Newton Raphson Zero Finder (Not in Base Package)

Determines a zero of a 1D function close to two points with the help of the derivative of this 1D function. The two values form a search limit for the unknown zero of the 1D function. Details  

	accuracy controls the accuracy of the zero determination. The default is 1.00E-8, which specifies the maximum deviation of the calculated solution from the actual solution.
	h is the delta value to calculate the derivative of the given formula. The default is 1E – 8.
	start is the start point of the interval. The default is 0.0.
	end is the end point of the interval. The default is 1.0.
	formula is a string representing the function under investigation.
	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. You can wire error to the Error Cluster From Error Code VI to convert the error code or warning into an error cluster.

Newton Raphson Zero Finder Details

Let f be the given function. The Newton Raphson Zero Finder VI uses a method that combines the simple midpoint strategy and the Newton strategy.

• Midpoint strategy:

  

• Newton strategy:

  

where x₁ and x₂ are given guesses with

f(x₁) · f(x₂) < 0

The following illustration demonstrates the Newton strategy.