Document Type
Honors Project - Open Access
Abstract
I study adaptive rational approximation for fixed points that arise in infinite-horizon dynamic programming. I integrate the Adaptive Antoulas–Anderson (AAA) algorithm into Bellman- and Euler-based fixed-point solvers by recomputing a barycentric rational interpolant at each update. In addition to standard AAA, which selects support points from interpolation residuals, I study a residual-weighted variant in which Bellman,Euler, or KKT diagnostics act as secondary weights on the greedy pivot rule. This alignment of approximation adaptivity with the underlying equilibrium conditions can concentrate degrees of freedom in regions of steep curvature, sharp transitions in localbehavior, and other localized features that typically degrade polynomial and spline methods. I develop a multivariate extension via a structured row/column support representation for two-dimensional state spaces. Numerical experiments on stress-test functions and growth-model benchmarks show that AAA-based representations can deliver high accuracy with compact support sets, with the largest gains over polynomial and spline methods occurring in problems with kinks or localized curvature, while the benefits of residual weighting are model-dependent and strongest in those same settings.
Recommended Citation
N'guettia, Adaye Sosthene Yvan, "Adaptive Rational Approximation in Dynamic Economic Models: A Novel Application of the AAA Algorithm to Economic Growth" (2026). Mathematics, Statistics, and Computer Science Honors Projects. 104.
https://digitalcommons.macalester.edu/mathcs_honors/104
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