Related papers: Digital terrain modeling with the Chebyshev polyno…
We demonstrate high fidelity enhancement of planetary digital elevation models (DEMs) using optical images and deep learning with convolutional neural networks. Enhancement can be applied recursively to the limit of available optical data,…
We proposed a simple yet effective morphological approach to convert a sparse Digital Elevation Model (DEM) to a dense Digital Elevation Model. The conversion is similar to that of the generation of high-resolution DEM from its…
Estimating the Domain of Attraction (DA) of non-polynomial systems is a challenging problem. Taylor expansion is widely adopted for transforming a nonlinear analytic function into a polynomial function, but the performance of Taylor…
This paper presents a novel approach to rigorously solving initial value problems for semilinear parabolic partial differential equations (PDEs) using fully spectral Fourier-Chebyshev expansions. By reformulating the PDE as a system of…
A procedure for constructing a digital elevation model (DEM) of the northern part of the Volga-Akhtuba interfluve is described. The basis of our DEM is the elevation matrix of Shuttle Radar Topography Mission (SRTM) for which we carried out…
Digital Elevation Model (DEM) is an essential aspect in the remote sensing domain to analyze and explore different applications related to surface elevation information. In this study, we intend to address the generation of high-resolution…
Digital Elevation Models (DEMs) are important datasets for modelling the line of sight, such as radio signals, sound waves and human vision. These are commonly analyzed using rotational sweep algorithms. However, such algorithms require…
A framework for Chebyshev spectral collocation methods for the numerical solution of functional and delay differential equations (FDEs and DDEs) is described. The framework combines interpolation via the barycentric resampling matrix with a…
We present numerical solutions for differential equations by expanding the unknown function in terms of Chebyshev polynomials and solving a system of linear equations directly for the values of the function at the extrema (or zeros) of the…
Recent times have seen an increase in demand of high quality Digital Elevation Models (DEMs) for the lunar surface, because they are highly important for studying the moon and planning future missions. However, there is an evident lack of…
We introduce a novel spectral, finite-dimensional approximation of general Sobolev spaces in terms of Chebyshev polynomials. Based on this polynomial surrogate model (PSM), we realise a variational formulation, solving a vast class of…
Classical approximation bases such as Chebyshev polynomials provide principled and interpretable representations, but their multivariate tensor-product constructions scale exponentially with dimension and impose axis-aligned structure that…
The Chebyshev points are commonly used for spectral differentiation in non-periodic domains. The rounding error in the Chebyshev approximation to the $n$-the derivative increases at a rate greater than $n^{2m}$ for the $m$-th derivative.…
Digital Elevation Models (DEMs) are indispensable in the fields of remote sensing and photogrammetry, with their refinement and enhancement being critical for a diverse array of applications. Numerous methods have been developed for…
In this article, we propose a new numerical approach to high-dimensional partial differential equations (PDEs) arising in the valuation of exotic derivative securities. The proposed method is extended from Reisinger and Wittum (2007) and…
This paper introduces a new method for discretizing and solving integral equation formulations of Maxwell's equations which achieves spectral accuracy for smooth surfaces. The approach is based on a hybrid Nystr\"om-collocation method using…
Exponential divided differences arise in numerical linear algebra, matrix-function evaluation, and quantum Monte Carlo simulations, where they serve as kernel weights for time evolution and observable estimation. Efficient and numerically…
Where data is available, it is desirable in geostatistical modelling to make use of additional covariates, for example terrain data, in order to improve prediction accuracy in the modelling task. While elevation itself may be important,…
This paper presents four novel domain decomposition algorithms integrated with nonlinear mapping techniques to address collocation-based solutions of eigenvalue problems involving sharp interfaces or steep gradients. The proposed methods…
Approximation theory plays a central role in numerical analysis, undergoing continuous evolution through a spectrum of methodologies. Notably, Lebesgue, Weierstrass, Fourier, and Chebyshev approximations stand out among these methods.…