Hybrid Computation Techniques Inferred from Functional Analysis

The research reported in this paper is concerned with the use of functional analysis and operator theory in providing insights into iterative computational methods. The computational methods are discussed in the context of obtaining the closed-loop response of a complex feedback system on a hybrid computer. The need for iterative solution arises in problems in which the feedback cannot be computed instantaneously, for instance, when there are partial differential equations, and/or where there is a large number of arithmetic and logical operations. The tools of functional analysis are used to devise computational schemes with improved convergence properties.