Numerical mathematics 2. An introduction -- under consideration of lectures by F. L. Bauer.
This is the fifth German edition of this highly successful book, the first edition of which appeared in 1973. The English translation has already seen its third edition in 2002. The previous editions were ably reviewed [see Introduction to numerical analysis. Transl. from the German by R. Bartels, W. Gautschi, and C. Witzgall. 3rd ed. [B] Texts in Applied Mathematics. 12. (New York, NY: Springer). (2002; Zbl 1004.65001), Introduction to numerical analysis. Translated from the German by R. Bartels, W. Gautschi and C. Witzgall. 2. ed. (English) Texts in Applied Mathematics. 12. (New York: Springer-Verlag). (1993; Zbl 0771.65002), Introduction to numerical analysis. Transl. by R. Bartels, W. Gautschi, and C. Witzgall. (English) (New York-Heidelberg-Berlin: Springer-Verlag) (1980; Zbl 0423.65002)] for the English translations and [Einführung in die Numerische Mathematik II. Unter Berücksichtigung von Vorlesungen von F. L. Bauer. (German) Heidelberger Taschenbücher. Band 114. (Berlin-Heidelberg-New York: Springer-Verlag) (1973; Zbl 0257.65001)] for the German original. The present German edition does not differ much from the previous one. It contains three big chapters: eigenvalue problems, ordinary differential equations and iterative methods for the solution of large linear problems. One of the new sections is 7.3.8 which describes advanced new methods to increase the efficiency of multiple shooting methods. Krylov space methods for the solution of large linear systems also are treated in more detail and in section 8.10 all Krylov space methods are included in a detailed comparison of iterative methods. The book is written with the same care as its predecessors and is a very valuable resource for teachers and researchers.
scientific article; zbMATH DE number 2152344