Ebook: Discrete Iterations: A Metric Study
- Tags: Numerical Analysis
- Series: Springer Series in Computational Mathematics 6
- Year: 1986
- Publisher: Springer-Verlag Berlin Heidelberg
- Edition: 1
- Language: English
- pdf
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.
Content:
Front Matter....Pages I-XIV
Discrete Iterations and Automata Networks: Basic Concepts....Pages 1-25
A Metric Tool....Pages 27-41
The Boolean Perron-Frobenius and Stein-Rosenberg Theorems....Pages 43-55
Boolean Contraction and Applications....Pages 57-78
Comparison of Operating Modes....Pages 79-93
The Discrete Derivative and Local Convergence....Pages 95-129
A Discrete Newton Method....Pages 131-166
General Conclusion....Pages 166-166
Back Matter....Pages 167-195
Content:
Front Matter....Pages I-XIV
Discrete Iterations and Automata Networks: Basic Concepts....Pages 1-25
A Metric Tool....Pages 27-41
The Boolean Perron-Frobenius and Stein-Rosenberg Theorems....Pages 43-55
Boolean Contraction and Applications....Pages 57-78
Comparison of Operating Modes....Pages 79-93
The Discrete Derivative and Local Convergence....Pages 95-129
A Discrete Newton Method....Pages 131-166
General Conclusion....Pages 166-166
Back Matter....Pages 167-195
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