Asynchronous block-iterative methods for almost linear equations

Abstract

This paper gives convergence conditions for asynchronous block-iterative methods for the solution of the almost linear equation Ax= F( x), where A is a linear operator, F a block-diagonal Lipschitz-continuous operator, and x a vector, in terms of a splitting of A and the Lipschitz constant of F. The methods used are a combination of the contraction-mapping approach using a vectorial norm and a large-scale systems approach using vector difference inequalities. The load-flow equations for a power system are almost linear in the above sense, and considerable speedup can be obtained on a four transputer machine.