Kyiv: Naukova Dumka, 1986. - 584 s. The reference manual contains a detailed description of modern effective methods of approximate solution on computers of many important and widespread problems of computational and applied mathematics. statistical data processing, approximation of functions, numerical integration and differentiation, solutions of operator equations, including integral equations and Cauchy problems for systems of ordinary differential equations, minimization of functions and mathematical programming. Particular attention is paid to poorly developed problems, for example, the calculation of special integrals, the solution of rigid systems of differential equations, etc. For many methods, tasks and computers, assessments of their main characteristics are given: complete error in solving problems on the computer, as well as the time and memory required to implement methods on the computer. For the first time, the results on optimization of numerical methods. are systematically presented. Examples, tables, graphs and other information are given to facilitate the use of a number of methods. For a wide range of specialists and students engaged in the development and application of methods for solving applied problems on computers . Content:General issues. Classes of problems of applied mathematics . Methods considered. Types of computers and aircraft used in the USSR. Characteristics of tasks, methods and computers . General theory of errors of calculations and solution of incorrectly set tasks. Methods for assessing the necessary memory and time of solving problems on a computer . On optimization of algorithms for solving problems on computers . Additions and comments to chapter. Statistical processing of experimental data. Pre-processing of data. Fundamentals of the theory of statistical estimates . Methods of estimating average values. Methods for evaluating the correlation functions of stationary ergodic processes. Methods of foaming of corresponding spectral densities. Methods for estimating the distribution laws of random vectors. Methods for solving some other processing problems. Approximation and calculation of functions. Classes of areas, functions and functions. Task setting and evaluation of the best approximation. Methods of interpolation. Medium-square approximation methods. Methods of Chebyshev (uniform) approximation . Methods of spline approximation. On Optimal Approximation Algorithms. Optimization of algorithms for calculating basic elementary functions on a computer. Calculation of special functions. Additions and comments to chapter. Numerical Integration and Differentiation. Optimization of numerical integration methods. Methods of calculation of special integrals . Methods of finding the first derivatives. Methods for finding higher order derivatives. Additions and comments to chapter. Solution of operator equations. General Theory of Approximate Methods . Direct methods for linear equations. Direct methods for nonlinear equations. Iterative methods for linear equations. Iterative methods for nonlinear equations. Combined methods. Additions and comments to chapter. Solution of integral equations. Linear integral equations of the Fredholm type of the second kind . Linear integral equations of the Fredholm type of the first kind . Linear Singular Integral Equations with Cauchy Core and Convolution Type. Nonlinear Integral Equations . Additions and comments to chapter. Numerical solution of Cauchy problems for ordinary differential equations. Common Numerical Methods for Solving the Cauchy Problem for ODU. Optimization of numerical solution of Cauchy problems for ODU. Solving Cauchy Problems for Systems of Linear Equations. Numerical methods of solving rigid systems. Additions and comments to chapter. Finding roots and solving functions minimization problems. Finding the roots of algebraic polynomials. Methods of minimising unimodal and convex functions. On Optimal Algorithms for Solving Multi-Extreme Problems . Additions and comments to chapter. Applications:Generalized Classification of Computational Mathematics Problems. Generalized Classification of Computational Mathematics Methods . Characteristics of the main domestic computers . Generalized classification of computing systems. Characteristics of VP and VS. Auxiliary values (40 true decimals). Normal distribution. t-distribution. Function values Lk(p). Lower 1 and upper 2 confidence interval boundaries. Equations whose solutions are e. f. Summary of Numerical Differentiation Formulas. References . Subject Index.