hw8_part2_solutions

hw8_part2_solutions - ylabel'f(x Problem 5 MATLAB Command...

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Problem 4
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MATLAB Command Window EDU>> HW8_Prob4 MATLAB m-file HW8_Prob4.m % original function xx = linspace(-1,1,100); yy_o = 1./(1+25*xx.^2); % part a x = linspace(-1,1,11); xa = x; y = 1./(1+25*x.^2); ya = y; p = polyfit(x,y,length(x)-1); pa = p; yy = polyval(p,xx); yy_a = yy; % part b i = 1:11; x = cos((2*i-1)/11*pi/2); xb = x; y = 1./(1+25*x.^2); yb = y; p = polyfit(x,y,length(x)-1); pb = p; [yy] = polyval(p,xx); yy_b = yy; % plot plot(xx,yy_o,'k'); hold on; plot(xa,ya,'om'); plot(xb,yb,'ob'); plot(xx,yy_a,'m') plot(xx,yy_b,'b') legend('original function','evenly spaced points','Chebysev points','polynomial by even spaced points','polynomial by Chebysev points') title('Comparison of Runge''s function with 10th-order polynomials') xlabel('x')
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