A First Course in Numerical Analysis

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Courier Corporation, 2001 - Mathematics - 606 pages
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This outstanding text by two well-known authors treats numerical analysis with mathematical rigor, but presents a minimum of theorems and proofs. Oriented toward computer solutions of problems, it stresses error analysis and computational efficiency, and compares different solutions to the same problem.
Following an introductory chapter on sources of error and computer arithmetic, the text covers such topics as approximation and algorithms; interpolation; numerical differentiation and numerical quadrature; the numerical solution of ordinary differential equations; functional approximation by least squares and by minimum-maximum error techniques; the solution of nonlinear equations and of simultaneous linear equations; and the calculation of eigenvalues and eigenvectors of matrices.
This second edition also includes discussions of spline interpolation, adaptive integration, the fast Fourier transform, the simplex method of linear programming, and simple and double QR algorithms. Problems — some strictly mathematical, others requiring a computer — appear at the end of each chapter.
 

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Contents

INTRODUCTION AND PRELIMINARIES
1
APPROXIMATION AND ALGORITHMS
31
INTERPOLATION
52
NUMERICAL DIFFERENTIATION NUMERICAL QUADRATURE AND SUMMATION
89
THE NUMERICAL SOLUTION OF ORDINARY DIFFERENTIAL EQUATIONS
164
FUNCTIONAL APPROXIMATION LEASTSQUARES TECHNIQUES
247
FUNCTIONAL APPROXIMATION MINIMUM MAXIMUM ERROR TECHNIQUES
285
THE SOLUTION OF NONLINEAR EQUATIONS
332
THE SOLUTION OF SIMULTANEOUS LINEAR EQUATIONS
410
THE CALCULATION OF EIGENVALUES AND EIGENVECTORS OF MATRICES
483
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About the author (2001)

Jeffrey J. McConnell, Professor of Computer Science and department chair, has been on the faculty of Canisius College, Buffalo, since 1983 and is the author of the textbook "Analysis of Algorithms: An Active Learning Approach" (Jones & Bartlett, 2001).

Anthony Ralston is an Academic Visitor in the Department of Computing at Imperial College, London, and Professor Emeritus in the Department of Computer Science at the State University of New York at Buffalo, which he founded in 1967 and chaired until 1980. He is the author or editor of more than a dozen books on computer science and related areas, and a frequent contributor to leading books and journals in the field. He has served as president of the American Federation for Information Processing Societies and the Association for Computing Machinery. He is a recipient of the ACM's Distinguished Service Award, a Fellow of the American Association for the Advancement of Science and a Fellow of the Royal Society of Arts.

Edwin D. Reilly is Professor Emeritus of Computer Science at the State University of New York at Albany. He served as the first chairman of its computer science department when founded in 1967 and as the first director of its computing center in 1965. Prior to that time, he served in computer management positions at the General Electric Knolls Atomic Power Laboratory in Schenectady, NY. He began his career in computing at the National Security Agency in Washington in 1955. He holds the Ph.D. in physics from Rensselaer Polytechnic Institute and is currently president of his consulting firm "Cybernetic Information Systems," He is the co-author of the textbooks "Pascalgorithms" (Houghton-Mifflin) and "VAX AssemblyLanguage" (Macmillan, US). He is a member of the Association for Computing Machinery, the IEEE Computer Society, the American Physical Society, the Mathematical Association of America, Sigma Xi, and the America Association for the Advancement of Science.

David Hemmendinger is Associate Professor of Computer Science and department chair at Union College, Schenectady, New York. He has also taught computer science at Wright State University, Ohio. His interests include programming languages, concurrent programming, and formal verification of hardware designs. He began work in computer science in 1981, having previously taught philosophy at the City University of New York, and at Antioch and Kenyon Colleges. He has degrees from Harvard (B.A.) and Stanford Universities (M.S. in mathematics), Yale (M.A., Ph.D. in philosophy) and Wright State University (M.S. in computer science). He is a senior member of the IEEE, and a member of the Association for Computing Machinery, Phi Beta Kappa, and Sigma Xi.

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