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S~dhan~, Vol. 24, Parts 4 & 5, August & October 1999, pp. 369--423. Printed in India Structure theorems for partially asynchronous iterations of a
 

Summary: S~dhan~, Vol. 24, Parts 4 & 5, August & October 1999, pp. 369--423. Printed in India
Structure theorems for partially asynchronous iterations of a
nonnegative matrix with random delays
REZA GHARAVI a and VENKAT ANANTHARAM b*
aSchool of Electrical Engineering, Cornell University, Ithaca, NY 14853, USA
bDepartment of Electrical Engineering and Computer Sciences, University of
California, Berkeley, CA 94720, USA
e-mail: ananth @vyasa.eecs.berkeley.edu
Abstract. We consider partially asynchronous parallel iteration of a fixed
nonnegative matrix with stationary ergodic interprocessor communication
delays. We study the iteration via a random graph describing the interprocessor
influences. Our major result is an invariant description of the rates of conver-
gence of arbitrary sequences of individual processor-time values. In the course
of proving this result a number of other invariant properties of the convergence
of the iteration are described. The convergence rates that appear in our results
are Lyapunov exponents of certain random matrix products derived from the
original matrix and the statistics of the delays.
Keywords. Structure theorems; asynchronous iterations; nonnegative matrix;
random delays.
1. Introduction

  

Source: Anantharam, Venkat - Department of Electrical Engineering and Computer Sciences, University of California at Berkeley

 

Collections: Engineering