Algorithms to Compute Discrete Residues of a Rational Function

dc.contributor.advisorZheng, Jie
dc.contributor.advisorArreche, Carlos
dc.contributor.committeeMemberWilliams, Nathan
dc.contributor.committeeMemberDabkowski, Mieczyslaw K.
dc.contributor.committeeMemberArnold, Maxim
dc.creatorSitaula, Hari Prasad 01-27-1985-
dc.creator.orcid0009-0006-5536-8875
dc.date.accessioned2023-10-23T20:34:55Z
dc.date.available2023-10-23T20:34:55Z
dc.date.created2023-08
dc.date.issuedAugust 2023
dc.date.submittedAugust 2023
dc.date.updated2023-10-23T20:34:55Z
dc.description.abstractThe classical notion of residue, for a rational function with complex coefficients, is a powerful and ubiquitous tool, having applications in many different areas. For example: Complex Analysis, Physics, Number Theory, Differential Equations, and Combinatorics, to name a few. In the last decade several new notions of discrete residues have been developed by different researchers, all of which have in common the following obstruction-theoretic feature: a given rational function f (x) is “special” (e.g., rationally integrable, or rationally summable, or rationally q-summable) if and only if all of its corresponding residues are zero. All of these notions of residue (both the classical one and also its discrete variants) are originally defined in terms of a complete partial fraction decomposition of the given rational function f (x), which is too expensive to carry out in practice due to the high computational cost of finding the complete factorization of the denominator. The main contribution of this dissertation is the development of an efficient factorization-free algorithm to compute the discrete residues of a rational function.
dc.format.mimetypeapplication/pdf
dc.identifier.uri
dc.identifier.urihttps://hdl.handle.net/10735.1/9952
dc.language.isoEnglish
dc.subjectMathematics
dc.titleAlgorithms to Compute Discrete Residues of a Rational Function
dc.typeThesis
dc.type.materialtext
thesis.degree.collegeSchool of Natural Sciences and Mathematics
thesis.degree.departmentMathematics
thesis.degree.grantorThe University of Texas at Dallas
thesis.degree.namePHD

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