Automatic Programming And Numerical Methods Of Analysis

Automatic Programming, Numerical Methods and Functional Analysis

Automatic Programming and Numerical Methods of Analysis

The present collection contains the results reported in 1970 at the Seminar on Approximate Com putations held by the Leningrad Section of the Mathematical Institute. Two trends are represented in the collection: automatic programming and numerical methods of analysis. V. N. Faddeeva CONTENTS On the Main Concepts of Parallel Sequencing. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 T. A. Tushkina and K. V. Shakhbazyan The Solution of Certain Parallel Sequencing Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 T. A. Tushkina and K. V. Shakhbazyan Choice of Enumeration in Parallel Sequencing Problems. . . . . . . . . . . . . . . . . . . . . . . . . . 13 K. V. Shakhbaz yan The PRORAB-Computer III (P, v) M-20 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 T. N. Smirnova, A. A. Aleksandrova, Yu. V. Rybakova, and N. A. Solov'eva Application of the PRORAB-Computer III (P, v) M-20 to the Solving of Linear Programming Problems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 T. N. Smirnova On a Matrix Inversion Method. . • . . . . . . . • . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 V. D. Vulichevich The Solution of a Particular Eigenvalue Problem for Certain Matrices of Special Form. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 V. D. Vulichevich and V. N. Kublanovskaya Solution of a Particular Eigenvalue Problem for a Polynomial Matrix. . . . . . . . . . . . . . . . . 65 M. I. Mavlyanova On a Method for Constructing the Matrix Solution for a Polynomial Matrix. . . . . . . . . . . . . . . 71 M. I. Mavlyanova On One Approach to the Solution of the Inverse Eigenvalue Problem. . . . . . . . . . . .. . . . . . . 80 V. N. Kublanovskaya Convergence of the Method of Lines when Solving Nonlinear Parabolic Boundary Value Problems with Discontinuous Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 A. P. Kubanskaya Some Applications of the Five-Point Scheme of the Method of Lines . . . . . . . . . . . . . . . . . . 93 A. P. Kubanskaya On Expansions into Nonminimal Sequences. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104 L. N.

Numerical Analysis with Algorithms and Programming

Numerical Analysis with Algorithms and Programming is the first comprehensive textbook to provide detailed coverage of numerical methods, their algorithms, and corresponding computer programs. It presents many techniques for the efficient numerical solution of problems in science and engineering. Along with numerous worked-out examples, end-of-chapter exercises, and Mathematica® programs, the book includes the standard algorithms for numerical computation: Root finding for nonlinear equations Interpolation and approximation of functions by simpler computational building blocks, such as polynomials and splines The solution of systems of linear equations and triangularization Approximation of functions and least square approximation Numerical differentiation and divided differences Numerical quadrature and integration Numerical solutions of ordinary differential equations (ODEs) and boundary value problems Numerical solution of partial differential equations (PDEs) The text develops students’ understanding of the construction of numerical algorithms and the applicability of the methods. By thoroughly studying the algorithms, students will discover how various methods provide accuracy, efficiency, scalability, and stability for large-scale systems.