Version:

Last Modified: March 15, 2017

Determines a zero of a function between two points with the help of the derivative of the function.

This node uses the Newton-Raphson method to determine a zero of a function.

Delta value to calculate the derivative of the given formula.

**Default: **1E-08

Function to calculate. The formula can contain any number of valid variables.

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.

Start value of the interval where this node starts searching for zeros.

**Default: **0

End value of the interval where this node stops searching for zeros.

**Default: **1

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.

**Default: **No error

Accuracy and maximum iterations used to determine the zeros.

Accuracy used to determine the zeros.

**Default: **1E-8

Maximum number of iterations that the node runs to find the zeros.

**Default: **200

Point of determined zero of **formula**. **zero** is the approximate value of the underlying zero of the function.

Function value at the point given by **zero**. The value should be very close to zero.

Number of evaluations that the formula performs in finding the zeros.

Error information.

The node produces this output according to standard error behavior.

Standard Error Behavior

**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.

The Newton-Raphson Method combines the simple midpoint strategy and the Newton strategy to determine a zero of a function. The midpoint strategy and the Newton strategy are defined by the following equation:

${x}_{\mathrm{new}}=\{\begin{array}{cc}\frac{{x}_{1}+{x}_{2}}{2}& \text{\hspace{0.17em}}(\mathrm{Midpoint}\text{\hspace{0.17em}}\mathrm{strategy})\\ {x}_{1}-\frac{f\left({x}_{1}\right)}{f\prime \left({x}_{1}\right)}& (\mathrm{Newton}\text{\hspace{0.17em}}\mathrm{strategy})\end{array}$

where

*x*_{1}and*x*_{2}are given guesses with*f*(*x*_{1}) **f*(*x*_{2}) < 0*f*is the given function

The following figure demonstrates the Newton strategy.

**Where This Node Can Run: **

Desktop OS: Windows

FPGA: This product does not support FPGA devices