This is an iterative program, but the result is wrong. Why?

这是一个迭代法的程序，但结果是错误的，这是为什么呢？

[Steven Lord]

What purpose do the sign calls in your code serve?

[VBBV]

Hi @希媛 the comparison of output values from the function based on some inputs is not a correct way to test the program correctness since sin & cos functions exhibit sign changes according to different values of inputs

g = @(x) cos(x);
p = 20; % initial value
xc = fpi(g,p,1e-6)

xc = 0.9179

cos(g(p))

ans = 0.9179

function xc = fpi(g,x0,tol)
   x(1) = g(x0); % <<<
   x(2) = g(x(1));
   i = 1;
  while abs(sign(i+1)-sign(x(i))) > tol
     x(i+2) = g(x(i+1));
     i=i+1;
  end
  xc = x(end);
end

Answer 1

[Torsten]

g = @(x) cos(x);
xc = fpi(g,1,1e-6)

xc = 0.7391

g(xc)

ans = 0.7391

function xc = fpi(g,x0,tol)
  xold = x0;
  error = 2*tol;
  while error > tol
    x = g(xold);
    error = abs(x-xold);
    xold = x;
  end
  xc = x;
end