The Alternating-Directions Method

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 11 in Numerical Methods for Grid Equations, 1989, pp 269-301 from Springer

Abstract: Abstract In this chapter we consider special iterative methods for solving grid elliptic equations of the form Au = f where the operator A possesses a definite structure. In Section 11.1 the alternating-directions method is studied in the commutative case; an optimal set of parameters is constructed. In Section 11.2 the method is illustrated with examples involving the solution of boundary-value problems for elliptic equations with separable variables. In Section 11.3 the alternating-directions method is examined in the non-commutative case.

Keywords: Arithmetic Operation; Iterative Scheme; Iteration Count; Sample Application; Commutative Case (search for similar items in EconPapers)
Date: 1989
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-0348-9142-4_7

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DOI: 10.1007/978-3-0348-9142-4_7

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