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Condition : the geometry of numerical algorithms

Author: Peter Bürgisser; Felipe Cucker
Publisher: Berlin ; Heidelberg ; New York [etc.] : Springer, cop. 2013.
Series: Grundlehren der mathematischen Wissenschaften, 349.
Edition/Format:   Print book : EnglishView all editions and formats
Database:WorldCat
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4e de couverture.
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Document Type: Book
All Authors / Contributors: Peter Bürgisser; Felipe Cucker
ISBN: 9783642388958 3642388957
OCLC Number: 863005871
Description: 1 vol. (XXXI-554 p.) : graph. ; 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 4.- 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: "The authors intend with this book to fill the gap by addressing the probabilistic analysis of the algorithms related to condition numbers. ... Under the vigilant eyes of so Read more...

 
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