A practical error formula for multivariate rational interpolation and approximation
Abstract We consider exact and approximate multivariate interpolation of a function f(x1 , . . . , xd) by a rational function pn,m/qn,m(x1 , . . . , xd) and develop an error formula for the difference f − pn,m/qn,m. The similarity with a well-known univariate formula for the error in rational interp...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Cuyt, Annie [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2010 |
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| Schlagwörter: |
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| Anmerkung: |
© Springer Science+Business Media, LLC. 2010 |
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| Übergeordnetes Werk: |
Enthalten in: Numerical algorithms - Springer US, 1991, 55(2010), 2-3 vom: 14. Apr., Seite 233-243 |
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| Übergeordnetes Werk: |
volume:55 ; year:2010 ; number:2-3 ; day:14 ; month:04 ; pages:233-243 |
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10.1007/s11075-010-9380-2 |
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| 520 | |a Abstract We consider exact and approximate multivariate interpolation of a function f(x1 , . . . , xd) by a rational function pn,m/qn,m(x1 , . . . , xd) and develop an error formula for the difference f − pn,m/qn,m. The similarity with a well-known univariate formula for the error in rational interpolation is striking. Exact interpolation is through point values for f and approximate interpolation is through intervals bounding f. The latter allows for some measurement error on the function values, which is controlled and limited by the nature of the interval data. To achieve this result we make use of an error formula obtained for multivariate polynomial interpolation, which we first present in a more general form. The practical usefulness of the error formula in multivariate rational interpolation is illustrated by means of a 4-dimensional example, which is only one of the several problems we tested it on. | ||
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10.1007/s11075-010-9380-2 doi (DE-627)OLC2051159262 (DE-He213)s11075-010-9380-2-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn Cuyt, Annie verfasserin aut A practical error formula for multivariate rational interpolation and approximation 2010 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media, LLC. 2010 Abstract We consider exact and approximate multivariate interpolation of a function f(x1 , . . . , xd) by a rational function pn,m/qn,m(x1 , . . . , xd) and develop an error formula for the difference f − pn,m/qn,m. The similarity with a well-known univariate formula for the error in rational interpolation is striking. Exact interpolation is through point values for f and approximate interpolation is through intervals bounding f. The latter allows for some measurement error on the function values, which is controlled and limited by the nature of the interval data. To achieve this result we make use of an error formula obtained for multivariate polynomial interpolation, which we first present in a more general form. The practical usefulness of the error formula in multivariate rational interpolation is illustrated by means of a 4-dimensional example, which is only one of the several problems we tested it on. Multivariate interpolation Rational interpolation Interpolation error Yang, Xianglan aut Enthalten in Numerical algorithms Springer US, 1991 55(2010), 2-3 vom: 14. Apr., Seite 233-243 (DE-627)130981753 (DE-600)1075844-6 (DE-576)029154111 1017-1398 nnns volume:55 year:2010 number:2-3 day:14 month:04 pages:233-243 https://doi.org/10.1007/s11075-010-9380-2 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_70 GBV_ILN_2006 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2088 GBV_ILN_4307 GBV_ILN_4317 AR 55 2010 2-3 14 04 233-243 |
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10.1007/s11075-010-9380-2 doi (DE-627)OLC2051159262 (DE-He213)s11075-010-9380-2-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn Cuyt, Annie verfasserin aut A practical error formula for multivariate rational interpolation and approximation 2010 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media, LLC. 2010 Abstract We consider exact and approximate multivariate interpolation of a function f(x1 , . . . , xd) by a rational function pn,m/qn,m(x1 , . . . , xd) and develop an error formula for the difference f − pn,m/qn,m. The similarity with a well-known univariate formula for the error in rational interpolation is striking. Exact interpolation is through point values for f and approximate interpolation is through intervals bounding f. The latter allows for some measurement error on the function values, which is controlled and limited by the nature of the interval data. To achieve this result we make use of an error formula obtained for multivariate polynomial interpolation, which we first present in a more general form. The practical usefulness of the error formula in multivariate rational interpolation is illustrated by means of a 4-dimensional example, which is only one of the several problems we tested it on. Multivariate interpolation Rational interpolation Interpolation error Yang, Xianglan aut Enthalten in Numerical algorithms Springer US, 1991 55(2010), 2-3 vom: 14. Apr., Seite 233-243 (DE-627)130981753 (DE-600)1075844-6 (DE-576)029154111 1017-1398 nnns volume:55 year:2010 number:2-3 day:14 month:04 pages:233-243 https://doi.org/10.1007/s11075-010-9380-2 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_70 GBV_ILN_2006 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2088 GBV_ILN_4307 GBV_ILN_4317 AR 55 2010 2-3 14 04 233-243 |
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A practical error formula for multivariate rational interpolation and approximation |
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Abstract We consider exact and approximate multivariate interpolation of a function f(x1 , . . . , xd) by a rational function pn,m/qn,m(x1 , . . . , xd) and develop an error formula for the difference f − pn,m/qn,m. The similarity with a well-known univariate formula for the error in rational interpolation is striking. Exact interpolation is through point values for f and approximate interpolation is through intervals bounding f. The latter allows for some measurement error on the function values, which is controlled and limited by the nature of the interval data. To achieve this result we make use of an error formula obtained for multivariate polynomial interpolation, which we first present in a more general form. The practical usefulness of the error formula in multivariate rational interpolation is illustrated by means of a 4-dimensional example, which is only one of the several problems we tested it on. © Springer Science+Business Media, LLC. 2010 |
| abstractGer |
Abstract We consider exact and approximate multivariate interpolation of a function f(x1 , . . . , xd) by a rational function pn,m/qn,m(x1 , . . . , xd) and develop an error formula for the difference f − pn,m/qn,m. The similarity with a well-known univariate formula for the error in rational interpolation is striking. Exact interpolation is through point values for f and approximate interpolation is through intervals bounding f. The latter allows for some measurement error on the function values, which is controlled and limited by the nature of the interval data. To achieve this result we make use of an error formula obtained for multivariate polynomial interpolation, which we first present in a more general form. The practical usefulness of the error formula in multivariate rational interpolation is illustrated by means of a 4-dimensional example, which is only one of the several problems we tested it on. © Springer Science+Business Media, LLC. 2010 |
| abstract_unstemmed |
Abstract We consider exact and approximate multivariate interpolation of a function f(x1 , . . . , xd) by a rational function pn,m/qn,m(x1 , . . . , xd) and develop an error formula for the difference f − pn,m/qn,m. The similarity with a well-known univariate formula for the error in rational interpolation is striking. Exact interpolation is through point values for f and approximate interpolation is through intervals bounding f. The latter allows for some measurement error on the function values, which is controlled and limited by the nature of the interval data. To achieve this result we make use of an error formula obtained for multivariate polynomial interpolation, which we first present in a more general form. The practical usefulness of the error formula in multivariate rational interpolation is illustrated by means of a 4-dimensional example, which is only one of the several problems we tested it on. © Springer Science+Business Media, LLC. 2010 |
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A practical error formula for multivariate rational interpolation and approximation |
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