glagtable.m

D:matlab mmintegrate.rar数值积分

function [x,w] = GLagTable(n)
% GLagTable  Nodes and weights for Gauss-Laguerre quadrature of order n<=15
%
% Synopsis:  [x,w] = GLagTable(n)
%
% Input:     n = number of nodes in quadrature rule, maximum: n = 25
%
% Output:    x = vector of nodes
%            w = vector of weights

% Numerical generated by makeGLagTable, and agree with those
% in "Handbook of Mathematical Functions", Abramowitz and Stegun, eds.,
% 1965 Dover (reprint), Table 25.9, p. 923

nn = fix(n);                %  Make sure number of nodes is an integer
x = zeros(nn,1);  w = x;    %  Preallocate x and w vectors

switch nn
  case 1
%      nodes                           weights
    x(1) =  1.000000000000000;     w(1) =    1.000000000000000e+00;

  case 2
%      nodes                           weights
    x(1) =  0.585786437626905;     w(1) =    8.535533905932735e-01;
    x(2) =  3.414213562373095;     w(2) =    1.464466094067262e-01;

  case 3
%      nodes                           weights
    x(1) =  0.415774556783479;     w(1) =    7.110930099291731e-01;
    x(2) =  2.294280360279041;     w(2) =    2.785177335692408e-01;
    x(3) =  6.289945082937479;     w(3) =    1.038925650158613e-02;

  case 4
%      nodes                           weights
    x(1) =  0.322547689619392;     w(1) =    6.031541043416339e-01;
    x(2) =  1.745761101158348;     w(2) =    3.574186924378002e-01;
    x(3) =  4.536620296921129;     w(3) =    3.888790851500540e-02;
    x(4) =  9.395070912301135;     w(4) =    5.392947055613275e-04;

  case 5
%      nodes                           weights
    x(1) =  0.263560319718141;     w(1) =    5.217556105828087e-01;
    x(2) =  1.413403059106517;     w(2) =    3.986668110831758e-01;
    x(3) =  3.596425771040723;     w(3) =    7.594244968170771e-02;
    x(4) =  7.085810005858831;     w(4) =    3.611758679922054e-03;
    x(5) = 12.640800844275784;     w(5) =    2.336997238577616e-05;

  case 6
%      nodes                           weights
    x(1) =  0.222846604179260;     w(1) =    4.589646739499636e-01;
    x(2) =  1.188932101672623;     w(2) =    4.170008307721207e-01;
    x(3) =  2.992736326059315;     w(3) =    1.133733820740450e-01;
    x(4) =  5.775143569104510;     w(4) =    1.039919745314910e-02;
    x(5) =  9.837467418382586;     w(5) =    2.610172028149328e-04;
    x(6) = 15.982873980601701;     w(6) =    8.985479064296189e-07;

  case 7
%      nodes                           weights
    x(1) =  0.193043676560362;     w(1) =    4.093189517012742e-01;
    x(2) =  1.026664895339192;     w(2) =    4.218312778617200e-01;
    x(3) =  2.567876744950745;     w(3) =    1.471263486575053e-01;
    x(4) =  4.900353084526483;     w(4) =    2.063351446871692e-02;
    x(5) =  8.182153444562857;     w(5) =    1.074010143280745e-03;
    x(6) = 12.734180291797818;     w(6) =    1.586546434856409e-05;
    x(7) = 19.395727862262543;     w(7) =    3.170315478995578e-08;

  case 8
%      nodes                           weights
    x(1) =  0.170279632305101;     w(1) =    3.691885893416376e-01;
    x(2) =  0.903701776799380;     w(2) =    4.187867808143428e-01;
    x(3) =  2.251086629866130;     w(3) =    1.757949866371717e-01;
    x(4) =  4.266700170287658;     w(4) =    3.334349226121565e-02;
    x(5) =  7.045905402393465;     w(5) =    2.794536235225675e-03;
    x(6) = 10.758516010180994;     w(6) =    9.076508773358203e-05;
    x(7) = 15.740678641278011;     w(7) =    8.485746716272529e-07;
    x(8) = 22.863131736889272;     w(8) =    1.048001174871506e-09;

  case 9
%      nodes                           weights
    x(1) =  0.152322227731809;     w(1) =    3.361264217979623e-01;
    x(2) =  0.807220022742256;     w(2) =    4.112139804239842e-01;
    x(3) =  2.005135155619348;     w(3) =    1.992875253708855e-01;
    x(4) =  3.783473973331234;     w(4) =    4.746056276565155e-02;
    x(5) =  6.204956777876616;     w(5) =    5.599626610794583e-03;
    x(6) =  9.372985251687579;     w(6) =    3.052497670932107e-04;
    x(7) = 13.466236911092109;     w(7) =    6.592123026075337e-06;
    x(8) = 18.833597788991714;     w(8) =    4.110769330349547e-08;
    x(9) = 26.374071890927379;     w(9) =    3.290874030350721e-11;

  case 10
%      nodes                           weights
    x(1) =  0.137793470540492;     w(1) =    3.084411157650207e-01;
    x(2) =  0.729454549503171;     w(2) =    4.011199291552737e-01;
    x(3) =  1.808342901740316;     w(3) =    2.180682876118094e-01;
    x(4) =  3.401433697854900;     w(4) =    6.208745609867763e-02;
    x(5) =  5.552496140063805;     w(5) =    9.501516975181109e-03;
    x(6) =  8.330152746764501;     w(6) =    7.530083885875356e-04;
    x(7) = 11.843785837900070;     w(7) =    2.825923349599557e-05;
    x(8) = 16.279257831378104;     w(8) =    4.249313984962717e-07;
    x(9) = 21.996585811980772;     w(9) =    1.839564823979625e-09;
    x(10) = 29.920697012273898;     w(10) =    9.911827219609029e-13;

  case 11
%      nodes                           weights
    x(1) =  0.125796442187968;     w(1) =    2.849332128942006e-01;
    x(2) =  0.665418255839228;     w(2) =    3.897208895278491e-01;
    x(3) =  1.647150545872169;     w(3) =    2.327818318489914e-01;
    x(4) =  3.091138143035254;     w(4) =    7.656445354619669e-02;
    x(5) =  5.029284401579831;     w(5) =    1.439328276735067e-02;
    x(6) =  7.509887863806610;     w(6) =    1.518880846484876e-03;
    x(7) = 10.605950999546968;     w(7) =    8.513122435471903e-05;
    x(8) = 14.431613758064179;     w(8) =    2.292403879574509e-06;
    x(9) = 19.178857403214653;     w(9) =    2.486353702767818e-08;
    x(10) = 25.217709339677569;     w(10) =    7.712626933691196e-11;
    x(11) = 33.497192847175533;     w(11) =    2.883775868323628e-14;

  case 12
%      nodes                           weights
    x(1) =  0.115722117358021;     w(1) =    2.647313710554435e-01;
    x(2) =  0.611757484515131;     w(2) =    3.777592758731382e-01;
    x(3) =  1.512610269776419;     w(3) =    2.440820113198774e-01;
    x(4) =  2.833751337743509;     w(4) =    9.044922221168074e-02;
    x(5) =  4.599227639418353;     w(5) =    2.010238115463406e-02;
    x(6) =  6.844525453115181;     w(6) =    2.663973541865321e-03;
    x(7) =  9.621316842456871;     w(7) =    2.032315926629993e-04;
    x(8) = 13.006054993306350;     w(8) =    8.365055856819753e-06;
    x(9) = 17.116855187462260;     w(9) =    1.668493876540914e-07;
    x(10) = 22.151090379396983;     w(10) =    1.342391030515027e-09;
    x(11) = 28.487967250983992;     w(11) =    3.061601635035012e-12;
    x(12) = 37.099121044466926;     w(12) =    8.148077467426124e-16;

  case 13
%      nodes                           weights
    x(1) =  0.107142388472252;     w(1) =    2.471887084299629e-01;
    x(2) =  0.566131899040402;     w(2) =    3.656888229005218e-01;
    x(3) =  1.398564336451020;     w(3) =    2.525624200576586e-01;
    x(4) =  2.616597108406412;     w(4) =    1.034707580241836e-01;
    x(5) =  4.238845929017034;     w(5) =    2.643275441556165e-02;
    x(6) =  6.292256271140078;     w(6) =    4.220396040254745e-03;
    x(7) =  8.815001941186980;     w(7) =    4.118817704727351e-04;
    x(8) = 11.861403588811243;     w(8) =    2.351547398155331e-05;
    x(9) = 15.510762037703755;     w(9) =    7.317311620249146e-07;
    x(10) = 19.884635663880221;     w(10) =    1.108841625703973e-08;
    x(11) = 25.185263864677768;     w(11) =    6.770826692205850e-11;
    x(12) = 31.800386301947270;     w(12) =    1.159979959905077e-13;
    x(13) = 40.723008669265582;     w(13) =    2.245093203892749e-17;

  case 14
%      nodes                           weights
    x(1) =  0.099747507032597;     w(1) =    2.318155771448655e-01;
    x(2) =  0.526857648851903;     w(2) =    3.537846915975430e-01;
    x(3) =  1.300629121251497;     w(3) =    2.587346102454282e-01;
    x(4) =  2.430801078730846;     w(4) =    1.154828935569231e-01;
    x(5) =  3.932102822293219;     w(5) =    3.319209215933736e-02;
    x(6) =  5.825536218301709;     w(6) =    6.192869437006579e-03;
    x(7) =  8.140240141565144;     w(7) =    7.398903778673880e-04;
    x(8) = 10.916499507366012;     w(8) =    5.490719466841721e-05;
    x(9) = 14.210805011161286;     w(9) =    2.409585764085366e-06;
    x(10) = 18.104892220218115;     w(10) =    5.801543981676485e-08;
    x(11) = 22.723381628269642;     w(11) =    6.819314692484891e-10;
    x(12) = 28.272981723248211;     w(12) =    3.221207751894853e-12;
    x(13) = 35.149443660592432;     w(13) =    4.221352440516609e-15;
    x(14) = 44.366081711117417;     w(14) =    6.052375022289181e-19;

  case 16
%      nodes                           weights
    x(1) =  0.087649410478928;     w(1) =    2.061517149578016e-01;
    x(2) =  0.462696328915081;     w(2) =    3.310578549508837e-01;
    x(3) =  1.141057774831228;     w(3) =    2.657957776442144e-01;
    x(4) =  2.129283645098383;     w(4) =    1.362969342963770e-01;
    x(5) =  3.437086633893207;     w(5) =    4.732892869412523e-02;
    x(6) =  5.078018614549770;     w(6) =    1.129990008033939e-02;
    x(7) =  7.070338535048236;     w(7) =    1.849070943526311e-03;
    x(8) =  9.438314336391938;     w(8) =    2.042719153082776e-04;
    x(9) = 12.214223368866158;     w(9) =    1.484458687398130e-05;
    x(10) = 15.441527368781626;     w(10) =    6.828319330871144e-07;
    x(11) = 19.180156856753154;     w(11) =    1.881024841079652e-08;
    x(12) = 23.515905693991925;     w(12) =    2.862350242973877e-10;
    x(13) = 28.578729742882135;     w(13) =    2.127079033224117e-12;
    x(14) = 34.583398702286665;     w(14) =    6.297967002517678e-15;
    x(15) = 41.940452647688311;     w(15) =    5.050473700035650e-18;
    x(16) = 51.701160339543343;     w(16) =    4.161462370372826e-22;

  case 17
%      nodes                           weights
    x(1) =  0.082638214708948;     w(1) =    1.953322052517708e-01;
    x(2) =  0.436150323558711;     w(2) =    3.203753572745405e-01;
    x(3) =  1.075176577511429;     w(3) =    2.673297263571708e-01;
    x(4) =  2.005193531649233;     w(4) =    1.451298543587585e-01;
    x(5) =  3.234256124047443;     w(5) =    5.443694324533853e-02;
    x(6) =  4.773513513700198;     w(6) =    1.435729776606183e-02;
    x(7) =  6.637829205364961;     w(7) =    2.662824735572763e-03;
    x(8) =  8.846685511169797;     w(8) =    3.436797271563025e-04;
    x(9) = 11.425529319373348;     w(9) =    3.027551783782896e-05;
    x(10) = 14.407823037481313;     w(10) =    1.768515053231681e-06;
    x(11) = 17.838284730701147;     w(11) =    6.576272886810442e-08;
    x(12) = 21.778268257722296;     w(12) =    1.469730932159536e-09;
    x(13) = 26.315317811248800;     w(13) =    1.816910362555468e-11;
    x(14) = 31.581771680456761;     w(14) =    1.095401388928672e-13;
    x(15) = 37.796093837477137;     w(15) =    2.617373882223325e-16;
    x(16) = 45.375716533988971;     w(16) =    1.672935693146154e-19;
    x(17) = 55.389751789839607;     w(17) =    1.065626316274051e-23;

  case 18
%      nodes                           weights
    x(1) =  0.078169166669706;     w(1) =    1.855886031469193e-01;
    x(2) =  0.412490085259130;     w(2) =    3.101817663702247e-01;
    x(3) =  1.016520179623539;     w(3) =    2.678665671485359e-01;
    x(4) =  1.894888509969760;     w(4) =    1.529797474680750e-01;
    x(5) =  3.054353113202662;     w(5) =    6.143491786096171e-02;
    x(6) =  4.504205538889891;     w(6) =    1.768721308077299e-02;