This book is the official proceedings of a conference on Numerical Methods in Approximation Theory which was held at the Mathematisches Forschungs- institut in Oberwolfach during the week of November 24 30, 1991. It contains refereed and edited papers by 20 of the 49 participants. The book is dedicated to the memory of Prof. Lothar Collatz who main- tained a long and active interest in numerical approximation. It is the ninth in a series of volumes published by Birkhiiuser resulting from conferences on the subject held at Oberwolfach, and co-organized by Prof. Collatz. We now briefly describe...