How do I make this function check error tolerance and the max number of iterations?

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Tony 2016-9-7

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https://ww2.mathworks.cn/matlabcentral/answers/302319-how-do-i-make-this-function-check-error-tolerance-and-the-max-number-of-iterations

评论： Walter Roberson 2016-9-8

This is the code I have so far

function [y,N] = sine_taylorN(x,es)
% This function evaluates the Taylor's series (Maclaurin's
% series) of the sine function evaluated at x and determines the number of
% terms required for convergence based on relative error.
% Inputs/Output:
%   x  = scalar value to be evaluated at
%   es = stopping criterion requited for relative error in %
%   N  = number of terms required in the series for convergence
%        to relative error accuracy of es
%   y  = approximate value of sine(x) by Maclaurin's series
y = 0; er = 100; k = 0;  % Initializations
yexact = sin(x);
while er >= es
    k = k +1;
    y = y + (-1)^(k+1)*x^(2*k-1)/factorial(2*k-1);
    er = abs((yexact-y)/yexact)*100;  % relative error in percentage
end
N = k;