Elements of the General Theory of Optimal Algorithms

Ivan V. / Zadiraka Sergienko - Collection Yellow Sale 2023

378 pages, parution le 11/01/2022

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Résumé

In this monograph, the authors develop a methodology that allows one to construct and substantiate optimal and suboptimal algorithms to solve problems in computational and applied mathematics.In this monograph, the authors develop a methodology that allows one to construct and substantiate optimal and suboptimal algorithms to solve problems in computational and applied mathematics. Throughout the book, the authors explore well-known and proposed algorithms with a view toward analyzing their quality and the range of their efficiency. The concept of the approach taken is based on several theories (of computations, of optimal algorithms, of interpolation, interlination, and interflatation of functions, to name several). Theoretical principles and practical aspects of testing the quality of algorithms and applied software, are a major component of the exposition. The computer technology in construction of T -efficient algorithms for computing -solutions to problems of computational and applied mathematics, is also explored. The readership for this monograph is aimed at scientists, postgraduate students, advanced students, and specialists dealing with issues of developing algorithmic and software support for the solution of problems of computational and applied mathematics.
-Preface.- Introduction.- List of symbols and abbreviations.- 1. Elements of the computing theory.- 2. Theories of computational complexity.- 3. Interlination of functions.- 4. Interflatation of functions.- 5. Cubature formulae using interlanation functions.- 6. Testing the quality of algorithm programs.- 7. Computer technologies of solving problems of computational and applied mathematics with fixed values of quality characteristics.- Bilbiography.- Index.- About the Authors. Ivan V. Sergienko is the Director of the V.M. Glushkov Institute of Cybernetics of the National Academy of Science of Ukraine.
Valeriy K. Zadiraka is Head of the Department of Numerical Methods for Optimization at the V.M. Glushkov Institute of Cybernetics of the National Academy of Science of Ukraine.
Oleg M. Lytvyn is Professor at the Department of Information Computing Technology and Mathematics at the Ukrainian Engineering Pedagogical Academy.