05-12-2014, 10:12 PM
Algorithm - Muller's Scheme
Given an equation f(x) = 0
Let the initial guesses be x0, x1 and x2
Let xi = x2, xi-1 = x1 and xi-2 = x0
Compute f(xi-2), f(xi-1) and f(xi)
Do
Compute
h = x - xi, hi = xi - xi-1 and hi-1 = xi-1 - xi-2
li = hi / hi-1, di = 1 + li
gi = li2 fi-2 - di2 fi-1 + ( li + di ) fi
ci = li (li fi-2 - di fi-1 + fi )
li+1 = min ( -2di fi / (gi ± Ö(gi2- 4di fici) ) )
(take minimum in absolute sense)
Then xi+1 = xi + ( xi - xi-1 ) li+1 , i = 2, 3, 4, . . .
Given an equation f(x) = 0
Let the initial guesses be x0, x1 and x2
Let xi = x2, xi-1 = x1 and xi-2 = x0
Compute f(xi-2), f(xi-1) and f(xi)
Do
Compute
h = x - xi, hi = xi - xi-1 and hi-1 = xi-1 - xi-2
li = hi / hi-1, di = 1 + li
gi = li2 fi-2 - di2 fi-1 + ( li + di ) fi
ci = li (li fi-2 - di fi-1 + fi )
li+1 = min ( -2di fi / (gi ± Ö(gi2- 4di fici) ) )
(take minimum in absolute sense)
Then xi+1 = xi + ( xi - xi-1 ) li+1 , i = 2, 3, 4, . . .