Related papers: Digital terrain modeling with the Chebyshev polyno…
The advection-diffusion and wave equations are the fundamental equations governing any physical law and therefore arise in many areas of physics and astrophysics. For complex problems and geometries, only numerical simulations can give…
For an arbitrary given span of high-dimensional multivariate Chebyshev polynomials, an approach to construct spatial discretizations is presented, i.e., the construction of a sampling set that allows for the unique reconstruction of each…
Unmanned aerial vehicle (UAV) photogrammetry allows for the creation of orthophotos and digital surface models (DSMs) of a terrain. However, DSMs of water bodies mapped with this technique reveal water surface distortions, preventing the…
Deep learning methods are used on spectroscopic data to predict drug content in tablets from near infrared (NIR) spectra. Using convolutional neural networks (CNNs), features are ex- tracted from the spectroscopic data. Extended…
Differential equations (DEs) are commonly used to describe dynamic systems evolving in one (ordinary differential equations or ODEs) or in more than one dimensions (partial differential equations or PDEs). In real data applications the…
Despite the demonstrated benefits of hyperspectral formalism for stem effect corrections in the context of fiber dose measurements, this approach has not been yet translated into volumetric measurements where cameras are typically used for…
In this paper we use a contour integral method to derive a generating function in the form of a double series involving the product of two Chebyshev polynomials over generalized independent indices expressed in terms of the incomplete gamma…
Contour map has contour lines that are significant in building a Digital Elevation Model (DEM). During the digitization and pre-processing of contour maps, the contour line intersects with each other or break apart resulting in broken…
Spectral methods are an important part of scientific computing's arsenal for solving partial differential equations (PDEs). However, their applicability and effectiveness depend crucially on the choice of basis functions used to expand the…
We consider a distributed optimization problem over a network of agents aiming to minimize a global objective function that is the sum of local convex and composite cost functions. To this end, we propose a distributed Chebyshev-accelerated…
In this paper we follow the general approach, proposed earlier by the first author, which is derived from the invariant theory field and provides a way of obtaining of the polynomial identities for any arbitrary polynomial family. We…
This work concerns the evolutionary approaches to distributed stochastic black-box optimization, in which each worker can individually solve an approximation of the problem with nature-inspired algorithms. We propose a distributed evolution…
In this paper, a spectral method based on conformal mappings is proposed to solve Steklov eigenvalue problems and their related shape optimization problems in two dimensions. To apply spectral methods, we first reformulate the Steklov…
High-resolution digital elevation models (DEMs) of the lunar surface are essential for surface mobility planning, landing site characterization, and planetary science. The Orbiter High Resolution Camera (OHRC) on board Chandrayaan-2 has the…
In this letter, we present a fast and well-conditioned spectral method based on the Chebyshev polynomials for computing the continuous part of the nonlinear Fourier spectrum. The algorithm achieves a complexity of $O(N_{\text{iter.}}N\log…
A new spectral type method for solving the one dimensional quantum-mechanical Lippmann-Schwinger integral equation in configuration space is described. The radial interval is divided into partitions, not necessarily of equal length. Two…
We present a new algorithm for finding isolated zeros of a system of real-valued functions in a bounded interval in $\mathbb{R}^n$. It uses the Chebyshev proxy method combined with a mixture of subdivision, reduction methods, and…
Additive models and generalized additive models are effective semiparametric tools for multidimensional data. In this article we propose an online smoothing backfitting method for generalized additive models with local polynomial smoothers.…
We propose Deep Estimators of Features (DEFs), a learning-based framework for predicting sharp geometric features in sampled 3D shapes. Differently from existing data-driven methods, which reduce this problem to feature classification, we…
Smooth-basis models such as Chebyshev polynomial regressors and radial basis function (RBF) networks are well established in numerical analysis. Their continuously differentiable prediction surfaces suit surrogate optimisation, sensitivity…