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 SM ISO690:2012CAPCELEA, Maria, CAPCELEA, Titu. Localization of singular points of meromorphic functions based on interpolation by rational functions. In: Mathematics and Information Technologies: Research and Education, Ed. 2021, 1-3 iulie 2021, Chişinău. Chișinău, Republica Moldova: 2021, pp. 20-21. |
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| Mathematics and Information Technologies: Research and Education 2021 | ||||||
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Conferința "Mathematics and Information Technologies: Research and Education" 2021, Chişinău, Moldova, 1-3 iulie 2021 | ||||||
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Let consider a function f (z) of a complex variable z, which is meromorphic on a finite domain ½ C so that the point 0 2 . The finite values fj := f (zj) of the function f (z) are known on the set fzjg, where the points zj belong to a simple closed contour ¡ ½ , that contains the point z = 0. We admit that points zj form a dense set on ¡. The function f (z) has a finite number of singular points of polar type on the domain , but their number and locations are not known. Also, on the contour ¡ the function f (z) can have both poles and jump discontinuity points (which can be considered as removable singularities). If the function f (z) has poles on the contour ¡, in order to avoid the computation difficulties, we consider that the values of the function f (z) at the points zj 2 ¡½ are given (here ¡½ represents a small perturbation of the contour ¡ ). We aim to determine the locations of the singular points on , in particular those on the contour ¡. In our earlier works we have already examined the Pad´e approximation with Laurent polynomials [1] and the Pad´e approximation with Faber polynomials [2]. In both cases we have considered the meromorphic functions on a finite domain of the complex plane with given values at the points of a simple closed contour from this domain. In this paper we examine two algorithms for localizing the singular points of meromorphic function f (z), both are based on the approximation by rational functions. The first one is based on global interpolation and gives the possibility to determine the singular points of the function on a domain . The second algorithm, based on piecewise interpolation, establishes the poles and the discontinuity points on the contour ¡. |
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<?xml version='1.0' encoding='utf-8'?> <resource xmlns:xsi='http://www.w3.org/2001/XMLSchema-instance' xmlns='http://datacite.org/schema/kernel-3' xsi:schemaLocation='http://datacite.org/schema/kernel-3 http://schema.datacite.org/meta/kernel-3/metadata.xsd'> <creators> <creator> <creatorName>Capcelea, M.A.</creatorName> <affiliation>Universitatea de Stat din Moldova, Moldova, Republica</affiliation> </creator> <creator> <creatorName>Capcelea, T.G.</creatorName> <affiliation>Universitatea de Stat din Moldova, Moldova, Republica</affiliation> </creator> </creators> <titles> <title xml:lang='en'>Localization of singular points of meromorphic functions based on interpolation by rational functions</title> </titles> <publisher>Instrumentul Bibliometric National</publisher> <publicationYear>2021</publicationYear> <relatedIdentifier relatedIdentifierType='ISBN' relationType='IsPartOf'></relatedIdentifier> <dates> <date dateType='Issued'>2021</date> </dates> <resourceType resourceTypeGeneral='Text'>Conference Paper</resourceType> <descriptions> <description xml:lang='en' descriptionType='Abstract'><p>Let consider a function f (z) of a complex variable z, which is meromorphic on a finite domain ­ ½ C so that the point 0 2 ­. The finite values fj := f (zj) of the function f (z) are known on the set fzjg, where the points zj belong to a simple closed contour ¡ ½ ­, that contains the point z = 0. We admit that points zj form a dense set on ¡. The function f (z) has a finite number of singular points of polar type on the domain ­, but their number and locations are not known. Also, on the contour ¡ the function f (z) can have both poles and jump discontinuity points (which can be considered as removable singularities). If the function f (z) has poles on the contour ¡, in order to avoid the computation difficulties, we consider that the values of the function f (z) at the points zj 2 ¡½ are given (here ¡½ represents a small perturbation of the contour ¡ ). We aim to determine the locations of the singular points on ­, in particular those on the contour ¡. In our earlier works we have already examined the Pad´e approximation with Laurent polynomials [1] and the Pad´e approximation with Faber polynomials [2]. In both cases we have considered the meromorphic functions on a finite domain of the complex plane with given values at the points of a simple closed contour from this domain. In this paper we examine two algorithms for localizing the singular points of meromorphic function f (z), both are based on the approximation by rational functions. The first one is based on global interpolation and gives the possibility to determine the singular points of the function on a domain ­. The second algorithm, based on piecewise interpolation, establishes the poles and the discontinuity points on the contour ¡.</p></description> </descriptions> <formats> <format>application/pdf</format> </formats> </resource>
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