Determines the coefficients of a rational polynomial to best suit a given set of derivatives.

## derivatives

Derivatives of the function.

## m

Degree of the numerator polynomial.

Default: 0

## n

Degree of the denominator polynomial.

Default: 0

## 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

## numerator

Numerator polynomial coefficients in ascending order of power.

## denominator

Denominator polynomial coefficients in ascending order of power.

## 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.

## Determining a Rational Polynomial with the Pade Approximation Algorithm

Let f be a given function with known derivatives and values: f(0), f'(0), ..., f(m + n)(0). This node determines the rational polynomial to best suit the derivatives of f by solving the following linear equation.

For mn,

$g\left(x\right)=\frac{{a}_{0}+{a}_{1}x+\dots +{a}_{m}{x}^{m}}{1+{b}_{1}x+\dots +{b}_{n}{x}^{n}}$

where

• g(x) is the rational polynomial
• m is the degree of the numerator polynomial
• n is the degree of the denominator polynomial
• a0, a1, …, am are the coefficients of the numerator polynomial
• b1, …, bn are the coefficients of the denominator polynomial

The rational polynomial g(x) agrees with f(x) to the highest possible order of m + n:

$g\left(0\right)=f\left(0\right)\phantom{\rule{0ex}{0ex}}g\prime \left(0\right)=f\prime \left(0\right)\phantom{\rule{0ex}{0ex}}⋮\phantom{\rule{0ex}{0ex}}{g}^{\left(m+n\right)}\left(0\right)={f}^{\left(m+n\right)}\left(0\right)$

Where This Node Can Run:

Desktop OS: Windows

FPGA: Not supported

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