In numerical linear algebra, the Chebyshev iteration is an
iterative method for determining the solutions of a system of linear equations. The method is named after Russian mathematician Pafnuty Chebyshev.
Chebyshev iteration avoids the computation of inner products as is necessary for the other nonstationary methods. For some distributed-memory architectures these inner products are a bottleneck with respect to efficiency. The price one pays for avoiding inner products is that the method requires enough knowledge about spectrum of the coefficient matrix A, that is an upper estimate for the upper eigenvalue and lower estimate for the lower eigenvalue. There are modifications of the method for nonsymmetric matrices A.
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In numerical linear algebra, the Chebysheviteration is an iterative method for determining the solutions of a system of linear equations. The method...
Chebyshev function in number theory Chebyshev integral ChebysheviterationChebyshev method Chebyshev nodes Chebyshev polynomials and the "Chebyshev form"...
The Chebyshev polynomials are two sequences of polynomials related to the cosine and sine functions, notated as T n ( x ) {\displaystyle T_{n}(x)} and...
Modified Richardson iteration is an iterative method for solving a system of linear equations. Richardson iteration was proposed by Lewis Fry Richardson...
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...
avoided). Each iteration of the Lanczos algorithm produces another column of the final transformation matrix V{\displaystyle V}, whereas an iteration of Householder...
Generalized minimal residual method (GMRES) — based on the Arnoldi iterationChebysheviteration — avoids inner products but needs bounds on the spectrum Stone's...
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...
Where Tn(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...
third order Chebyshev polynomial of the first kind. The coefficients should be pre-calculated and hard-coded. Then in the loop, use an iteration which cubes...
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...
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)...
several important classes of filter including the Butterworth filter, the Chebyshev filter and the Elliptic filter. It was originally intended to be applied...
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...
the lower and mid frequencies, and then switch to a higher steepness Chebyshev attenuation at the higher frequencies. The Gaussian function is for x...
other mathematicians also contributed to refinement of the law, including Chebyshev, Markov, Borel, Cantelli, Kolmogorov and Khinchin. Markov showed that...
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