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Roots of the Chebyshev polynomials of the first kind
numerical analysis, Chebyshev nodes (also called Chebyshev points or a Chebyshev grid) are a set of specific algebraic numbers used as nodes for polynomial
Chebyshev_nodes
Pair of polynomial sequences
1]. The roots of the Chebyshev polynomial of the first kind are sometimes called Chebyshev nodes because they are used as nodes in polynomial interpolation
Chebyshev_polynomials
Type of analog or digital filter
Chebyshev filters are analog or digital filters that have a steeper roll-off than Butterworth filters, and have either passband ripple (type I) or stopband
Chebyshev_filter
Numerical technique
t 1 < … < t p < 1 {\displaystyle -1<t_{1}<\ldots <t_{p}<1} be the Chebyshev nodes of order p ≥ 2 , {\displaystyle p\geq 2,} and let u 1 ( y ) , … , u
Fast_multipole_method
Mathematical mentod
{\pi }{n+1}}\sin ^{2}\left({\frac {i}{n+1}}\pi \right).\,} Chebyshev polynomials Chebyshev nodes Abramowitz, M & Stegun, I A, Handbook of Mathematical Functions
Chebyshev–Gauss_quadrature
Failure of convergence in interpolation
is a table of nodes on which the interpolation process converges. [citation needed] Chebyshev interpolation (i.e., on Chebyshev nodes) converges uniformly
Runge's_phenomenon
Chebyshev function in number theory Chebyshev integral Chebyshev iteration Chebyshev method Chebyshev nodes Chebyshev polynomials and the "Chebyshev form"
List of things named after Pafnuty Chebyshev
List_of_things_named_after_Pafnuty_Chebyshev
Constants related to interpolation errors
constants (depending on a set of nodes and of its size) give an idea of how good the interpolant of a function (at the given nodes) is in comparison with the
Lebesgue_constant
of Chebyshev nodes and coefficients of a function in Chebyshev polynomial basis. Like the Chebyshev polynomials, it is named after Pafnuty Chebyshev. The
Discrete_Chebyshev_transform
Algorithm to approximate functions
of nodes can be expressed as Λ ¯ n − Λ _ n ≥ 0. {\displaystyle {\overline {\Lambda }}_{n}-{\underline {\Lambda }}_{n}\geq 0.} For Chebyshev nodes, which
Remez_algorithm
Form of interpolation
that Chebyshev nodes are a very good choice for polynomial interpolation, as the growth in n is exponential for equidistant nodes. However, those nodes are
Polynomial_interpolation
Polynomials used for interpolation
equispaced nodes, Lagrange interpolation is susceptible to Runge's phenomenon of large oscillation. Given a set of k + 1 {\displaystyle k+1} nodes { x 0
Lagrange_polynomial
Numerical integration method
"quadrature", that are based on an expansion of the integrand in terms of Chebyshev polynomials. Equivalently, they employ a change of variables x = cos
Clenshaw–Curtis_quadrature
Numerical analysis concept
weights and nodes, which are accurate to within double-precision machine epsilon for any choice of n ≥ 21. This allows for computation of nodes and weights
Gauss–Legendre_quadrature
Linear interpolation Runge's phenomenon Vandermonde matrix Chebyshev polynomials Chebyshev nodes Lebesgue constants Different forms for the interpolant:
List of numerical analysis topics
List_of_numerical_analysis_topics
Numerical analysis technique for waves
alternative approach is using Chebyshev polynomials as spatial basis functions, which are evaluated at Chebyshev nodes to minimize Runge phenomenon. This
Pseudospectral time-domain method
Pseudospectral_time-domain_method
Algorithm used for pathfinding and graph traversal
arbitrarily fewer nodes than A* on some non-pathological problems. Optimal efficiency is about the set of nodes expanded, not the number of node expansions (the
A*_search_algorithm
Numerical method for solving optimal control problems
In PS optimal control, Legendre and Chebyshev polynomials are commonly used. Mathematically, quadrature nodes are able to achieve high accuracy with
Pseudospectral optimal control
Pseudospectral_optimal_control
Approximation of the definite integral of a function
result for polynomials of degree 2n − 1 or less by a suitable choice of the nodes xi and weights wi for i = 1, ..., n. The modern formulation using orthogonal
Gaussian_quadrature
Plotting by a computer application
using Chebyshev distance over Euclidean distance in two-dimensional space.) As the value of the heuristic increases, A* examines fewer nodes but no longer
Pathfinding
Main-belt asteroid
2010 Chebyshev, provisional designation 1969 TL4, is a rare-type carbonaceous asteroid from the outer regions of the asteroid belt, approximately 25 kilometers
2010_Chebyshev
Type of artificial neural network architecture
effective in approximating functions with non-linear or clustered structures. Chebyshev polynomials: Offer efficient approximation with minimized error in the
Kolmogorov–Arnold_Networks
Formulation of the finite element method
polynomials are usually orthogonal Chebyshev polynomials or very high order Lagrange polynomials over non-uniformly spaced nodes. In SEM computational error
Spectral_element_method
information between the nodes. Because the Gauss–Lobatto nodes cluster at the boundary points, Ross et al. suggested that if the node density around the initial
Bellman_pseudospectral_method
Technique in mathematics
numerical solution instead, for instance by a Chebyshev spectral method using n = 21 {\displaystyle n=21} Chebyshev—Lobatto points x k = cos ( π ( n − 1 −
Quasilinearization
Natural number
of the form 4k + 1 than of the form 4k + 3 up to the number, against Chebyshev's bias 26896 = 1642, palindromic in base 9: 408049 27405 = heptagonal number
20,000
Graph drawing used to study Riemann surfaces
sequences for their black nodes and white nodes: both have a black node with degree three, two black nodes with degree two, two white nodes with degree two, and
Dessin_d'enfant
Spline function
\end{aligned}}} A piecewise cubic B-spline is formed by a set of nodes and each four consecutive nodes define a cubic piece of the curve with the formulation above
B-spline
Polynomial sequence
scarcely recognizable form, and studied in detail by Pafnuty Chebyshev in 1859. Chebyshev's work was overlooked, and they were named later after Charles
Hermite_polynomials
Symbols for constants, special functions
cursive form of theta, often used in handwriting, represents the first Chebyshev function in number theory Theta role in linguistics ι {\displaystyle \iota
Greek letters used in mathematics, science, and engineering
Greek_letters_used_in_mathematics,_science,_and_engineering
Discrete Fourier transform algorithm
(e.g. fast DCT used for JPEG and MPEG/MP3 encoding and decoding), fast Chebyshev approximation, solving difference equations, computation of isotopic distributions
Fast_Fourier_transform
Analytic function in mathematics
representation of the zeta function is essentially an interpolation with nodes, where the nodes are points s = 2, 4, 6, ..., i.e. exactly those where the zeta values
Riemann_zeta_function
Mathematical arithmetic dynamics function
automorphism of T d {\displaystyle T^{d}} is a bijection of the set of nodes that preserves vertex-edge connectivity. The group A u t ( T d ) {\displaystyle
Arboreal Galois representation
Arboreal_Galois_representation
Orbital mechanics term
without a first guess: Polynomialization of Kepler's equation through Chebyshev polynomial equation of the sine". Applied Numerical Mathematics. 57 (1):
Kepler's_equation
Technique used in signal processing and data compression
related to Chebyshev polynomials, and fast DCT algorithms (below) are used in Chebyshev approximation of arbitrary functions by series of Chebyshev polynomials
Discrete_cosine_transform
Asteroid
v t e Minor planets navigator 2010 Chebyshev 2011 Veteraniya 2012 Guo Shou-Jing
2011_Veteraniya
Optimal control technique
of Gauss-Lobatto or Gauss-Radau distribution arising from Legendre or Chebyshev polynomials. The Gauss-Lobatto pseudospectral points are used for finite-horizon
Ross–Fahroo pseudospectral method
Ross–Fahroo_pseudospectral_method
indicate that there is some form of interaction between a pair of voters (nodes). The opinions of any given voter on some issue changes at random times
Voter_model
Parts of a whole which carry only relative information
presence of such noise, any attempt to use the central limit theorem and Chebyshev's inequality to define a strict boundary between signal and noise fails
Compositional_data
Carbonaceous asteroid
v t e Minor planets navigator 2008 Konstitutsiya 2009 Voloshina 2010 Chebyshev
2009_Voloshina
Formal power series
generated by more complex generating functions include: Appell polynomials Chebyshev polynomials Difference polynomials Generalized Appell polynomials q-difference
Generating_function
List of definitions of terms and concepts used in electrical engineering and electronics
electrical networks. mesh networking A topology where infrastructure nodes connect to other nodes such as to convey information. Metadyne A DC electric machine
Glossary of electrical and electronics engineering
Glossary_of_electrical_and_electronics_engineering
Technique to solve geological problems by computational simulation
Cengage Learning. ISBN 978-1-305-63511-1. Boyd, John P. (2001-12-03). Chebyshev and Fourier Spectral Methods: Second Revised Edition. Courier Corporation
Numerical_modeling_(geology)
Type of signal processing filter
element approximations to an ideal filter response of the Butterworth and Chebyshev filters can both readily be realised. As with the electrical counterpart
Mechanical_filter
Charactron Charge pump Charge transfer switch Charge-coupled device CHAYKA Chebyshev filter Chemistry Choke (electronics) Chopper (electronics) Circle diagram
Index of electrical engineering articles
Index_of_electrical_engineering_articles
slowly. This is because the error Krylov based methods are restricted by Chebyshev polynomial bound. To solve this problem, methods such as BARBs are proposed
Automatic basis function construction
Automatic_basis_function_construction
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