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  Example

	accuracy controls the accuracy of the zero determination. The default is 1.00E-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.
	error returns any error or warning from the VI. 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). You can wire error to the Error Cluster From Error Code VI to convert the error code or warning into an error cluster.

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, c_new, and end are the base for the new iteration, depending on whether

f(start) · f(c_new) < 0

or

f(c_new) · f(end) < 0

The algorithm stops, if |a – b| < 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.

Example

Refer to the Street Illumination Problem VI in the labview\examples\math\misc.llb directory for an example of using the Ridders Zero Finder VI.