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Triangular Iterative Methods

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 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

Suggested Citation

  • Aleksandr A. Samarskii & Evgenii S. Nikolaev, 1989. "Triangular Iterative Methods," Springer Books, in: Numerical Methods for Grid Equations, chapter 0, pages 189-223, Springer.
    • Handle: RePEc:spr:sprchp:978-3-0348-9142-4_5
    DOI: 10.1007/978-3-0348-9142-4_5
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