Fuzzy Least Squares Approximation Using Fuzzy Polynomial

In this paper, the fuzzy polynomial is introduced and applied to investigate the least squares approximation problem based on LR fuzzy numbers. A new and simple approach to solve the original problem is constructed by using approximate fuzzy polynomial. Two numerical examples are given to illustrate the proposed method. Since a large number of data exist as an uncertain property and need a function relation to reflect the laws between different variables, our results enrich fuzzy numerical approximation theory.

Worst-case Recovery Guarantees for Least Squares Approximation Using Random Samples

We construct a least squares approximation method for the recovery of complex-valued functions from a reproducing kernel Hilbert space on $$D \subset \mathbb {R}^d$$ D ⊂ R d . The nodes are drawn at random for the whole class of functions, and the error is measured in $$L_2(D,\varrho _{D})$$ L 2 ( D , ϱ D ) . We prove worst-case recovery guarantees by explicitly controlling all the involved constants. This leads to new preasymptotic recovery bounds with high probability for the error of hyperbolic Fourier regression on multivariate data. In addition, we further investigate its counterpart hyperbolic wavelet regression also based on least squares to recover non-periodic functions from random samples. Finally, we reconsider the analysis of a cubature method based on plain random points with optimal weights and reveal near-optimal worst-case error bounds with high probability. It turns out that this simple method can compete with the quasi-Monte Carlo methods in the literature which are based on lattices and digital nets.

Real-Time Estimation of R0 for COVID-19 Spread

We propose a real-time approximation of R0 in an SIR-type model that applies to the COVID-19 epidemic outbreak. A very useful direct formula expressing R0 is found. Then, various type of models are considered, namely, finite differences, cubic splines, Piecewise Cubic Hermite interpolation and linear least squares approximation. Preserving the monotonicity of the formula under consideration proves to be of crucial importance. This latter property is preferred over accuracy, since it maintains positive R0. Only the Linear Least Squares technique guarantees this, and is finally proposed here. Tests on real COVID-19 data confirm the usefulness of our approach.