| dbo:abstract |
Simple rational approximation (SRA) is a subset of interpolating methods using rational functions. Especially, SRA interpolates a given function with a specific rational function whose poles and zeros are simple, which means that there is no multiplicity in poles and zeros. Sometimes, it only implies simple poles. The main application of SRA lies in finding the zeros of secular functions. A divide-and-conquer algorithm to find the eigenvalues and eigenvectors for various kinds of matrices is well known in numerical analysis. In a strict sense, SRA implies a specific interpolation using simple rational functions as a part of the divide-and-conquer algorithm. Since such secular functions consist of a series of rational functions with simple poles, SRA is the best candidate to interpolate the zeros of the secular function. Moreover, based on previous researches, a simple zero that lies between two adjacent poles can be considerably well interpolated by using a two-dominant-pole rational function as an approximating function. (en) |
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https://zenodo.org/record/1236142/files/article.pdf |
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dbr:Interpolation dbr:Matrix_(mathematics) dbr:Eigenvectors dbr:Stanford_University dbr:Halley's_method dbr:Pole_(complex_analysis) dbr:Divide-and-conquer_algorithm dbr:Edmond_Halley dbr:Numerical_analysis dbr:Rational_function dbc:Interpolation dbr:Society_for_Industrial_and_Applied_Mathematics dbr:Root_of_a_function dbr:Eigenvalues dbr:Secular_function |
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dbc:Interpolation |
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dbo:ProgrammingLanguage |
| rdfs:comment |
Simple rational approximation (SRA) is a subset of interpolating methods using rational functions. Especially, SRA interpolates a given function with a specific rational function whose poles and zeros are simple, which means that there is no multiplicity in poles and zeros. Sometimes, it only implies simple poles. (en) |
| rdfs:label |
Simple rational approximation (en) |
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freebase:Simple rational approximation wikidata:Simple rational approximation https://global.dbpedia.org/id/4uiED |
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wikipedia-en:Simple_rational_approximation?oldid=1032330915&ns=0 |
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wikipedia-en:Simple_rational_approximation |
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dbr:Interpolation dbr:List_of_numerical_analysis_topics dbr:Maamar_Bettayeb dbr:Rational_approximation |
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wikipedia-en:Simple_rational_approximation |