Описание: Functional analysis arose from traditional topics of calculus and integral and differential equations. This text starts with problems in numerical analysis, showing how they lead naturally to the concepts of functional analysis. Topics include Banach and Hilbert spaces, contraction mappings, convergence, differentiation and integration, and Euclidean space. 1978 edition.
Описание: This text explores aspects of matrix theory that are most useful in developing and appraising computational methods for solving systems of linear equations and for finding characteristic roots. Suitable for advanced undergraduates and graduate students, it assumes an understanding of the general principles of matrix algebra, including the Cayley-Hamilton theorem, characteristic roots and vectors, and linear dependence. An introductory chapter covers the Lanczos algorithm, orthogonal polynomials, and determinantal identities. Succeeding chapters examine norms, bounds, and convergence; localization theorems and other inequalities; and methods of solving systems of linear equations. The final chapters illustrate the mathematical principles underlying linear equations and their interrelationships. Topics include methods of successive approximation, direct methods of inversion, normalization and reduction of the matrix, and proper values and vectors. Each chapter concludes with a helpful set of references and problems.
Автор: Pettofrezzo Anthony J. Название: Introductory Numerical Analysis ISBN: 0486450163 ISBN-13(EAN): 9780486450162 Издательство: Dover Рейтинг: Цена: 1489 р. Наличие на складе: Поставка под заказ.
Описание: This text features the principles involved in numerical analysis. Its main theme is interpolation of the standpoint of finite differences, least squares theory, and harmonic analysis. Also covers the numerical solutions of ordinary differential equations and approximation through Fourier series. Over 70 examples and 280 exercises. Includes 16 figures and 33 tables. 1967 edition.
Описание: Well-known, respected introduction, updated to integrate concepts and procedures associated with computers. Computation, approximation, interpolation, numerical differentiation and integration, smoothing of data, more. Includes 150 additional problems in this edition.
Numerical analysis is a subject of extreme interest to mathematicians and computer scientists, who will welcome this first inexpensive paperback edition of a groundbreaking classic text on the subject. In an introductory chapter on numerical methods and their relevance to computing, well-known mathematician Richard Hamming ("the Hamming code," "the Hamming distance," and "Hamming window," etc.), suggests that the purpose of computing is insight, not merely numbers. In that connection he outlines five main ideas that aim at producing meaningful numbers that will be read and used, but will also lead to greater understanding of how the choice of a particular formula or algorithm influences not only the computing but our understanding of the results obtained. The five main ideas involve (1) insuring that in computing there is an intimate connection between the source of the problem and the usability of the answers (2) avoiding isolated formulas and algorithms in favor of a systematic study of alternate ways of doing the problem (3) avoidance of roundoff (4) overcoming the problem of truncation error (5) insuring the stability of a feedback system. In this second edition, Professor Hamming (Naval Postgraduate School, Monterey, California) extensively rearranged, rewrote and enlarged the material. Moreover, this book is unique in its emphasis on the frequency approach and its use in the solution of problems. Contents include: I. Fundamentals and Algorithms II. Polynomial Approximation- Classical Theory Ill. Fourier Approximation- Modern Theory IV. Exponential Approximation ... and more Highly regarded by experts in the field, this is a book with unlimited applications for undergraduate and graduate students of mathematics, science and engineering. Professionals and researchers will find it a valuable reference they will turn to again and again.
Описание: Eastlake was the president of the British Royal Academy and director of the National Gallery in London; these positions, together with his own painting career, provided him access to the vast array of paintings that formed the basis for his study. This Dover reprint contains both volumes of his 1847
Описание: In addition to traditional topics in numerical analysis, this text covers modern subjects such as optimal control problems, linear programming, and boundary value problems. Suitable for advanced undergraduate and graduate courses, it is highly relevant to students in a variety of disciplines, including computer science, applied mathematics, and engineering. 1972 edition.
Описание: This book by a prominent mathematician is appropriate for a single-semester course in applied numerical analysis for computer science majors and other upper-level undergraduate and graduate students. Although it does not cover actual programming, it focuses on the applied topics most pertinent to science and engineering professionals. An extensive range of topics includes round-off and function evaluation, real zeros of a function, simultaneous linear equations and matrices, interpolation and roundoff estimation, integration, and ordinary differential equations. Additional subjects include optimization, least squares, orthogonal functions, Fourier series, Chebyshev approximation, and random processes. The author stresses the teaching of mathematical concepts through visual aids, and numerous diagrams and illustrations complement the text.
Описание: This updated introduction to modern numerical analysis is a complete revision of a classic text originally written in Fortran but now featuring the programming language C++. It focuses on a relatively small number of basic concepts and techniques. Many exercises appear throughout the text, most with solutions. An extensive tutorial explains how to solve problems with C++.
Описание: Useful to programmers and stimulating for theoreticians, this text covers the major methods of numerical integration. It offers a balanced presentation: certain sections derive from or allude to deep results of analysis, but most of the final results are expressed in a form accessible to anyone with a background in calculus. An extensive introduction outlines the uses and advantages of numerical integration and includes formulas and guides to orthogonal polynomials and specific integrals. Subsequent chapters explore approximate integration over finite and infinite intervals, error analysis, approximate integration in two or more dimensions, and automatic integration. Five helpful appendixes conclude the text.
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