Nonlinear System Solver (Not in Base Package)

Determines a set of solutions of a nonlinear system of equations in n dimensions beginning with a randomly chosen start point in n dimensions. Details  Example

	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.
	number of trials is the elaborate number of randomly chosen start points. The algorithm starts with these points and looks for zeros close to these points. The default is 5.
	h is a small distance to calculate derivatives. The default is 1E – 8.
	Start is an array describing the left corner of the n-dimension interval. The randomly chosen start points of the zero-finding algorithm can be found in the n-dimensional rectangle spanned by Start and End.
	End is an array describing the right corner of the n-dimension interval. The randomly chosen start points of the zero-finding algorithm can be found in the n-dimensional rectangle spanned by Start and End.
	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 Solver Details

As an example of using the Nonlinear System Solver VI, determine the solutions for the following nonlinear system.

2x + 3y + z² – 6 = 0

–4x + y² – 4z + 7 = 0

x² + y + z – 3 = 0

To obtain solutions for the preceding nonlinear system, enter the following values on the front panel.

• Start: [-1, -1, -1]
• End: [4, 4, 4]
• X: [x, y, z]
• F(X): [2*x + 3*y + z*z - 6, -4*x + y*y - 4*z + 7, x*x + y + z - 3]

Note  You only need to enter the left side of the equations describing the nonlinear system into F(X). The VI assumes that the right side is zero.

The solutions determined by the VI and returned in Zeroes are (1.0000, 1.0000, 1.0000) and (–0.4050, 0.5931, 2.2429).

This algorithm is based on the Nonlinear System Single Solution VI.

Note  The algorithm used to find the solution to the nonlinear system is fundamentally stochastic in nature. For example, if number of trials is 3, the VI generates three separate n-dimensional starting points and finds a solution to the system using each of the three starting points. If the nonlinear system has two solutions, the VI might not find both solutions. Generally, the VI finds the solution closest to the starting point for a particular trial. If all three starting points are closest to a particular solution than other solutions, the VI finds the solution closest to the three starting points three times and does not identify other solutions. To improve the chances of finding all solutions, increase number of trials.

Example

Refer to the Equation Explorer Example VI in the labview\examples\math\math.llb directory for an example of using the Nonlinear System Solver VI.