Ridders Zero Finder (Not in Base Package)

Determines a zero of a 1D function in a given interval. The function has to be continuous and has to have different signs at the end points of the interval. Details

accuracy controls the accuracy of the zero determination. The default is 1E - 8.
start is the leftmost point of the interval. The default is 0.0.
end is the rightmost point of the interval. The default is 0.0.
formula is a string describing the function.
zero is the determined zero of formula. zero is a good approximation only for the exact value.
f(zero) is the function value at the point given by zero. The answer should be very close to zero.
ticks is the time effort for the whole calculation of the function values in milliseconds.
When start > end, the application interprets it as an error condition. The function values at the points start and end must have different signs to guarantee the existence of a zero in (start,end).

Ridders Zero Finder Details

Given the function

f(x)

with

f(a)*f(b) < 0.

Ridders method determines

c = (a + b)/2

and calculates the new guess

The triplets start, , and end are the base for the new iteration, depending on whether

or

The algorithm stops, if |ab| < accuracy

Ridders method is very fast and reliable.

Ridders method is a generalization of the depicted estimation of a zero, as shown in the following illustration.