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Convergence of Asynchronous Iterative Methods

In: Matrix Diagonal Stability in Systems and Computation

Author

Listed:
  • Eugenius Kaszkurewicz

    (Federal University of Rio de Janeiro, COPPE/UFRJ, Department of Electrical Engineering)

  • Amit Bhaya

    (Federal University of Rio de Janeiro, COPPE/UFRJ, Department of Electrical Engineering)

Abstract

The objective of this chapter is to show how Jacobi-type iterative methods for the solution of linear and nonlinear equations and, more specifically asynchronous versions of these methods, can be analyzed in the framework introduced in this book. By regarding these methods as discrete-time interconnected systems with varying delays in the interconnections, the analysis based on a diagonal-type Liapunov function introduced in Chapter 3 leads to computable conditions for convergence based on nonnegative stable (and hence diagonally stable) matrices, as well as estimates for the speed of convergence of different iterative methods. A perspective on the analysis of interconnected systems using diagonal-type Liapunov functions that complements the approach in this chapter is to be found in Chapter 6.

Suggested Citation

  • Eugenius Kaszkurewicz & Amit Bhaya, 2000. "Convergence of Asynchronous Iterative Methods," Springer Books, in: Matrix Diagonal Stability in Systems and Computation, chapter 4, pages 128-153, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4612-1346-8_4
    DOI: 10.1007/978-1-4612-1346-8_4
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