# Discrete Iterations

## A Metric Study

Part of the Springer Series in Computational Mathematics book series (SSCM, volume 6)

Part of the Springer Series in Computational Mathematics book series (SSCM, volume 6)

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.

Eigenvalue Mathematica Matrix Newton's method algebra algorithms boundary element method convergence eXist efficiency iteration numerical analysis proof set tool

- DOI https://doi.org/10.1007/978-3-642-61607-5
- Copyright Information Springer-Verlag Berlin Heidelberg 1986
- Publisher Name Springer, Berlin, Heidelberg
- eBook Packages Springer Book Archive
- Print ISBN 978-3-642-64882-3
- Online ISBN 978-3-642-61607-5
- Series Print ISSN 0179-3632
- About this book