MASS DATA PROCESSING. ALGEBRAIC MODELS AND METHODS
Authors:
Type:
Monographie
ISBN:
978-5-16-018035-9
Status:
In work
Language:
Russian
Quantity of pages:
229
Publisher:
INFRA-M Academic Publishing LLC.
Abstract (English):
The monograph is devoted to mathematical and algorithmic support of mass data processing based on algebraic models. One of the most common classes of mass processing is considered - processing of highly active structured data. The construction of algebraic models of data and calculations and methods of proving their correspondence are analyzed. Three algebraic systems are studied, which can be used both as data models and as models of calculations. The algebraic and axiomatic methods of proving the correspondence of these models are investigated. A proof of their correspondence is given: homomorphism and isomorphism. The problem of optimizing the processes of mass processing of data presented in the form of algebraic expressions in the proposed algebra models is raised. The algorithms of synthesis and optimization of calculation of these expressions, the method of symmetric horizontal data distribution providing parallel implementation of calculation of algebraic expressions and generalization of the block algorithm of parallel matrix multiplication for the case of multiplication of multidimensional matrices are described in detail. Architectures of software and hardware complexes for effective parallel implementation of operations in the considered algebra models are proposed. A number of real-world examples illustrating the application of the proposed methods are given. For students, postgraduates and teachers of technical and physical-mathematical universities and faculties.
The monograph is devoted to mathematical and algorithmic support of mass data processing based on algebraic models. One of the most common classes of mass processing is considered - processing of highly active structured data. The construction of algebraic models of data and calculations and methods of proving their correspondence are analyzed. Three algebraic systems are studied, which can be used both as data models and as models of calculations. The algebraic and axiomatic methods of proving the correspondence of these models are investigated. A proof of their correspondence is given: homomorphism and isomorphism. The problem of optimizing the processes of mass processing of data presented in the form of algebraic expressions in the proposed algebra models is raised. The algorithms of synthesis and optimization of calculation of these expressions, the method of symmetric horizontal data distribution providing parallel implementation of calculation of algebraic expressions and generalization of the block algorithm of parallel matrix multiplication for the case of multiplication of multidimensional matrices are described in detail. Architectures of software and hardware complexes for effective parallel implementation of operations in the considered algebra models are proposed. A number of real-world examples illustrating the application of the proposed methods are given. For students, postgraduates and teachers of technical and physical-mathematical universities and faculties.
