APPLICATION OF LINEAR ALGEBRA METHODS FOR OPTIMISING DATA PROCESSING AND STORAGE SN MODERN INFORMANION SYSTEMS

Kraychuk O. та Kraychuk S. та Ostapchuk N. (2026) APPLICATION OF LINEAR ALGEBRA METHODS FOR OPTIMISING DATA PROCESSING AND STORAGE SN MODERN INFORMANION SYSTEMS. BULLETIN of Cherkasy State Technological University, 2026 (Vol.31): No.2. с. 85-96.

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Анотація

The aim of the study was to generalise approaches to coordinating decisions at the stages of planning, execution, and physical level of data representation in information systems under the dominance of resource constraints when operating with massive sets. The methodology was based on system-analytical formalisation, comparative-analytical generalisation and typology, comparative analysis, systematisation and integrative synthesis. It was established that linear algebra formalises the representation of data as matrices/vectors and calculations as a sequence of transformations. The generalisation of operations (semirings) extends these primitives to graph and Boolean problems, and Graph Basic Linear Algebra Subprograms standardises the implementation for sparse structures. Efficiency is determined by the consistent chain of “rewrite→cost model→physical execution”: rewrite reduces intermediate data, and the cost model chooses a plan based on data input/output, memory, sparsity, and parallelism, without it, heuristics remain. Factorised representations have been found to reduce redundancy and pressure on memory and data input/output (for joins/groups) with system support. Randomised Numerical Linear Algebra and sketching reduce costs and manage the “accuracy-resources” trade-off in streaming processing. Matrix compression (low-rank representation, reduced precision) reduces memory and traffic and speeds up computations with a controlled loss of precision. In vector database management systems and distributed systems, the bottleneck is data input/output and redistribution between nodes, so DShuffle moves some processing closer to the data, emphasising the role of infrastructure optimisation. The linear algebraic representation of computations provides a basis for consistent optimisation of rewriting, plan selection, and execution, reducing materialisation and data movement under input/output, memory, and bandwidth constraints. The practical significance of the results lies in the possibility of the application by information-systems developers and engineers for the consistent selection of data formats, execution plans, and computational primitives to reduce materialisation and I/O, memory, and network overhead

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