MathTL: numerics/gauss_data.h Source File

00001 // -*- c++ -*-
00002 
00003 // +--------------------------------------------------------------------+
00004 // | This file is part of MathTL - the Mathematical Template Library    |
00005 // |                                                                    |
00006 // | Copyright (c) 2002-2009                                            |
00007 // | Thorsten Raasch, Manuel Werner                                     |
00008 // +--------------------------------------------------------------------+
00009 
00010 #ifndef _MATHTL_GAUSS_DATA_H
00011 #define _MATHTL_GAUSS_DATA_H
00012 
00016 static double GaussPoints[][10] = {
00017   {+0.0},
00018   {-0.5773502691896258,  // -sqrt(3)/3
00019    +0.5773502691896258}, // +sqrt(3)/3
00020   {-0.7745966692414834,  // -sqrt(15)/5
00021    +0.0,
00022    +0.7745966692414834}, // +sqrt(15)/5
00023   {-0.8611363115940526,  // -sqrt(525+70*sqrt(30))/35
00024    -0.3399810435848563,  // -sqrt(525-70*sqrt(30))/35
00025    +0.3399810435848563,  // +sqrt(525-70*sqrt(30))/35
00026    +0.8611363115940526}, // +sqrt(525+70*sqrt(30))/35
00027   {-0.9061798459386640,  // -sqrt(245+14*sqrt(70))/21
00028    -0.5384693101056831,  // -sqrt(245-14*sqrt(70))/21
00029    +0.0,
00030    +0.5384693101056831,  // +sqrt(245-14*sqrt(70))/21
00031    +0.9061798459386640}, // +sqrt(245+14*sqrt(70))/21
00032   {-0.9324695142031520,  // from here on Maple-checked!
00033    -0.6612093864662645,  // (16 significant digits)
00034    -0.2386191860831972,
00035    +0.2386191860831972,
00036    +0.6612093864662645,
00037    +0.9324695142031520},
00038   {-0.9491079123427585,
00039    -0.7415311855993944,
00040    -0.4058451513773972,
00041    +0.0,
00042    +0.4058451513773972,
00043    +0.7415311855993944,
00044    +0.9491079123427585},
00045   {-0.9602898564975362,
00046    -0.7966664774136267,
00047    -0.5255324099163290,
00048    -0.1834346424956498,
00049    +0.1834346424956498,
00050    +0.5255324099163290,
00051    +0.7966664774136267,
00052    +0.9602898564975362},
00053   {-0.9681602395076261,
00054    -0.8360311073266358,
00055    -0.6133714327005904,
00056    -0.3242534234038089,
00057    +0.0,
00058    +0.3242534234038089,
00059    +0.6133714327005904,
00060    +0.8360311073266358,
00061    +0.9681602395076261},
00062   {-0.9739065285171717,
00063    -0.8650633666889845,
00064    -0.6794095682990244,
00065    -0.4333953941292472,
00066    -0.1488743389816312,
00067    +0.1488743389816312,
00068    +0.4333953941292472,
00069    +0.6794095682990244,
00070    +0.8650633666889845,
00071    +0.9739065285171717}
00072 };
00073 
00074 static double GaussWeights[][10] = {
00075   {+1.0},
00076   {+0.5,
00077    +0.5},
00078   {+0.2777777777777778,     // 5/18
00079    +0.4444444444444444,     // 4/9
00080    +0.2777777777777778},    // 5/18
00081   {+0.1739274225687269,     // (3*sqrt(30)-5)*sqrt(30)/360
00082    +0.3260725774312731,     // (3*sqrt(30)+5)*sqrt(30)/360
00083    +0.3260725774312731,     // (3*sqrt(30)+5)*sqrt(30)/360
00084    +0.1739274225687269},    // (3*sqrt(30)-5)*sqrt(30)/360
00085   {+0.1184634425280945,     // 3*(7+5*sqrt(70))*sqrt(70)/200/(35+2*sqrt(70))
00086    +0.2393143352496832,     // 3*(-7+5*sqrt(70))*sqrt(70)/200/(35-2*sqrt(70))
00087    +0.2844444444444444,     // 64/225
00088    +0.2393143352496832,     // 3*(-7+5*sqrt(70))*sqrt(70)/200/(35-2*sqrt(70))
00089    +0.1184634425280945},    // 3*(7+5*sqrt(70))*sqrt(70)/200/(35+2*sqrt(70))
00090   {+0.8566224618958517e-1,  // from here on Maple-checked!
00091    +0.1803807865240693,     // (16 significant digits)
00092    +0.2339569672863455,
00093    +0.2339569672863455,
00094    +0.1803807865240693,
00095    +0.8566224618958517e-1},
00096   {+0.6474248308443485e-1,
00097    +0.1398526957446383,
00098    +0.1909150252525595,
00099    +0.2089795918367347,
00100    +0.1909150252525595,
00101    +0.1398526957446383,
00102    +0.6474248308443485e-1},
00103   {+0.5061426814518813e-1,
00104    +0.1111905172266872,
00105    +0.1568533229389436,
00106    +0.1813418916891810,
00107    +0.1813418916891810,
00108    +0.1568533229389436,
00109    +0.1111905172266872,
00110    +0.5061426814518813e-1},
00111   {+0.4063719418078721e-1,
00112    +0.9032408034742870e-1,
00113    +0.1303053482014677,
00114    +0.1561735385200014,
00115    +0.1651196775006299,
00116    +0.1561735385200014,
00117    +0.1303053482014677,
00118    +0.9032408034742870e-1,
00119    +0.4063719418078721e-1},
00120   {+0.3333567215434407e-1,
00121    +0.7472567457529030e-1,
00122    +0.1095431812579910,
00123    +0.1346333596549982,
00124    +0.1477621123573764,
00125    +0.1477621123573764,
00126    +0.1346333596549982,
00127    +0.1095431812579910,
00128    +0.7472567457529030e-1,
00129    +0.3333567215434407e-1}
00130 };
00131 
00132 #endif