LOGIC DERIVATION OF PARALLEL LINEAR EQUATION SYSTEM SOLVERS WITHIN ELIMINATION STRATEGY

Abstract

In this paper we describe a systematic technique for designing parallel algorithms to solve linear systems. Our approach is based on the logic derivation of a target algorithm from specification of basic relations in the linear equations domain and their properties. Both input specification and the resulting algorithm are expressed in the declarative computer-independent form. The methodology is illustrated by deriving the parallel Gaussian triangular solver.

KEY WORDS:

• algorithm synthesis
• Formal specification
• Gaussian elimination
• logic derivation
• numerical algorithms
• parallel computations

C.R. CATEGORIES:

• D.2.1
• E3.1
• 1.2.3
• G.1.3