Why is the loop infinite?

Question

Jacob Savona 2015-3-12

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/182719-why-is-the-loop-infinite

编辑： Jacob Savona 2015-3-12

Trying to do False Position method for the taylor series expansion of sin(x)= sigma(sum)]k=0=inf ((-1^k)/(2*p+1)!)*((x)^(2*k+1)). Input k, bounds between a small number>0 and 3pi/2, Error<.0001. Function should also find the error between the root of the series and the actual root of the function. Error = abs(actual_value-estimate/ actual_value)Actual root should equal pi/2 because I'm solving for sin(x)=0 right? There are two outputs for the function, the estimate root and the error of the root. On one figure plot: 1) Sin(x)-- 2) The polynomial produced from the first k terms of the Taylor expansion-- 3) The false position guesses-- 4). The actual root of sin(x) Code:

function [root,root_error]= HW7_JAS_2(k)
x_lower=.000001;%initial lower bound
x_upper=(3*pi)/2;%initial upper bound
x_true=pi/2;%actual value for x
x_root=0;
lower_b=zeros(1,k+1);
upper_b=zeros(1,k+1);
it=1;
while abs((x_true-x_root)/x_true) > .0001
    for p=0:k
    lower_b(p+1)=((-1^p)/factorial(2*p+1))*((x_lower).^(2*p+1));%put through taylor series expansion
    upper_b(p+1)=((-1^p)/factorial(2*p+1))*((x_upper).^(2*p+1));%put through taylor series expansion
    end
    sumlower_b=sum(lower_b);%f(lower bound)
    sumupper_b=sum(upper_b);%f(upper bound)
    x_root=(x_upper)-(((sumlower_b)*(x_lower-x_upper))/(sumlower_b-sumupper_b));%calculates root
    fx_root=sin(x_root);%f(root)
    if lower_b * fx_root <0
        x_upper= x_root;
    elseif upper_b * fx_root <0
        x_lower= x_root;
    elseif lower_b * fx_root ==0
        root = x_root;
    end
    plot(it,x_root,'g*');%plots false position guesses
    hold on%allows each guess to be plotted
    xlabel('Iterations');
    ylabel('Estimated time values');
    legend('Iterations vs Estimated time values');
    it=it+1;%new iteration
end
root_error= abs((x_true-x_root)/x_true);%error in the root
x=0:.1:2*pi;
plot(x,sin(x),'r-');
xlabel('x values');
ylabel('sin(x) values');
legend('sin(x)');
hold on
x1=0:.1:root;
plot(x1,sin(root),'b-');
xlabel('x values stopped at root value');
ylabel('sin(x) values stopped at sin(root)');
legend('sin(root)');% The polynomial produced from the first k terms of the Taylor expansion
hold on
plot(x_true,sin(x_true),'yx');
xlabel('x values');
ylabel('y values');
legend('Real root of sin(x)');
end