5 papers
Parameter estimation for evaporation-driven tear film model in two space dimensions
Qinying Chen, Tobin Driscoll
The tear film (TF) plays a critical role in maintaining ocular surface health, and its disruption through tear breakup (TBU) is closely associated with dry eye disease. Evaporation…
Stable evaluation of derivatives for barycentric and continued fraction representations of rational functions
Tobin A. Driscoll, Yuxing Zhou
Fast algorithms for approximation by rational functions exist for both barycentric and Thiele continued fraction (TCF) representations. We present the first numerically stable meth…
Operator learning for models of tear film breakup
Qinying Chen, Arnab Roy, Tobin A. Driscoll
Tear film (TF) breakup is a key driver of understanding dry eye disease, yet estimating TF thickness and osmolarity from fluorescence (FL) imaging typically requires solving comput…
RationalFunctionApproximation.jl: Rational Approximation On Discrete and Continuous Domains
Tobin A. Driscoll
Unlike polynomials, rational functions can represent functions having poles or branch cuts with root-exponential convergence and no Runge phenomenon. Recent developments of the AAA…
Greedy Thiele continued-fraction approximation on continuum domains in the complex plane
Tobin A. Driscoll, Yuxing Zhou
We describe an adaptive greedy algorithm for Thiele continued-fraction approximation of a function defined on a continuum domain in the complex plane. The algorithm iteratively sel…