作者：Conte, de Boor. 1980

This is the third edition of a book on elementary numerical analysis which
is designed specifically for the needs of upper-division undergraduate
students in engineering, mathematics, and science including, in particular,
computer science. On the whole, the student who has had a solid college
calculus sequence should have no difficulty following the material.
Advanced mathematical concepts, such as norms and orthogonality, when
they are used, are introduced carefully at a level suitable for undergraduate
students and do not assume any previous knowledge. Some familiarity
with matrices is assumed for the chapter on systems of equations and with
differential equations for Chapters 8 and 9. This edition does contain some
sections which require slightly more mathematical maturity than the previous edition. However, all such sections are marked with asterisks and all
can be omitted by the instructor with no loss in continuity.
This new edition contains a great deal of new material and significant
changes to some of the older material. The chapters have been rearranged
in what we believe is a more natural order. Polynomial interpolation
(Chapter 2) now precedes even the chapter on the solution of nonlinear
systems (Chapter 3) and is used subsequently for some of the material in
all chapters. The treatment of Gauss elimination (Chapter 4) has been
simplified. In addition, Chapter 4 now makes extensive use of Wilkinson’s
backward error analysis, and contains a survey of many well-known
methods for the eigenvalue-eigenvector problem. Chapter 5 is a new
chapter on systems of equations and unconstrained optimization. It contains an introduction to steepest-descent methods, Newton’s method for
nonlinear systems of equations, and relaxation methods for solving large
linear systems by iteration. The chapter on approximation (Chapter 6) has
been enlarged. It now treats best approximation and good approximation
ix
x PREFACE
by polynomials, also approximation by trigonometric functions, including
the Fast Fourier Transforms, as well as least-squares data fitting, orthogonal polynomials, and curve fitting by splines. Differentiation and integration are now treated in Chapter 7, which contains a new section on
adaptive quadrature. Chapter 8 on ordinary differential equations contains
considerable new material and some new sections. There is a new section
on step-size control in Runge-Kutta methods and a new section on stiff
differential equations as well as an extensively revised section on numerical
instability. Chapter 9 contains a brief introduction to collocation as a
method for solving boundary-value problems.
This edition, as did the previous one, assumes that students have
access to a computer and that they are familiar with programming in some
procedure-oriented language. A large number of algorithms are presented
in the text, and FORTRAN programs for many of these algorithms have
been provided. There are somewhat fewer complete programs in this
edition. All the programs have been rewritten in the FORTRAN 77
language which uses modern structured-programming concepts. All the
programs have been tested on one or more computers, and in most cases
machine results are presented. When numerical output is given, the text
will indicate which machine (IBM, CDC, UNIVAC) was used to obtain
the results.
The book contains more material than can usually be covered in a
typical one-semester undergraduate course for general science majors. This
gives the instructor considerable leeway in designing the course. For this, it
is important to point out that only the material on polynomial interpolation in Chapter 2, on linear systems in Chapter 4, and on differentiation
and integration in Chapter 7, is required in an essential way in subsequent
chapters. The material in the first seven chapters (exclusive of the starred
sections) would make a reasonable first course.
We take this opportunity to thank those who have communicated to us
misprints and errors in the second edition and have made suggestions for
improvement. We are especially grateful to R. E. Barnhill, D. Chambless,
A. E. Davidoff, P. G. Davis, A. G. Deacon, A. Feldstein, W. Ferguson,
A. O. Garder, J. Guest, T. R. Hopkins, D. Joyce, K. Kincaid, J. T. King,
N. Krikorian, and W. E. McBride.
S. D. Conte
Carl de Boo