Nonlinear System Single Solution (Not in Base Package)

Determines the solutions of nonlinear systems of equations in n dimensions beginning with a starting point in n dimensions. 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 a small distance to calculate derivatives. The default is 1E – 8.
	Start is the start point in n dimension.
	X is an array of strings representing the x variables.
	F(X) is an array of strings defining the functions in n dimensions.
	Zeroes contains the determined zeros of F(X).
	f(Zeroes) contains the function values of Zeroes. Usually, these values are close to 0.
	ticks is the time in milliseconds to analyze the formula and to produce the Zeroes.
	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.

Nonlinear System Single Solution Details

Let F be the n dimension function and let X be a given point in n dimensions.

Furthermore, let

f = 0.5F²

The algorithm is looking for such a vector P that

F(X + dP) F(X)

for all 0 d 1.

In a second step, an appropriate value, d*, is calculated, so that

F(X + d*P)

is considerably smaller than F(X). This process is repeated until F(X) 0 is reached. What follows is an approximation for F(X) = 0.