• Source: Chebyshev iteration

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.




Example code in MATLAB



Code translated from

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See also


Iterative method. Linear systems
List of numerical analysis topics. Solving systems of linear equations
Jacobi iteration
Gauss–Seidel method
Modified Richardson iteration
Successive over-relaxation
Conjugate gradient method
Generalized minimal residual method
Biconjugate gradient method
Iterative Template Library
IML++




References


"Chebyshev iteration method", Encyclopedia of Mathematics, EMS Press, 2001 [1994]




External links


Chebyshev Iteration. From MathWorld
Chebyshev Iteration. Implementation on Go language

Kata Kunci Pencarian:

• Chebyshev iteration
• Chebyshev filter
• List of things named after Pafnuty Chebyshev
• Chebyshev polynomials
• Modified Richardson iteration
• Edge-preserving smoothing
• Newton's method
• Iterated function
• Functional square root
• Approximation theory