numerical analysis, Chebyshev nodes (also called Chebyshev points or a Chebyshev grid) are a set of specific algebraic numbers used as nodes for polynomial...

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 filters are analog or digital filters that have a steeper roll-off than Butterworth filters, and have either passband ripple (type I) or stopband...

is a table of nodes on which the interpolation process converges. [citation needed] Chebyshev interpolation (i.e., on Chebyshev nodes) converges uniformly...

of Chebyshev nodes and coefficients of a function in Chebyshev polynomial basis. Like the Chebyshev polynomials, it is named after Pafnuty Chebyshev. The...

example simulation after nodes 2 and 4 are eliminated. The nodes of the reduced table are renumbered to 1 and 2. Since the Chebyshev frequency response is...

{\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...

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 p...

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...

Chebyshev function in number theory Chebyshev integral Chebyshev iteration Chebyshev method Chebyshev nodes Chebyshev polynomials and the "Chebyshev form"...

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...

equispaced nodes, Lagrange interpolation is susceptible to Runge's phenomenon of large oscillation. Given a set of k + 1 {\textstyle k+1} nodes { x 0 , x...

"quadrature", that are based on an expansion of the integrand in terms of Chebyshev polynomials. Equivalently, they employ a change of variables x = cos ⁡...

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...

of nodes can be expressed as Λ ¯ n − Λ _ n ≥ 0. {\displaystyle {\overline {\Lambda }}_{n}-{\underline {\Lambda }}_{n}\geq 0.} For Chebyshev nodes, which...

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...

Linear interpolation Runge's phenomenon Vandermonde matrix Chebyshev polynomials Chebyshev nodes Lebesgue constants Different forms for the interpolant:...

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...

In PS optimal control, Legendre and Chebyshev polynomials are commonly used. Mathematically, quadrature nodes are able to achieve high accuracy with...

using Chebyshev distance over Euclidean distance in two-dimensional space.) As the value of the heuristic increases, A* examines fewer nodes but no longer...

\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...

2010 Chebyshev, provisional designation 1969 TL4, is a rare-type carbonaceous asteroid from the outer regions of the asteroid belt, approximately 25 kilometers...

scarcely recognizable form, and studied in detail by Pafnuty Chebyshev in 1859. Chebyshev's work was overlooked, and they were named later after Charles...

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 −...

polynomials are usually orthogonal Chebyshev polynomials or very high order Lagrange polynomials over non-uniformly spaced nodes. In SEM computational error...

include Euclidean distance, Manhattan distance, Minkowski distance, and Chebyshev distance. The Euclidean distance formula is used to find the distance...

cursive form of theta, often used in handwriting, represents the first Chebyshev function in number theory Theta role in linguistics ι {\displaystyle \iota...

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...

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...

representation of the zeta function is essentially an interpolation with nodes, where the nodes are points s = 2 , 4 , 6 , … {\displaystyle s=2,4,6,\ldots } , i...