Methods for Solving Equations with Indefinite and Singular Operators

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 12 in Numerical Methods for Grid Equations, 1989, pp 303-350 from Springer

Abstract: Abstract In this chapter we study direct and iterative methods for solving equations with indefinite non-singular operators, with complex operators, and also with singular operators. In Section 12.1, we consider a method with Chebyshev parameters and also a method of variational type for the solution of an equation with an indefinite operator. In Section 12.2 complex versions of the simple iteration method and the alternating-directions method are constructed for an equation with a complex operator of special form. In Section 12.3 we study general iterative methods for solving equations with singular operators, but where the preconditioning operator is non-singular. Section 12.4 is concerned with the construction of special direct and iterative methods for equations with singular operators.

Keywords: Iterative Method; Iterative Scheme; Normal Solution; Iteration Count; Singular Operator (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_8

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DOI: 10.1007/978-3-0348-9142-4_8

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