An application of a summation formula to numerical computation of integrals over the sphere
Summary This paper discusses a method to approximate an integral over the (unit) sphere by a linear combination of the values of the integrand at given points. The main concept of this method is the observation, that on the sphere for each sufficiently smooth function the integral can be expressed b...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Freeden, W. [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
1978 |
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| Schlagwörter: |
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| Anmerkung: |
© Bureau Central de L'Association Internationale de Géodésie 1978 |
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| Übergeordnetes Werk: |
Enthalten in: Journal of geodesy - Berlin : Springer, 1995, 52(1978), 3 vom: Sept., Seite 165-175 |
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| Übergeordnetes Werk: |
volume:52 ; year:1978 ; number:3 ; month:09 ; pages:165-175 |
| Links: |
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| DOI / URN: |
10.1007/BF02521770 |
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| Katalog-ID: |
SPR001575902 |
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| 041 | |a eng | ||
| 100 | 1 | |a Freeden, W. |e verfasserin |4 aut | |
| 245 | 1 | 3 | |a An application of a summation formula to numerical computation of integrals over the sphere |
| 264 | 1 | |c 1978 | |
| 336 | |a Text |b txt |2 rdacontent | ||
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| 338 | |a Online-Ressource |b cr |2 rdacarrier | ||
| 500 | |a © Bureau Central de L'Association Internationale de Géodésie 1978 | ||
| 520 | |a Summary This paper discusses a method to approximate an integral over the (unit) sphere by a linear combination of the values of the integrand at given points. The main concept of this method is the observation, that on the sphere for each sufficiently smooth function the integral can be expressed by a summation formula. A method is given for optimizing the accuracy of the computation for a given set of sample points for the function being integrated. | ||
| 650 | 4 | |a Unit Sphere |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Spherical Harmonic |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Orthogonal Transformation |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Summation Formula |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Cubature Formula |7 (dpeaa)DE-He213 | |
| 773 | 0 | 8 | |i Enthalten in |t Journal of geodesy |d Berlin : Springer, 1995 |g 52(1978), 3 vom: Sept., Seite 165-175 |w (DE-627)271175389 |w (DE-600)1478938-3 |x 1432-1394 |7 nnns |
| 773 | 1 | 8 | |g volume:52 |g year:1978 |g number:3 |g month:09 |g pages:165-175 |
| 856 | 4 | 0 | |u https://dx.doi.org/10.1007/BF02521770 |z lizenzpflichtig |3 Volltext |
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| 952 | |d 52 |j 1978 |e 3 |c 09 |h 165-175 | ||
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w f wf |
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article:14321394:1978----::nplctooaumtofruaoueiacmuainf |
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1978 |
| publishDate |
1978 |
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10.1007/BF02521770 doi (DE-627)SPR001575902 (SPR)BF02521770-e DE-627 ger DE-627 rakwb eng Freeden, W. verfasserin aut An application of a summation formula to numerical computation of integrals over the sphere 1978 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Bureau Central de L'Association Internationale de Géodésie 1978 Summary This paper discusses a method to approximate an integral over the (unit) sphere by a linear combination of the values of the integrand at given points. The main concept of this method is the observation, that on the sphere for each sufficiently smooth function the integral can be expressed by a summation formula. A method is given for optimizing the accuracy of the computation for a given set of sample points for the function being integrated. Unit Sphere (dpeaa)DE-He213 Spherical Harmonic (dpeaa)DE-He213 Orthogonal Transformation (dpeaa)DE-He213 Summation Formula (dpeaa)DE-He213 Cubature Formula (dpeaa)DE-He213 Enthalten in Journal of geodesy Berlin : Springer, 1995 52(1978), 3 vom: Sept., Seite 165-175 (DE-627)271175389 (DE-600)1478938-3 1432-1394 nnns volume:52 year:1978 number:3 month:09 pages:165-175 https://dx.doi.org/10.1007/BF02521770 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_121 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_224 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_374 GBV_ILN_602 GBV_ILN_647 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2018 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2043 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2158 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2193 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_2808 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4277 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4346 GBV_ILN_4367 GBV_ILN_4393 GBV_ILN_4700 GBV_ILN_4753 AR 52 1978 3 09 165-175 |
| spelling |
10.1007/BF02521770 doi (DE-627)SPR001575902 (SPR)BF02521770-e DE-627 ger DE-627 rakwb eng Freeden, W. verfasserin aut An application of a summation formula to numerical computation of integrals over the sphere 1978 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Bureau Central de L'Association Internationale de Géodésie 1978 Summary This paper discusses a method to approximate an integral over the (unit) sphere by a linear combination of the values of the integrand at given points. The main concept of this method is the observation, that on the sphere for each sufficiently smooth function the integral can be expressed by a summation formula. A method is given for optimizing the accuracy of the computation for a given set of sample points for the function being integrated. Unit Sphere (dpeaa)DE-He213 Spherical Harmonic (dpeaa)DE-He213 Orthogonal Transformation (dpeaa)DE-He213 Summation Formula (dpeaa)DE-He213 Cubature Formula (dpeaa)DE-He213 Enthalten in Journal of geodesy Berlin : Springer, 1995 52(1978), 3 vom: Sept., Seite 165-175 (DE-627)271175389 (DE-600)1478938-3 1432-1394 nnns volume:52 year:1978 number:3 month:09 pages:165-175 https://dx.doi.org/10.1007/BF02521770 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_121 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_224 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_374 GBV_ILN_602 GBV_ILN_647 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2018 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2043 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2158 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2193 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_2808 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4277 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4346 GBV_ILN_4367 GBV_ILN_4393 GBV_ILN_4700 GBV_ILN_4753 AR 52 1978 3 09 165-175 |
| allfields_unstemmed |
10.1007/BF02521770 doi (DE-627)SPR001575902 (SPR)BF02521770-e DE-627 ger DE-627 rakwb eng Freeden, W. verfasserin aut An application of a summation formula to numerical computation of integrals over the sphere 1978 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Bureau Central de L'Association Internationale de Géodésie 1978 Summary This paper discusses a method to approximate an integral over the (unit) sphere by a linear combination of the values of the integrand at given points. The main concept of this method is the observation, that on the sphere for each sufficiently smooth function the integral can be expressed by a summation formula. A method is given for optimizing the accuracy of the computation for a given set of sample points for the function being integrated. Unit Sphere (dpeaa)DE-He213 Spherical Harmonic (dpeaa)DE-He213 Orthogonal Transformation (dpeaa)DE-He213 Summation Formula (dpeaa)DE-He213 Cubature Formula (dpeaa)DE-He213 Enthalten in Journal of geodesy Berlin : Springer, 1995 52(1978), 3 vom: Sept., Seite 165-175 (DE-627)271175389 (DE-600)1478938-3 1432-1394 nnns volume:52 year:1978 number:3 month:09 pages:165-175 https://dx.doi.org/10.1007/BF02521770 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_121 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_224 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_374 GBV_ILN_602 GBV_ILN_647 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2018 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2043 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2158 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2193 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_2808 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4277 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4346 GBV_ILN_4367 GBV_ILN_4393 GBV_ILN_4700 GBV_ILN_4753 AR 52 1978 3 09 165-175 |
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10.1007/BF02521770 doi (DE-627)SPR001575902 (SPR)BF02521770-e DE-627 ger DE-627 rakwb eng Freeden, W. verfasserin aut An application of a summation formula to numerical computation of integrals over the sphere 1978 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Bureau Central de L'Association Internationale de Géodésie 1978 Summary This paper discusses a method to approximate an integral over the (unit) sphere by a linear combination of the values of the integrand at given points. The main concept of this method is the observation, that on the sphere for each sufficiently smooth function the integral can be expressed by a summation formula. A method is given for optimizing the accuracy of the computation for a given set of sample points for the function being integrated. Unit Sphere (dpeaa)DE-He213 Spherical Harmonic (dpeaa)DE-He213 Orthogonal Transformation (dpeaa)DE-He213 Summation Formula (dpeaa)DE-He213 Cubature Formula (dpeaa)DE-He213 Enthalten in Journal of geodesy Berlin : Springer, 1995 52(1978), 3 vom: Sept., Seite 165-175 (DE-627)271175389 (DE-600)1478938-3 1432-1394 nnns volume:52 year:1978 number:3 month:09 pages:165-175 https://dx.doi.org/10.1007/BF02521770 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_121 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_224 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_374 GBV_ILN_602 GBV_ILN_647 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2018 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2043 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2158 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2193 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_2808 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4277 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4346 GBV_ILN_4367 GBV_ILN_4393 GBV_ILN_4700 GBV_ILN_4753 AR 52 1978 3 09 165-175 |
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10.1007/BF02521770 doi (DE-627)SPR001575902 (SPR)BF02521770-e DE-627 ger DE-627 rakwb eng Freeden, W. verfasserin aut An application of a summation formula to numerical computation of integrals over the sphere 1978 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Bureau Central de L'Association Internationale de Géodésie 1978 Summary This paper discusses a method to approximate an integral over the (unit) sphere by a linear combination of the values of the integrand at given points. The main concept of this method is the observation, that on the sphere for each sufficiently smooth function the integral can be expressed by a summation formula. A method is given for optimizing the accuracy of the computation for a given set of sample points for the function being integrated. Unit Sphere (dpeaa)DE-He213 Spherical Harmonic (dpeaa)DE-He213 Orthogonal Transformation (dpeaa)DE-He213 Summation Formula (dpeaa)DE-He213 Cubature Formula (dpeaa)DE-He213 Enthalten in Journal of geodesy Berlin : Springer, 1995 52(1978), 3 vom: Sept., Seite 165-175 (DE-627)271175389 (DE-600)1478938-3 1432-1394 nnns volume:52 year:1978 number:3 month:09 pages:165-175 https://dx.doi.org/10.1007/BF02521770 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_121 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_224 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_374 GBV_ILN_602 GBV_ILN_647 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2018 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2043 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2158 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2193 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_2808 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4277 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4346 GBV_ILN_4367 GBV_ILN_4393 GBV_ILN_4700 GBV_ILN_4753 AR 52 1978 3 09 165-175 |
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English |
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Enthalten in Journal of geodesy 52(1978), 3 vom: Sept., Seite 165-175 volume:52 year:1978 number:3 month:09 pages:165-175 |
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Enthalten in Journal of geodesy 52(1978), 3 vom: Sept., Seite 165-175 volume:52 year:1978 number:3 month:09 pages:165-175 |
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Freeden, W. |
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Freeden, W. misc Unit Sphere misc Spherical Harmonic misc Orthogonal Transformation misc Summation Formula misc Cubature Formula An application of a summation formula to numerical computation of integrals over the sphere |
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application of a summation formula to numerical computation of integrals over the sphere |
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An application of a summation formula to numerical computation of integrals over the sphere |
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Summary This paper discusses a method to approximate an integral over the (unit) sphere by a linear combination of the values of the integrand at given points. The main concept of this method is the observation, that on the sphere for each sufficiently smooth function the integral can be expressed by a summation formula. A method is given for optimizing the accuracy of the computation for a given set of sample points for the function being integrated. © Bureau Central de L'Association Internationale de Géodésie 1978 |
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Summary This paper discusses a method to approximate an integral over the (unit) sphere by a linear combination of the values of the integrand at given points. The main concept of this method is the observation, that on the sphere for each sufficiently smooth function the integral can be expressed by a summation formula. A method is given for optimizing the accuracy of the computation for a given set of sample points for the function being integrated. © Bureau Central de L'Association Internationale de Géodésie 1978 |
| abstract_unstemmed |
Summary This paper discusses a method to approximate an integral over the (unit) sphere by a linear combination of the values of the integrand at given points. The main concept of this method is the observation, that on the sphere for each sufficiently smooth function the integral can be expressed by a summation formula. A method is given for optimizing the accuracy of the computation for a given set of sample points for the function being integrated. © Bureau Central de L'Association Internationale de Géodésie 1978 |
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