% cheb_interp.m
% A near-minimax approximation polynomial interpolation of f(x)
% Using Chebyshev-Gauss points as nodes
function cheb_interp(n,a,b)
f = @(x) cos(x); % Function to be interpolated
xjc = cos(pi*(2*[0:n]+1)./(2*n+2)); % Chebyshev points [-1,1]
xje = linspace(-1,1,n+1); % Equispaced points
xjc = (xjc+1)/2*(b-a)+a; xje = (xje+1)/2*(b-a)+a; % transform to [a,b]
yjc = f(xjc); yje = f(xje); % y-data
xv = linspace(a,b,201); % x-values for figure
fv = f(xv); % y-values of function f(x)
yvc = interp_dd(xjc,yjc,xv); % y-values of interpolation with Cheby
yve = interp_dd(xje,yje,xv); % y-values of interpolation with Equispace pts
% plot
plot(xv,fv-yvc,'r',xv,fv-yve,'b'); grid
title('Error plots of interpolation using Chebyshev(Red), Equispace(Blue)')
xlabel X ; ylabel Y
%%%% Subroutine %%%
% Find interpolation using divide difference method
function yvalues = interp_dd(nodes,fnodes,xvalues);
m = length(nodes);
dd = divdif(nodes,fnodes);
yvalues = dd(m)*ones(size(xvalues));
for i=m-1:-1:1
yvalues = dd(i) + ( xvalues-nodes(i) ).*yvalues;
end
% Find divide differences
function dd = divdif(x,f)
dd = f;
m = length(x);
for i=2:m
for j=m:-1:i
dd(j) = ( dd(j)-dd(j-1) )/( x(j)-x(j-i+1) );
end
end
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이름검색
Least-squares method to approximate a function
수학2 성적
