# Find a Zero nD System (Formula) (G Dataflow)

Determines a solution of a nonlinear system of equations in n dimensions beginning with a start point. You define the equations with formulas.  ## h

Step size that this node uses to calculate the numerical derivatives of the given functions.

Default: 1E-08 ## formulas

Formulas that define the n-dimension functions.

You only need to enter the left side of the equations that describe the nonlinear system. This node assumes that the right side is zero.

Entering Valid Variables

This node accepts variables that use the following format rule: variables must start with a letter or an underscore followed by any number of alphanumeric characters or underscores. ## variables

Names of the variables.

Variable names must start with a letter or an underscore followed by any number of alphanumeric characters or underscores. ## start

Start values of the n-dimension interval where this node starts searching for the solutions. Each element in this array represents the start value of the corresponding variable in variables. ## error in

Error conditions that occur before this node runs.

The node responds to this input according to standard error behavior.

Standard Error Behavior

Many nodes provide an error in input and an error out output so that the node can respond to and communicate errors that occur while code is running. The value of error in specifies whether an error occurred before the node runs. Most nodes respond to values of error in in a standard, predictable way.

error in does not contain an error error in contains an error  If no error occurred before the node runs, the node begins execution normally.

If no error occurs while the node runs, it returns no error. If an error does occur while the node runs, it returns that error information as error out.

If an error occurred before the node runs, the node does not execute. Instead, it returns the error in value as error out.

Default: No error ## accuracy

Maximum deviation of the calculated solution from the actual solution when determining the zeros.

The node stops running if the difference between two consecutive approximations is equal to or less than the value of accuracy.

Default: 1E-08 ## zeros

Determined values of the variables where the n-dimensional functions evaluate to zero.

These values are an approximation of the actual values of the variables where the functions evaluate to zero. ## f(zeros)

Function values at zeros. The values are expected to be nearly zero. ## error out

Error information.

The node produces this output according to standard error behavior.

Standard Error Behavior

Many nodes provide an error in input and an error out output so that the node can respond to and communicate errors that occur while code is running. The value of error in specifies whether an error occurred before the node runs. Most nodes respond to values of error in in a standard, predictable way.

error in does not contain an error error in contains an error  If no error occurred before the node runs, the node begins execution normally.

If no error occurs while the node runs, it returns no error. If an error does occur while the node runs, it returns that error information as error out.

If an error occurred before the node runs, the node does not execute. Instead, it returns the error in value as error out.

## How This Node Determines a Solution of a Nonlinear System of Equations

This node determines a solution of an n-dimension equation F(X) = 0 in the following way:

Let f = 0.5F 2.

This node looks for a vector P that always satisfies f(X + d P) ≤ f(X) when 0 ≤ d ≤1.

If F(X) ≈ 0 is false, this node calculates an appropriate value d' so that f(X + d'P) < f(X) to a large extent. This node repeats this process until F(X) ≈ 0 is true.

To determine a solution for the following nonlinear system with start points of 1 and 0 for the variables x and y, respectively, enter the following values on the panel:

sin(x + y) = 0

cos(x - y) = 0

 formula [sin(x+y), cos(x-y)] variables [x, y] start [1, 0]

The following table lists the outputs of this node.

 zeros [0.785398, -0.785398] f(zeros) [-1.88627E-13, 1.06277E-12]

Where This Node Can Run:

Desktop OS: Windows

FPGA: Not supported

Web Server: Not supported in VIs that run in a web application