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Article title DESCRIPTION OF JACOBI ALGORITHM FOR SOLUTION OF LINEAR EQUATION SYSTEM IN ARCHITECTURE-INDEPENDENT SET@L PROGRAMMNING LANGUAGE
Authors I. I. Levin, A. I. Dordopulo, I. V. Pisarenko, A. K. Melnikov
Section SECTION I. METHODS, MODELS AND ALGORITHMS OF INFORMATION PROCESSING
Month, Year 05, 2018 @en
Index UDC 004.432.4
DOI
Abstract Software porting between high-performance computer systems with different architectures requires a considerable code revision due to the architectural limitation of existing programming languages. To solve the problem, we proposed architecture-independent Set@l programming language based on the principles of set-theoretic codeview and aspect-oriented programming. Set@l program consists of a source code, which describes an information graph of a problem, and aspects, which adapt an algorithm to architecture and configuration of a computer system. If an algorithm remains unchanged during its adaptation, calculations and their parallelizing are described by the set theory of Cantor and Bolzano. In the case of algorithm modernization, some collections are indefinite, and we can not treat them as traditional sets. To describe indefinite objects, Set@l applies the alternative set theory developed by P. Vopenka. In Set@l, a class is a collection characterized by indefinite type and structure at some abstraction level. If indefiniteness represents an essential attribute of a collection, it is classified as a semiset. Application of classes, sets and semisets allows to describe various methods of algorithm implementation and parallelizing as an entire Set@l program. In this paper, the Jacobi algorithm for the solution of linear equation systems is considered as an example for the utilization of classes and semisets.

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Keywords Architecture-independent programming; Set@l programming language; alternative set theory; aspect-oriented approach.
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