Triangular Iterative Methods

Aleksandr A. Samarskii and Evgenii S. Nikolaev
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Aleksandr A. Samarskii: Moscow University, Department of Computational, Mathematics and Cybernetics
Evgenii S. Nikolaev: Moscow University, Department of Computational, Mathematics and Cybernetics

Chapter Chapter 9 in Numerical Methods for Grid Equations, 1989, pp 189-223 from Springer

Abstract: Abstract In this chapter we study implicit two-level iterative methods whose operators B correspond to triangular matrices. In Section 1 we look at the Gauss-Seidel method and formulate sufficient conditions for its convergence. In Section 2, the successive over-relaxation method is investigated. Here the choice of the iteration parameter is examined, and an estimate is obtained for the spectral radius of the transformation operator. In Section 3 a general matrix iterative scheme is investigated, selection of the iterative parameter is examined, and the method is shown to converge in H A

Keywords: Iterative Method; Spectral Radius; Iterative Scheme; Relaxation Method; Iteration Count (search for similar items in EconPapers)
Date: 1989
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DOI: 10.1007/978-3-0348-9142-4_5

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