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Condition : the geometry of numerical algorithms /

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 shape...

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Bibliographic Details
Main Authors: Bürgisser, Peter, 1962- (Author), Cucker, Felipe, 1958- (Author)
Corporate Author: SpringerLink (Online service)
Format: Online Book
Language:English
Published: Berlin : Springer, [2013]
Series:Grundlehren der mathematischen Wissenschaften ; 349.
Subjects:
Online Access:Online version
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100 1 |a Bürgisser, Peter,  |d 1962-  |e author. 
245 1 0 |a Condition :  |b the geometry of numerical algorithms /  |c Peter Bürgisser, Felipe Cucker. 
264 1 |a Berlin :  |b Springer,  |c [2013] 
264 4 |c ©2013 
300 |a 1 online resource (xxxi, 554 pages) :  |b illustrations. 
336 |a text  |b txt  |2 rdacontent 
337 |a computer  |b c  |2 rdamedia 
338 |a online resource  |b cr  |2 rdacarrier 
490 1 |a Grundlehren der mathematischen Wissenschaften ;  |v 349 
505 0 |a 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 . 
504 |a Includes bibliographical references and index. 
588 |a Description based on print version record. 
520 |a 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. The book puts special emphasis on the probabilistic analysis of numerical algorithms via the analysis of the corresponding condition. The exposition's level increases along the book, starting in the context of linear algebra at an undergraduate level and reaching in its third part the recent developments and partial solutions for Smale's 17th problem which can be explained within a graduate course. Its middle part contains a condition-based course on linear programming that fills a gap between the current elementary expositions of the subject based on the simplex method and those focusing on convex programming. 
506 |a Electronic access restricted to Villanova University patrons. 
650 0 |a Numerical analysis. 
650 0 |a Algorithms. 
700 1 |a Cucker, Felipe,  |d 1958-  |e author. 
776 0 8 |i Print version:  |a Bürgisser, Peter, 1962- author.  |t Condition  |z 9783642388958  |w (OCoLC)855200598 
710 2 |a SpringerLink (Online service) 
830 0 |a Grundlehren der mathematischen Wissenschaften ;  |v 349. 
856 4 0 |u http://ezproxy.villanova.edu/login?URL=http://dx.doi.org/10.1007/978-3-642-38896-5  |z Online version 
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852 |b WWW