Introduction to Numerical Analysis

This is the third edition of a venerable introduction to numerical analysis by two authors who have contributed much to the subject.  It is intended for advanced undergraduates and beginning graduate students.  Many of the topics they treat are still quite relevant, although the subject has evolved considerably over the years. The first edition actually includes references to some algorithms written in Algol.

 

The authors are known for significant work in several areas, especially rational function extrapolation methods for tabulated data and for numerical solutions of initial value problems in differential equations.

 

Topics that get the most attention are solutions of linear systems by a variety of methods (standard and iterative), eigenvalue problems, numerical solutions of ordinary differential equations, and interpolation methods.  Almost a quarter of this quite lengthy book is devoted to differential equations.

 

The book is probably most useful now as a reference.  It would be a difficult text for someone new to the subject.  It is densely written and not much inclined to motivate topics as it introduces them.  The treatment mostly emphasizes the theoretical aspects and offers very few examples of actual numerical computation. Even the many exercises concentrate chiefly on theory.

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Bill Satzer (bsatzer@gmail.com), now retired from 3M Company, spent most of his career as a mathematician working in industry on a variety of applications. He did his PhD work in dynamical systems and celestial mechanics.