`pade`

Padé approximant: a rational function that approximates an expression.

Syntax

r = pade(f, x)

Padé approximant of f around x = 0 with the default order.

r = pade(f, x, 'Order', [m n])

Numerator of degree m and denominator of degree n.

Description

A Padé approximant matches the Taylor series of f up to order m + n using a ratio of polynomials instead of a single polynomial. Rational functions can follow poles and large excursions that a Taylor polynomial misses, so they are common for approximating delays in control theory: the [2 2] approximant of exp(x) is (x^2 + 6x + 12)/(x^2 - 6x + 12).

Input arguments

f: Symbolic expression.
x: Symbolic variable.
Order: Degrees [m n] of numerator and denominator.

Output arguments

r: Ratio of two polynomials in x.

Example

Padé of exp

syms x
r = pade(exp(x), x, 'Order', [2 2])

Output

r = (x^2 + 6*x + 12)/(x^2 - 6*x + 12)

Notes

The form with an expansion point, pade(f, x, a, 'Order', ...), is not accepted by MatLivre; expansion is around 0.

pade