Convergence of Asynchronous Iterative Methods

Eugenius Kaszkurewicz and Amit Bhaya
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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

Chapter 4 in Matrix Diagonal Stability in Systems and Computation, 2000, pp 128-153 from Springer

Abstract: 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.

Keywords: Iterative Method; Convergence Condition; Nonnegative Matrix; Liapunov Function; Reference Matrix (search for similar items in EconPapers)
Date: 2000
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DOI: 10.1007/978-1-4612-1346-8_4

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