Matrix analysis and omega calculus.

dc.contributor.authorFrancisco Neto, Antônio
dc.date.accessioned2022-01-28T19:42:55Z
dc.date.available2022-01-28T19:42:55Z
dc.date.issued2020pt_BR
dc.description.abstractIn this work we introduce a new operator based approach to matrix analysis. Our main technical tool comprises an extension of a tool introduced long ago by MacMahon to analyze the partitions of natural numbers: the Omega operator calculus. More precisely, we construct an operator acting linearly on absolutely convergent matrix valued expansions which selects appropriate terms of those expansions. In the context of our framework a new representation of matrix valued functions is available. Our representation is simple, requiring only the computation of matrix inverses and basic manipulations of the Taylor series of scalar functions. To show the usefulness of our approach we obtain fundamental results related to the basic theory of ODEs, perturbative calculations, multiple integrals involving the matrix exponential, the Sylvester equation, the multivariate Fa`a di Bruno formula, Hermite polynomials, queuing theory, and graph theory.pt_BR
dc.identifier.citationFRANCISCO NETO, A. Matrix analysis and omega calculus. Siam Review, v. 62, n. 1, p. 264-280, fev. 2020. Disponível em: <https://epubs.siam.org/doi/abs/10.1137/19M1241362>. Acesso em: 12 set. 2021.pt_BR
dc.identifier.doihttps://doi.org/10.1137/19M1241362pt_BR
dc.identifier.issn1095-7200
dc.identifier.urihttp://www.repositorio.ufop.br/jspui/handle/123456789/14409
dc.identifier.uri2https://epubs.siam.org/doi/abs/10.1137/19M1241362pt_BR
dc.language.isoen_USpt_BR
dc.rightsrestritopt_BR
dc.subjectGenerating functionspt_BR
dc.subjectGraphspt_BR
dc.subjectMatrix functionspt_BR
dc.subjectMultiple integralspt_BR
dc.subjectOmega calculuspt_BR
dc.titleMatrix analysis and omega calculus.pt_BR
dc.typeArtigo publicado em periodicopt_BR

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