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Showing 1 to 19 of 19 for “"Chebyshev polynomials"”.
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An application of Chebyshev polynomials to the solution of a two-dimensional elliptic boundary-value problem
… investigate the feasibility of using a bivariate Chebyshev polynomial to approximate solutions to the two-dimensional neutron diffusion equation. The two-dimensional two-group neutron diffusion equations are solved by expanding neutron fluxes in a finite series of Chebyshev polynomials over large …
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Chebyshev-like polynomials, conic distribution of roots, and continued fractions
… of the properties of the roots of translated Chebyshev polynomials of the first kind (call these complex numbers Chebyshev points), are illuminated by the study of geometric properties of the ellipse and conversely. This includes the following; Chebyshev points lie on certain ellipses centered …
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Discriminants: calculation, properties, and connection to the root distribution of polynomials with rational generating functions
… q-analogues relate to the root distribution of polynomials. This topic includes the connections between the root distribution of a sequence of polynomials and the discriminant of the denominator of its generating function. A more specialized aspect of this area of this research concerns the root …
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The use of stochastic collocation for sampling from expensive distributions with applications in finance
… is the investigation of the roots of Chebyshev polynomials of the first kind as collocation points, as opposed to Gaussian quadrature points used by Babuˇska et al. (2007), Loeven et al. (2007) and Grzelak et al. (2015). The roots of the Chebyshev polynomials are constrained to lie in …
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Chebyshev spectral methods for potential field computation
We investigate Chebyshev spectral methods for solving Poisson's equation and the generalized Poisson's equations and apply them to 3-D gravity and DC resistivity modeling. When we approximate a function by a finite sum of Chebyshev polynomials, there are two kinds of errors: truncation and …
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VLSI implementation of an efficient method for the computation of line spectral frequencies
… properties of the symmetric and antisymmetric polynomials to map the upper portion of the unit circle onto the real interval [-1,1] by converting the polynomials into a Chebyshev polynomial series representation. Because Chebyshev polynomials may be evaluated efficiently using the Clenshaw …
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Key-Based Authentication Scheme for eVTOL Drones Using Chebyshev Chaotic Maps
… a key-based authentication scheme that utilizes Chebyshev polynomials as chaotic maps, hash functions, and the AES-256 encryption technique. The network members can securely generate all encryption keys without sharing secret data, which solves one of the main problems of the symmetric encryption …
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Application of Chebyshev Formalism to Identify Nonlinear Magnetic Field Components in Beam Transport System
… that depend on the order of the nonlinearity. Chebyshev polynomials and their unique properties allow one to directly quantify the magnitude of the nonlinearity with the minimum error. A calibration standard was developed using one of the sextupole magnets in a CEBAF beamline. The technique was …
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Sensitivity analysis of the static aeroelastic response of a wing
… the field outside of the aerodynamic code. Chebyshev polynomials are used to globally fit the pressure field. This approach had some difficulties in representing local variations in the field, so a variety of local interpolation polynomial pressure representations are also implemented. These …
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Vibration Analysis of a Composite Wing Box with Arbitrarily Shaped Spars and Ribs
… model are developed according to the FSDT. The Chebyshev polynomials are the bases of the displacement and rotation functions in the Ritz method. To assess the accuracy and feasibility of the proposed model, several numerical cases of the free vibration and aeroelastic flutter of stiffened …
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Mathematical modeling of adhesive layer cracks utilizing integral equations
… is utilized to represent the crack. A series of Chebyshev polynomials to approximate the unknown dislocations. The resulting integral equations are solved through the collocation method and the series coefficients are recovered. Several numerical packages, Mathcad 5.0+ and Mathematica 2.2.1, were …
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A new optimization method for reservoir systems
… (also known as the "curse of dimensionality"). Chebyshev polynomials are used as basis functions to develop accurate and efficient approximations of key DP functionals, markedly reducing the DP computational requirements while maintaining solution optimality and implementation ease. OFDP …
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Millimeter-Wave and Sub-Terahertz Parametric Harmonic Generation
… 1/N. The related P-V curves are described by the Chebyshev polynomials. Impulse representation of pumped parameters is also developed to represent a transient train of pulses to describe the resistive multipliers. Several circuits are designed to demonstrate the validity of the theory and explore …
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Regularized weighted Chebyshev approximations for support estimation
… analysis relies on introducing a new weighted Chebyshev polynomial approximation method, jointly optimizing the bias and variance components of the risk, and combining the weighted minmax polynomial approximation method with discretized semi-infinite programming solvers. Such a setting allows …
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Graph Neural Networks: Techniques and Applications
… suffer from drawbacks: graph CNNs rely on Chebyshev polynomial approximation which results in oscillatory approximation at jump discontinuities since Chebyshev polynomials require degree $Omega$(poly(1/$epsilon$)) to approximate a jump signal such as $|x|$. To reduce complexity, RatioanlNet …
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A coupled rotor-fuselage aeroelastic analysis using complex rotor modes
… technique, based on curve fitting using Chebyshev polynomials coupled with analytical integration, is devised and shown for the first time to minimise the inherent numerical problems associated with Force Integration. Finally, applications of the analytical model to include the effects of …
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High order numerical methods applied to the analysis of transport phenomena in combustion
… nodes. By following the philosophy behind the Chebyshev polynomials, the idea of an optimum grid for piecewise polynomial interpolations of degree q _ N is introduced. It is then shown, that when q = N, this polynomial interpolation on optimum nodes coincides with the Chebyshev interpolation, …
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Fast Fluorescence Lifetime Imaging Using a Full-Field Homodyne System with Applications in Biology
A fast, full-field fluorescence lifetime imaging system based on the homodyne technique was built and used for several applications. Also contained herein is the basic theory and background for fluorescence lifetime imaging, as well as data analysis of lifetime distributions. The fast, easy-to-use …
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Spectral hulls: a degree of freedom reducing hp-strategy in space/time
… using various methods including Fourier-Chebyshev collocation, Continuous Galerkin (CG), Discontinuous Galerkin (DG) and Discontinuous Least-Squares (DLS) on structured and/or arbitrary unstructured grids. The feasibility of such procedure is first investigated in time only by letting the …