Rational Function Approximation as Constrained Optimization

Function approximation traditionally writes the target function as a linear combination of a set of basis functions {Pn(x)}. However, when written as a rational function with an n-degree polynomial divided by an m-degree polynomial, it gives an approximation as good as using n + m basis functions. Rational functions have the added benefit of providing better approximations to non-smooth functions. We propose a new method for rational function approximation. Using Bernstein Polynomials, we pose the problem as a constrained optimization problem, which is solved approximately using a computationally cheap iteration scheme. We also present preliminary approximation bounds.

Jul 14, 2023 12:00 AM — Jul 17, 2023 12:00 AM