Definition:Padé Approximant

Definition

Let $f$ be a function on which an approximation $f'$ has been obtained by Padé approximation.

The rational function $f'$ so obtained is called a Padé approximant to $f$.

Examples

Exponential

Let $f: \R \to \R$ denote the real function $f: x \mapsto e^x$.

A Padé approximant to $f$ with numerator and denominator of degree $2$ is:

$\dfrac {x^2 + 6 x + 12} {x^2 - 6 x + 12}$

Also see

• Results about Padé approximants can be found here.

Source of Name

This entry was named for Henri Eugène Padé.

Sources

• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Padé approximation