nD Nonlinear System Single Solution VI

Owning Palette: Zeros VIs

Requires: Full Development System

Determines the solutions of nonlinear systems of equations in n dimensions beginning with a starting point in n dimensions. You must manually select the polymorphic instance to use.

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nD Nonlinear System Single Solution (Formula)

	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. If the array of strings contains the variable t, the VI returns an error.
	F(X) is an array of strings defining the functions in n dimensions. The formula can contain any number of valid variables.
	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 Zeros.
	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.

nD Nonlinear System Single Solution (VI)

	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.
	data contains arbitrary values that pass to the VI that implements the function.
	F(X) is a strictly typed reference to the VI that implements the function. Create this VI by starting from the VI template located in labview\vi.lib\gmath\zero.llb\Zero Finder f(x) nD.vit.  Open template
	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 Zeros.
	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.

nD 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.