Elements of the General Theory of Optimal Algorithms

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 developingalgorithmic and software support for the solution of problems of computational and applied mathematics.

Results provide methods to solve problems that have been unsolvable until now Provides know-how in computer technology for computational processes for various computational models Results can be used in the design of plates and shells of complex shapes made of modern composite materials

Autorentext

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.

Inhalt
-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.