Determines a set of solutions of a nonlinear system of equations in n dimensions beginning with a randomly chosen start point in n dimensions. You must manually select the polymorphic instance to use.


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As an example of using the nD 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 Zeros are (1.0000, 1.0000, 1.0000) and (–0.4050, 0.5931, 2.2429).

This algorithm is based on the nD 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.

Examples

Refer to the following example files included with LabVIEW.

  • labview\examples\Mathematics\Scripts and Formulas\Equation Explorer.vi