Rational approximation

Abstract

Potential theory for rational approximation is reviewed by means of examples computed with the AAA algorithm.

Figures (6)

• Figure 1: Entire function, $f(z) = \exp(z)$
• Figure 2: Meromorphic function, $f(z) = \tan(z^2)$
• Figure 3: Function with essential singularities, $f(z) = \exp(\tan(z^2))$. Inset: zoom near $z = \sqrt{\pi/2}$
• Figure 4: Function with branch points, $f(z) = \sqrt{(1.5-z)(1.5 i-z)}$
• Figure 5: Function with singularity on the approximation domain, $f(z) = |z|$ on $[-1,1]$