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

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希媛
希媛 2024-3-18
编辑： VBBV 2024-3-19
这是一个迭代法的程序，但结果是错误的，这是为什么呢？
  2 个评论
VBBV
VBBV 2024-3-19
编辑：VBBV 2024-3-19
Ran in:
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

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回答（1 个）

Torsten
Torsten 2024-3-18
编辑：Torsten 2024-3-18
Ran in:
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

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