atan Taylor Polynomial using polyval function.
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I need to write a function that computes the Taylor polynomial P_n(x) for a general odd number n>=1 using the built-in Matlab function polyval. I have the following function so far for the Taylor polynomial:
[ y ] = ost_arctanTaylor(n, x)
%Computes the Taylor polynomial for f(x) = atan(x)
for i = 1:2:n
y = ((-1).^(i)).*((x.^(2.*i-1))./(2.*i-1));
end
end
I am confused on how to integrate the polyval function into this code. Any help?
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John D'Errico
2015년 2월 17일
You are trying to evaluate the polynomial itself in a loop, although the loop as you wrote it will not do what you think.
The requirement was for polyval to evaluate it, NOT you. So you need to build the coefficients of the polynomial, and pass them into polyval. Let it do the work.
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John D'Errico
2015년 2월 18일
Polyval does not care if you give it zero coefficients. Make the even term coefficients zero. It WILL use those zero coefficients, effectively multiplying by zero, but who cares? You will just create a vector of coefficients, with the HIGHEST order coefficient first. So, for example, the atan series looks like
x - x^3/3 + x^5/5 ...
then the polynomial as polyval would care about it would be:
P = [1/5 0 -1./3 0 1 0];
Don't forget that zero'th order (constant) term at the end. It is important.
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Evelia Coss
2021년 2월 18일
x = input('Number that you want to analyze');
i = input('Number of iterations:');
% Create an cumulative variable
y = 0;
for n = 0:i
arctang = ((-1).^n).*(x.^(2.*n+1)./(2.*n+1));
y = y + arctang;
end
disp('Arctangent value of x is:');
disp(y);
I used the integral of arctang, see the link: https://math.stackexchange.com/questions/29649/why-is-arctanx-x-x3-3x5-5-x7-7-dots
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