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Condition : the geometry of numerical algorithms

Author: Peter Bürgisser; Felipe Cucker
Publisher: [Place of publication not identified] : [publisher not identified], 2013.
Series: Grundlehren der mathematischen Wissenschaften.
Edition/Format:   eBook : Document : 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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Genre/Form: Electronic books
Additional Physical Format: Print version:
Bürgisser, Peter.
Condition : The Geometry of Numerical Algorithms.
Dordrecht : Springer, ©2013
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Peter Bürgisser; Felipe Cucker
ISBN: 9783642388965 3642388965
OCLC Number: 862201145
Description: 1 online resource.
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 4.- 21 Probabilistic Analysis of Conic Condition Numbers: II. The Real Case.- Appendix.
Series Title: Grundlehren der mathematischen Wissenschaften.
Responsibility: by Peter Bürgisser, Felipe Cucker.
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"The book under review is divided into three parts, 'which approximately correspond to themes of conditioning in linear algebra, linear programming, and polynomial equation solving'. ... Given its Read more...

 
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