Originally published in 1987, this book is devoted to the approximation of real functions by real rational functions. These are, in many ways, a more convenient tool than polynomials, and interest in them was growing, especially since D. Newman's work in the mid-sixties. The authors aim at presenting the basic achievements of the subject and, for completeness, also discuss some topics from complex rational approximation. Certain classical and modern results from linear approximation theory and spline approximation are also included for comparative purposes. This book will be of value to anyone with an interest in approximation theory and numerical analysis.
1. Qualitative theory of linear approximation;
2. Qualitative theory of the best rational approximation;
3. Some classical results in the linear theory;
4. Approximation of some important functions;
5. Uniform approximation of some function classes;
6. Converse theorems for rational approximation;
7. Spline approximation and Besov spaces;
8. Relations between rational and spline approximations;
9. Approximation with respect to Hausdorff distance;
10. The o-effect;
11. Lower bounds;
12. Padé approximations; Appendix; References; Author index; Notation and subject index.