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The Alternating-Directions Method

In: Numerical Methods for Grid Equations

Author

Listed:
  • Aleksandr A. Samarskii

    (Moscow University, Department of Computational, Mathematics and Cybernetics)

  • Evgenii S. Nikolaev

    (Moscow University, Department of Computational, Mathematics and Cybernetics)

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.

Suggested Citation

  • Aleksandr A. Samarskii & Evgenii S. Nikolaev, 1989. "The Alternating-Directions Method," Springer Books, in: Numerical Methods for Grid Equations, chapter 0, pages 269-301, Springer.
    • Handle: RePEc:spr:sprchp:978-3-0348-9142-4_7
    DOI: 10.1007/978-3-0348-9142-4_7
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