Recursion function-Chebyshev polynomials

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?

Answer 1

[Walter Roberson]

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.

[Tho Gonzalez]

can I use for in else?

[Tho Gonzalez]

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