Recurrences in Solving Triangular Systems of Linear Equations: Representation in the Structural Blanks Method

Issue title: Programming Theory, Information System Engineering, Software Engineering, and Artificial Intelligence

Article type: Research Article

Authors: Čyras, Vytautas^;

Affiliations: Department of Computer Science, Vilnius University, Naugarduko 24, 2600 Vilnius, Lithuania | Institute of Mathematics and Informatics, Akademijos 4, 2600 Vilnius, Lithuania. E-mail: [email protected]

Abstract: In the paper we examine data dependencies in the algorithm of back substitution in the problem of solving triangular systems of linear equations. The aim of the paper is to illustrate the structural blanks (SB) notation in consistency proof of data dependencies in loop programs. Data dependency semantics of programs is introduced and investigated. The introduced notation constitutes the theoretical basis of data dependencies in SB. Two structural modules – a sequential S-module and a parallel one – are examined.

Keywords: data dependency, a loop program, triangular system of linear equations, S-module's consistency proof

DOI: 10.3233/INF-1999-10104

Journal: Informatica, vol. 10, no. 1, pp. 45-70, 1999