Recursion function-Chebyshev polynomials

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Tho Gonzalez
Tho Gonzalez 2016-9-4
编辑： Walter Roberson 2016-9-5
Question:
Chebyshev polynomials are defined recursively. Chebyshev polynomials are separated into two kinds: first and second. Chebyshev polynomials of the first kind, Tn(x), and of the second kind, Un(x), are defined by the following recurrence relations:
Tn(x) = 1 if n = 0;
= x if n = 1;
= 2xTn−1(x) − Tn−2(x) otherwise;
Write a function with header [y] = myChebyshevPoly1(n,x), where y is the n-th Chebyshev polynomial of the first kind evaluated at x.Be sure your function can take array inputs for x. You may assume that x is a row vector. The output variable, y, must be a row vector also.
function [y] = myChebyshevPoly1(n,x)
% y = chebyshev polynimial
%Tn(x) = 1 if n=0
%Tn(x) =x if n=1
%Tn(x) = 2xTn-1(x) - Tn-2(x)
%function can take array
% get array x
xleng=length(x);
if n ==0
y=1;
elseif n==1
y = x;
else
for i= 1: xleng
y= 2*(x)*myChebyshevPoly1(n-1,x) - myChebyshevPoly1(n-2,x);
end
end
end
end
Comment: the code doesnt run because the array can't multiply together, how can I fix this?

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采纳的回答

Walter Roberson
Walter Roberson 2016-9-4
Remember .* instead of *
But notice that in every iteration of your loop, you are overwriting all of y based on all of x. You need to rethink that loop.
  2 个评论
Tho Gonzalez
Tho Gonzalez 2016-9-5
编辑：Walter Roberson 2016-9-5
function y = myChebyshevPoly2(n,x)
%--------------------------------------------------------------------------
% y = myChebyshevPoly2(n,x)
% Chebyshev polynomials of the ?rst kind, Tn(x)
% Author: Hien NGUYEN
% Date: 05 Sept 2016
%--------------------------------------------------------------------------
m = length(x);
if n == 0
y = ones(1,m);
else
if n == 1
y = x;
else
y = 2 * x .* myChebyshevPoly2(n-1,x)-myChebyshevPoly2(n-2,x);
end
end
end

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