Numerical algorithms for the real zeros of hypergeometric functions
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2004
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| _version_ | 1866911217590730752 |
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| author | Gil, Amparo Koepf, Wolfram Segura, Javier |
| author_facet | Gil, Amparo Koepf, Wolfram Segura, Javier |
| contents | Algorithms for the computation of the real zeros of hypergeometric functions which are solutions of second order ODEs are described. The algorithms are based on global fixed point iterations which apply to families of functions satisfying first order linear difference differential equations with continuous coefficients. In order to compute the zeros of arbitrary solutions of the hypergeometric equations, we have at our disposal several different sets of difference differential equations (DDE). We analyze the behavior of these different sets regarding the rate of convergence of the associated fixed point iteration. It is shown how combinations of different sets of DDEs, depending on the range of parameters and the dependent variable, is able to produce efficient methods for the computation of zeros with a fairly uniform convergence rate for each zero. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_math_0401116 |
| institution | arXiv |
| publishDate | 2004 |
| record_format | arxiv |
| spellingShingle | Numerical algorithms for the real zeros of hypergeometric functions Gil, Amparo Koepf, Wolfram Segura, Javier Numerical Analysis Classical Analysis and ODEs 33Cxx, 65H05 Algorithms for the computation of the real zeros of hypergeometric functions which are solutions of second order ODEs are described. The algorithms are based on global fixed point iterations which apply to families of functions satisfying first order linear difference differential equations with continuous coefficients. In order to compute the zeros of arbitrary solutions of the hypergeometric equations, we have at our disposal several different sets of difference differential equations (DDE). We analyze the behavior of these different sets regarding the rate of convergence of the associated fixed point iteration. It is shown how combinations of different sets of DDEs, depending on the range of parameters and the dependent variable, is able to produce efficient methods for the computation of zeros with a fairly uniform convergence rate for each zero. |
| title | Numerical algorithms for the real zeros of hypergeometric functions |
| topic | Numerical Analysis Classical Analysis and ODEs 33Cxx, 65H05 |
| url | https://arxiv.org/abs/math/0401116 |