Related papers: Digital terrain modeling with the Chebyshev polyno…

We discuss two approaches to solving the parametric (or stochastic) eigenvalue problem. One of them uses a Taylor expansion and the other a Chebyshev expansion. The parametric eigenvalue problem assumes that the matrix $A$ depends on a…

Efficient climate change monitoring and modeling rely on high-quality geospatial and environmental datasets. Due to limitations in technical capabilities or resources, the acquisition of high-quality data for many environmental disciplines…

Local polynomial smoothing is a widespread technique in data analysis, and Savitzky-Golay (SG) filters are one of its most well-known realizations. In real settings, the effectiveness of SG filtering depends critically on proper tuning of…

Digital Surface Models (DSM) offer a wealth of height information for understanding the Earth's surface as well as monitoring the existence or change in natural and man-made structures. Classical height estimation requires multi-view…

We compute the spectral functions for the two-site dynamical cluster theory and for the two-orbital dynamical mean-field theory in the density-matrix renormalization group (DMRG) framework using Chebyshev expansions represented with matrix…

We present an adaptive delaminating Levin method for evaluating bivariate oscillatory integrals over rectangular domains. Whereas previous analyses of Levin methods impose non-resonance conditions that exclude stationary and resonance…

Digital terrain maps (DTMs) are an important part of planetary exploration, enabling operations such as terrain relative navigation during entry, descent, and landing for spacecraft and aiding in navigation on the ground. As robotic…

Due to the COVID-19 global pandemic, computer-assisted diagnoses of medical images have gained much attention, and robust methods of semantic segmentation of Computed Tomography (CT) images have become highly desirable. In this work, we…

We present a PDE-based approach for the multidimensional extrapolation of smooth scalar quantities across interfaces with kinks and regions of high curvature. Unlike the commonly used method of [2] in which normal derivatives are…

In this paper, we will provide an introduction to the derivative-free optimization algorithms which can be potentially applied to train deep learning models. Existing deep learning model training is mostly based on the back propagation…

The accuracy of mapping agricultural fields across large areas is steadily improving with high-resolution satellite imagery and deep learning (DL) models, even in regions where fields are small and geometrically irregular. However,…

Polynomial expansions are important in the analysis of neural network nonlinearities. They have been applied thereto addressing well-known difficulties in verification, explainability, and security. Existing approaches span classical Taylor…

Digital Elevation models (DEM) are images having terrain information embedded into them. Using cognitive mapping concepts for DEM registration, has evolved from this basic idea of using the mapping between the space to objects and defining…

A spectral method is developed for the direct solution of linear ordinary differential equations with variable coefficients. The method leads to matrices which are almost banded, and a numerical solver is presented that takes O(m^2n)…

The numerical solution of partial differential equations (PDEs) is challenging because of the need to resolve spatiotemporal features over wide length and timescales. Often, it is computationally intractable to resolve the finest features…

We present a novel and unifying framework for constructing spectral approximations to fractional integral operators. These spectral approximations are based on transplanted Chebyshev polynomials, which are obtained by composing Chebyshev…

In the last decades, the development of smartphones, drones, aerial patrols, and digital cameras enabled high-quality photographs available to large populations and, thus, provides an opportunity to collect massive data of the nature and…

We focus on two central themes in this dissertation. The first one is on decomposing polytopes and polynomials in ways that allow us to perform nonlinear optimization. We start off by explaining important results on decomposing a polytope…

We present an advanced algorithm for the determination of watershed lines on Digital Elevation Models (DEMs), which is based on the iterative application of Invasion Percolation (IIP). The main advantage of our method over previosly…

Almost universally in computer vision, when surface derivatives are required, they are computed using only first order accurate finite difference approximations. We propose a new method for computing numerical derivatives based on 2D…