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A family of methods with three‐term recursion formulae
Author(s) -
Papadrakakis M.
Publication year - 1982
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620181204
Subject(s) - chebyshev filter , conjugate gradient method , mathematics , recursion (computer science) , chebyshev iteration , iterative method , chebyshev polynomials , term (time) , derivation of the conjugate gradient method , conjugate residual method , algorithm , mathematical optimization , mathematical analysis , computer science , gradient descent , machine learning , artificial neural network , physics , quantum mechanics
A state‐of‐the‐art survey of a family of vector iterative methods with three‐term recursion formulae is presented. The methods can be classified under two broad categories. The Chebyshev semi‐iterative type of methods and the conjugate gradient type of methods. Relationships between the iteration parameters of the methods are established and computational techniques for estimating these parameters are presented. Numerical tests confirm the superiority of the conjugate gradient method for linear problems and the Chebyshev semi‐iterative methods for nonlinear problems.