Generalised rational approximation and its application to improve deep learning classifiers

V Peiris, N Sharon, N Sukhorukova, J Ugon - Applied Mathematics and …, 2021 - Elsevier
A rational approximation (that is, approximation by a ratio of two polynomials) is a flexible
alternative to polynomial approximation. In particular, rational functions exhibit accurate …

Multivariate approximation by polynomial and generalized rational functions

R Díaz Millán, V Peiris, N Sukhorukova, J Ugon - Optimization, 2022 - Taylor & Francis
In this paper, we develop an optimization-based approach to multivariate Chebyshev
approximation on a finite grid. We consider two models: multivariate polynomial …

Rational and generalised rational Chebyshev approximation problems and their applications

V Peiris - Bulletin of the Australian Mathematical Society, 2023 - cambridge.org
In Chebyshev (uniform) approximation, the goal is to minimise the maximum deviation of the
approximation from the original function. Classical rational Chebyshev approximation is …

Rational approximation and its application to improving deep learning classifiers

V Peiris, N Sharon, NSJ Ugon - arXiv preprint arXiv:2002.11330, 2020 - arxiv.org
A rational approximation by a ratio of polynomial functions is a flexible alternative to
polynomial approximation. In particular, rational functions exhibit accurate estimations to …

The extension of the linear inequality method for generalized rational Chebyshev approximation to approximation by general quasilinear functions

V Peiris, N Sukhorukova - Optimization, 2022 - Taylor & Francis
In this paper, we demonstrate that a well-known linear inequality method developed for
rational Chebyshev approximation is equivalent to the application of the bisection method …

Linear least squares problems involving fixed knots polynomial splines and their singularity study

ZR Zamir, N Sukhorukova - Applied Mathematics and Computation, 2016 - Elsevier
In this paper, we study a class of approximation problems appearing in data approximation
and signal processing. The approximations are constructed as combinations of polynomial …

Chebyshev approximation by linear combinations of fixed knot polynomial splines with weighting functions

N Sukhorukova, J Ugon - Journal of Optimization Theory and Applications, 2016 - Springer
In this paper, we derive conditions for best uniform approximation by fixed knots polynomial
splines with weighting functions. The theory of Chebyshev approximation for fixed knots …

Chebyshev approximation for multivariate functions

N Sukhorukova, J Ugon, D Yost - arXiv preprint arXiv:1510.06076, 2015 - arxiv.org
In this paper, we derive optimality conditions (Chebyshev approximation) for multivariate
functions. The theory of Chebyshev (uniform) approximation for univariate functions is very …

Application of convex optimization techniques for feature extraction from EEG signals

ZR Zamir - 2016 - figshare.swinburne.edu.au
The analysis of electroencephalogram signals is essential for extracting the relevant
information from the human brain activities in order to diagnose brain diseases and …