Discrete Iterations: A Metric Study (Springer Series in Computational Mathematics) - Hardcover

Robert, Francois; Rokne, Jon [Translator]

Hardcover

ISBN 10: 3540136231 ISBN 13: 9783540136231

Publisher: Springer, 1986

Synopsis

a c 9 h In presenting this monograph, I would like to indicate both its orientation as well as my personal reasons for being interested in discrete iterations (that is, iterations on a generally very large,jinite set). While working in numerical analysis I have been interested in two main aspects: - the algorithmic aspect: an iterative algorithm is a mathematical entity which behaves in a dynamic fashion. Even if it is started far from a solution, it will often tend to get closer and closer. - the mathematical aspect: this consists of a coherent and rigorous analy­ sis of convergence, with the aid of mathematical tools (these tools are mainly the use of norms for convergence proofs, the use of matrix algebra and so on). One may for example refer to the algorithmic and mathematical aspects of Newton's method in JRn as well as to the QR algorithm for eigenvalues of matrices. These two algorithms seem to me to be the most fascinating algorithms in numerical analysis, since both show a remarkable practical efficiency even though there exist relatively few global convergence results for them.

About this title

Language Notes

Text: English, French (translation)

Edition details

• Publisher: Springer
• Publication date: 1986
• ISBN 10: 3540136231
• ISBN 13: 9783540136231
• Binding: Hardcover
• Language: English
• Edition number: 1