S. A. Inyutin, Doctor Technical Science (PhD), Full Professor, e-mail: inyutin_int@mail.ru, Moscow Aviation Institute (Nation Research University) (MAI), Moscow, Russian Federation

Metrics for Modular Vectors Space

Modular representations of numerical quantities in the form of residue vectors by prime modules from a finite set can be considered as a set of modular vectors. The set of modular vectors is considered as a linear subspace in a vector space containing vectors with components of limited size; its ring structure is not taken into account. The properties of a linear modular subspace, methods for determining new scalar products are analyzed, which allows us to introduce new metrics. The introduced algebraic constructions are designed to analyze the convergence of multi-bit parallel computing processes in large computer ranges that operate with numerical values in the modular representation. The introduced numerical vector representations are oriented for application in modular reconfigurable computing systems of SIMD architecture.
Keywords: modular vector subspace, modular scalar products, modular metrics, parallel modular computing process, multiprocessor reconfigurable system

P. 570–576