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f(x) = -x²-x+3
Find a root of f(x) in the range of [0,1] with 0.01 Machine Epsilon (x ∈ [1,2])
f(1) = 1
f(2) = -3
f(1)*f(2) < 0 (has root)
xt = 1 + 2 / 2 (Bisection Method) -
REGULA FALSI (False Position Method)
(xh, f(xh)), (xl, f(xl))
g(x) - y1 = m(x - x1) g(x) - f(xh) = (f(xh) - f(xl) / xh - xl) * (x - xh) g(xt) = 0 = (f(xh) - f(xl) / xh - xl) * (xt - xh) + f(xh)
-f(xh) = ( xt(f(xh) - f(xl)) - xhf(xh) + xhf(xl) ) / ( xh - xl )
xt = ( -xhf(xh) + xlf(xh) + xhf(xh) - xhf(xl) ) / ( f(xh) - f(xl) )
xt = xlf(xh) - xhf(xl) / f(xh) - f(xl)| xl - xh | !< Epsilon -> continue iteration