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Condition : the geometry of numerical algorithms

Author: Peter Bürgisser; Felipe Cucker
Publisher: Berlin : Springer, 2013
Series: Grundlehren der mathematischen Wissenschaften, 349
Edition/Format:   Book : EnglishView all editions and formats
Database:WorldCat
Summary:
This book gathers threads that have evolved across different mathematical disciplines into seamless narrative. It deals with condition as a main aspect in the understanding of the performance --regarding both stability and complexity-- of numerical algorithms. While the role of condition was shaped in the last half-century, so far there has not been a monograph treating this subject in a uniform and systematic way.  Read more...
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Document Type: Book
All Authors / Contributors: Peter Bürgisser; Felipe Cucker
ISBN: 9783642388958 3642388957
OCLC Number: 859140096
Notes: Textbook for graduates
Description: xxxi, 554 p. : illustrations ; 25 cm.
Contents: Preface. Overture: on the condition of numerical problems and the numbers that measure it. I. Condition in linear algebra (adagio). 1. Normwise condition of linear equation solving ; 2. Probabilistic analysis ; 3. Error analysis of triangular linear systems ; 4. Probabilistic analysis of rectangular matrices ; 5. Condition numbers and iterative algorithms. Intermezzo I: condition of structured data. II. Condition in linear optimization (andante). 6. A condition number for polyhedral conic systems ; 7. The ellipsoid method ; 8. Linear programs and their solution sets ; 9. Interior-point methods ; 10. The linear programming feasibility problem ; 11. Condition and linear programming optimization ; 12. Average analysis of the RCC condition number ; 13. Probabilistic analyses of the GCC condition number. Intermezzo II: the condition of the condition. III. Condition in polynomial equation solving (allegro con brio). 14. A geometric framework for condition numbers ; 15. Homotopy continuation and Newton's method ; 16. Homogeneous polynomial systems ; 17. Smale's 17th problem: I ; 18. Smale's 17th problem: II ; 19. Real polynomial systems ; 20. Probabilistic analysis of conic condition numbers: I. the complex case ; 21. Probabilistic analysis of conic condition numbers: II. the real case. Appendix
Series Title: Grundlehren der mathematischen Wissenschaften, 349
Responsibility: Peter Bürgisser, Felipe Cucker
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From the book reviews: "This book studies a type of numerical imprecision that arises universally. ... Burgisser (Technical Univ. of Berlin, Germany) and Cucker (City Univ. of Hong Kong) provide the Read more...

 
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