Lab6 is ready for checking

lab6/action.m

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+function action
+  % 1. Interpolation Runge against by uniform       points
+  % 2. Interpolation Runge against by Chebyshev's   points
+  %
+  % 3. Draw plot for 1. and 2. against exact Runge-function (on at least 100 point)
+  % 4. Interpolate function y = 0.5x^2 + 8x^-1 + 8, a = -4, b = -1
+  %      for n = {11,6}
+  % 5. Interpolate by Matlab
+  % 6. Compute errors vectors
+  % 7. Draw plots
+
+  % Runge plot
+  uniform_source  = -1:2/10:1;
+  cheb_source     = cheb(-1,1,11);
+  x               = -1:2/100:1;
+
+  uniform_value   = runge(uniform_source);
+  cheb_value      = runge(cheb_source);
+
+  uniform_y = arrayfun(@(x)( ipol_lagr(uniform_source,uniform_value,x) ),x);
+  cheb_y    = arrayfun(@(x)( ipol_lagr(cheb_source,cheb_value,x) ),x);
+  runge_y   = runge(x);
+
+  subplot(3,1,1);
+  runge_plot = [uniform_y; cheb_y; runge_y];
+  H = plot(x, runge_plot);
+  legend('Uniform','Cheb','Exact');
+
+  % Task plot
+  x = -4:5/100:-1;
+  f = @(x)(0.5*x.^2 + 8*x.^-1 + 8);
+  source_n6 = -4:5/6:-1;
+  source_n11 = -4:5/11:-1;
+
+  value_n6  = f(source_n6);
+  value_n11 = f(source_n11);
+
+  y_n6  = arrayfun(@(x)( ipol_lagr(source_n6,value_n6,x) ),x);
+  y_n11 = arrayfun(@(x)( ipol_lagr(source_n11,value_n11,x) ),x);
+
+  a_n6  = polyfit(source_n6, value_n6, 6);
+  a_n11 = polyfit(source_n11, value_n11, 11);
+
+  y_n6m  = arrayfun(@(x)( polyval(a_n6,x)), x);
+  y_n11m = arrayfun(@(x)( polyval(a_n11,x)), x);
+
+  y_plot = [y_n6; y_n11; y_n6m; y_n11m];
+
+  subplot(3,1,2);
+  plot(x, y_plot);
+  legend('y_n6','y_n11','y_n6m','y_n11m');
+
+  % Error plot
+  y_n6_e = abs(y_n6 - y_n6m)
+  y_n11_e = abs(y_n11 - y_n11m)
+
+  y_error = [y_n6_e; y_n11_e]
+
+  subplot(3,1,3);
+  plot(x, y_error);
+  legend('y_n6_error','y_n11_error');
+end

lab6/cheb.m

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+function xo = cheb(a,b,n)
+  xo = [];
+  for i = 0:n-1
+    r = (a + b)/2 + (b-a)/2*cos(((2*i +1)*pi)/(2*(n-1)+2));
+    xo = [xo r];
+  end
+end

lab6/ipol_lagr.m

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+function y = runge_lagr(xo,yo,x)
+  len = length(xo);
+  r_sum = 0;
+
+  for i = 1:len
+    r_mul = 1;
+
+    for j = 1:len
+      if j == i
+        continue;
+      else
+        r_mul = r_mul * (x - xo(j))/(xo(i) - xo(j));
+      end
+    end
+
+    r_sum = r_sum + yo(i)*r_mul;
+  end
+
+  y = r_sum;
+end

lab6/runge.m

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+function y = runge(x)
+  y = (1 + 25*x.^2).^-1;
+end