Introduction to Numerical Computation in PascalOur intention in this book is to cover the core material in numerical analysis normally taught to students on degree courses in computer science. The main emphasis is placed on the use of analysis and programming techniques to produce well-designed, reliable mathematical software. The treatment should be of interest also to students of mathematics, science and engineering who wish to learn how to write good programs for mathematical computations. The reader is assumed to have some acquaintance with Pascal programming. Aspects of Pascal particularly relevant to numerical computation are revised and developed in the first chapter. Although Pascal has some drawbacks for serious numerical work (for example, only one precision for real numbers), the language has major compensating advantages: it is a widely used teaching language that will be familiar to many students and it encourages the writing of clear, well structured programs. By careful use of structure and documentation, we have produced codes that we believe to be readable; particular care has been taken to ensure that students should be able to understand the codes in conjunction with the descriptive material given in the book. |
Contents
Programming in Pascal | 3 |
2 | 22 |
Principles of Mathematical Software | 28 |
Copyright | |
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absolute error adsimp algorithm approximation aprod array BEGIN bisection method boolean calculate coefficients composite trapezoidal rule conjugate gradient method constant correct data types decimal places defined derivative digits eflag equation errbnd error numbers errormessage estimate the integral extrapolation f(xx formula FORTRAN function f(x Gauss-Seidel method Gaussian elimination Gaussian rule gaussint graph integer integrand interval iteration ivalue library routine limiting precision linear lufac lusolv mathematical mathlib library matrix mult Newton's method obtain output parameter pivot polnewt polsum polynomial positive definite poweri real numbers real root required accuracy right hand side Romberg integration Romberg table rounding error Routines called secant method simple root Simpson's rule singular solution solve step stepwidth subintegral subinterval subprogram theorem tolmin transformation trapezoidal rule triangular triangular factors truncation error underflow variable vector write writeln x₁ xmem zero