External software for the MIR-2 computer

The general case of incompatible systems of linear algebraic equations with matrices of arbitrary rank is considered. The estimates for total errors are obtained for all the considered cases under conditions of approximate data. In solving systems by iterative methods, the conditions of completion of iterative processes that provide solutions with a prescribed accuracy are considered in detail. A special attention is given to the solution of incompatible systems with symmetric positive semidefinite matrices by the method of three-stage regularization in which an algorithm for choosing the regularization parameter is proposed that allows finding solutions with the required accuracy.Keywords: approximate initial data, incompatible systems, total error of the solution, iterative methods.

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“…The study [10] estimates the accuracy of the solution of system (1) depending on the accuracy of the initial data:…”

Section: Slae With Nondegenerate Matricesmentioning

confidence: 99%

Methods for obtaining reliable solutions to systems of linear algebraic equations

2011

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Algebraic School of V.M. Glushkov and Insertion Modeling

Letychevskyi

2023

Cybernetics and Computer Technologies

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The Algebraic School of Viktor Mykhailovych Glushkov already has several generations of scientists, most of whom have already identified and are developing their own scientific directions. This school, started at the Institute of Cybernetics, was shaped by research that had the significance of inventions at the level of world science and the computer industry and in many ways predicted their further development. The work considers the formation of the paradigm of insertion modeling as a generalization of the main achievements of the Glushkov school, starting from the theory of automata and up to modern computer algebra systems. The main concepts from which insertion modeling was formed are considered, namely, symbolic computations, which were implemented even in the first personal machine of the MIR series. It is also the theory of agents and environments, parallel computing, and methods of artificial intelligence, developed at the Institute of Cybernetics, in the 60s and 70s. Numerous deployments of insertion modeling methods in cyber security, research in natural sciences, blockchain technology, in verification and testing of software and hardware, have shown the practicality and value of theoretical research conducted by followers of the Glushkov school. Keywords: symbolic computation, algebraic modeling, insertional modeling.

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External software for the MIR-2 computer

Cited by 2 publications

References 2 publications

Methods for obtaining reliable solutions to systems of linear algebraic equations

Methods for obtaining reliable solutions to systems of linear algebraic equations

Algebraic School of V.M. Glushkov and Insertion Modeling

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