In numerical linear algebra, the Chebyshev iteration is an iterative method for determining the solutions of a system of linear equations. The method...

The Chebyshev polynomials are two sequences of orthogonal polynomials related to the cosine and sine functions, notated as T n ( x ) {\displaystyle T_{n}(x)}...

Modified Richardson iteration is an iterative method for solving a system of linear equations. Richardson iteration was proposed by Lewis Fry Richardson...

the iteration can be determined directly from the difference between the location of the iteration from the left and the location of the iteration from...

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...

leading to the idea of combining the filter with an iterative method, e.g., the Chebyshev iteration and the conjugate gradient method are proposed in for...

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

function, using the Chebyshev polynomials instead of the usual trigonometric functions. If one calculates the coefficients in the Chebyshev expansion for a...

or several times. The process of repeatedly applying the same function is called iteration. In this process, starting from some initial object, the result of applying...

Generalized minimal residual method (GMRES) — based on the Arnoldi iteration Chebyshev iteration — avoids inner products but needs bounds on the spectrum Stone's...

matrices. Some of the supported solutions methods are: Richardson Iteration Chebyshev Iteration Conjugate Gradient (CG) Conjugate Gradient Squared (CGS) BiConjugate...

functional square root of g(x) = 8x4. A functional square root of the nth Chebyshev polynomial, g ( x ) = T n ( x ) {\displaystyle g(x)=T_{n}(x)} , is f (...

filter becomes a type I Chebyshev filter. As the ripple in the passband approaches zero, the filter becomes a type II Chebyshev filter and finally, as...

James McClellan and Thomas Parks in 1972, is an iterative algorithm for finding the optimal Chebyshev finite impulse response (FIR) filter. The Parks–McClellan...

Slow division algorithms produce one digit of the final quotient per iteration. Examples of slow division include restoring, non-performing restoring...

n ( y ) {\displaystyle T_{n}(y)} is the nth cardinal function of the Chebyshev polynomials of the first kind with input argument y. If N=4 then the following...

first iteration (at least) can be solved exactly, but is already somewhat complicated. A numerical solution instead, for instance by a Chebyshev spectral...

Each iteration of the Lanczos algorithm produces another column of the final transformation matrix V {\displaystyle V} , whereas an iteration of Householder...

1934, is an iterative algorithm used to find simple approximations to functions, specifically, approximations by functions in a Chebyshev space that are...

to Pseudospectral Methods. Cambridge University Press, Cambridge, UK Chebyshev and Fourier Spectral Methods by John P. Boyd. Canuto C., Hussaini M. Y...

several important classes of filter including the Butterworth filter, the Chebyshev filter and the Elliptic filter. It was originally intended to be applied...

unity, it depends on the prime factorization of n. Prime omega functions Chebyshev functions Liouville function, λ(n) = (–1)Ω(n) Von Mangoldt function, Λ(n)...

gradients. Conjugate gradients squared. Chebyshev iteration. Generalized minimal residual (GMRES). Iterative refinement (Richardson's method). Quasi-minimal...

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

i.e. on each iteration, in the double iteration method, the iteration step value is repeated twice and changes only through one iteration. Hence the designation...

without a first guess: Polynomialization of Kepler's equation through Chebyshev polynomial equation of the sine". Applied Numerical Mathematics. 57 (1):...

1 < 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...

that amounts to iterating a mapping from some algebraic variety to itself. The related theory of arithmetic dynamics studies iteration over the rational...

is very close to zero, the Halley's method iteration is almost the same as the Newton's method iteration. When deriving Newton's method, a proof starts...

quadrature is based on approximating f by a polynomial interpolant at Chebyshev nodes and integrates polynomials of degree up to n exactly when given...