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 ε 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.