数学建模--插值和拟合实例

数学建模–插值和拟合实例

原文：http://blog.csdn.net/qq_34861102/article/details/76945362

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求导数：

 - dV = gradient(V,t);

较为准确的插值（形成一个平滑的曲线，可以看最后一问）：

pp = csape(t0,dV);
fdv = ppval(pp,tt0);
plot(tt0,fdv);

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• 拟合(polyfit和polyval)

  

  a = [1 -6 5 3];
  x = -5:0.3:5;
  y = polyval(a,x);
  subplot(2,2,1);
  plot(x,y,'-');
  title('原图形');
  L = length(x);
  no = randn(1,L);
  %拟合
  b1 = polyfit(x,y+no,2);
  b2 = polyfit(x,y+no,3);
  b3 = polyfit(x,y+no,4);
  
  y1 = polyval(b1,x);
  y2 = polyval(b2,x);
  y3 = polyval(b3,x);
  
  subplot(2,2,2);
  plot(x,y1,'-');
  title('2图形');
  
  subplot(2,2,3);
  plot(x,y2,'-');
  title('3图形');
  
  subplot(2,2,4);
  plot(x,y3,'-');
  title('4图形');

  

  

  x = [1 2 3 4 5 6 7 8];
  y0 = [15.3 20.5 27.4 36.6 49.1 65.6 87.87 117.6];
  y = log(y0);
  b = polyfit(x,y,1);
  a = exp(b(2))
  k = (b(1)

  • 插值

  

  t = [0 3316 6635 10619 13937 17921 21240 25223 28543 32284 35932 39332 39435 43318 44636 49953 53936 57254 60574 64554 68535 71854 75021 79254 82649 85968 89953 93270];
  h = [3175 3110 3054 2994 2947 2892 2850 2795 2752 2697 -1 -1 3550 3445 3350 3260 3167 3087 3012 2927 2842 2767 2697 -1 -1 3475 3397 3340];
  t0 = t./3600;
  V = pi/4*(57*0.3024).*h*0.3024;
  dV = -gradient(V,t0);
  no1 = find(h == -1);
  no2 = [no1(1) - 1 : no1(2) + 1, no1(3) - 1:no1(4) + 1 ];
  t0(no2) = [];
  dV(no2) = [];
  tt0 = 0:0.05:t0(end);
  pp = csape(t0,dV);
  fdv = ppval(pp,tt0);
  plot(tt0,fdv);