On different classes of monoparametric stationary iterative methods for the solution of linear systems

S. Galanis, A. Hadjidimos and D. Noutsos

Mathematics and Computers in Simulation (MATCOM), 1986, vol. 28, issue 2, 115-128

Abstract: The class of monoparametric k-step methods x(m)=ωTx(m−1)+(1−ω)x(m−k)+ωc used for the solution of the linear system (I − T)x = c is studied. Under certain conditions the spectrum σ(T) of T must satisfy, for ω >1 and given k(⩾ 2) and p∈ (0, 1) (a quantity defined in the paper), (optimum) convergent methods (1) are derived. Next, an equivalence between (optimum) convergent methods (1) and a class of Successive Overrelation (SOR.) ones is established. Then, based on (1), a class of new monoparametric methods, called k2-step block iterative methods faster than those in (1), is introduced and studied. Finally, various applications and numerical examples in support of the theory developed in this paper are provided.

Date: 1986
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:28:y:1986:i:2:p:115-128

DOI: 10.1016/0378-4754(86)90106-0

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