities between multicomplex and multidual algebras allowed us to create a unified library to use either one for sensitivity analysis. This library can be used to compute arbitrary order derivates of functions of a single variable or multiple variables. The storage of matrix representations of multicomplex and multidual numbers is avoided using a combination of one-dimensional resizable arrays and an indexation method based on binary bitwise operations. To provide high computational efficiency and low memory usage, the multiplication of hypercomplex numbers up to sixth order is carried out using a hard-coded algorithm. For higher hypercomplex orders, the library uses by default a multiplication method based on binary bitwise operations. The computation of algebraic and transcendental functions is achieved using a Taylor series approximation. Fortran and Python versions were developed, and extensions to other languages are self-evident. © 2020 ACM.eng
dc.identifierhttps://eafit.fundanetsuite.com/Publicaciones/ProdCientif/PublicacionFrw.aspx?id=12173
dc.identifier.doi10.1145/3378538
dc.identifier.issn00983500
dc.identifier.issn15577295
dc.identifier.otherWOS;000575731600003
dc.identifier.otherSCOPUS;2-s2.0-85083812729
dc.identifier.urihttp://hdl.handle.net/10784/29229
dc.language.isoengeng
dc.publisherAssociation for Computing Machinery (ACM)
dc.publisher.departmentUniversidad EAFIT. Departamento de Ingeniería Mecánicaspa
dc.relation.urihttps://www.scopus.com/inward/record.uri?eid=2-s2.0-85083812729&doi=10.1145%2f3378538&partnerID=40&md5=a8b24ba282eab6489d34fe6e96dca860
dc.rightsAssociation for Computing Machinery (ACM)
dc.sourceACM TRANSACTIONS ON MATHEMATICAL SOFTWARE
dc.subject.keywordAlgebraeng
dc.subject.keywordOne dimensionaleng
dc.subject.keywordSensitivity analysiseng
dc.subject.keywordBitwise operationseng
dc.subject.keywordHigh order derivativeseng
dc.subject.keywordHypercomplex numbereng
dc.subject.keywordMachine precisioneng
dc.subject.keywordMatrix representationeng
dc.subject.keywordNumerical computationseng
dc.subject.keywordTaylor series approximationeng
dc.subject.keywordTranscendental functionseng
dc.subject.keywordComputational efficiencyeng
dc.titleMultiZ: A Library for Computation of High-order Derivatives Using Multicomplex or Multidual Numberseng
dc.typeinfo:eu-repo/semantics/articleeng
dc.typearticleeng
dc.typeinfo:eu-repo/semantics/publishedVersioneng
dc.typepublishedVersioneng
dc.type.localArtículospa

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