Felipe Cucker: Condition | Buch

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Cover: 9783642388958 | Condition | The Geometry of Numerical Algorithms | Cucker (u. a.)

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Sprache: Englisch

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Beschreibung

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.

Über den Autor

Peter Bürgisser is an internationally recognized expert in complexity theory. He is associate editor of the journal Computational Complexity and he was invited speaker at the 2010 International Congress Mathematicians. Felipe Cucker is well known for his work on complexity over the real numbers, jointly with L. Blum, S. Smale and M. Shub. He also worked in learning theory and made seminal contributions to condition numbers in optimization and their probabilistic analyses. F.C. is former chair of the Society for the Foundations of Computational Mathematics and the current managing editor of the society's journal.

Zusammenfassung

Unique book combining methods from numerical computation and complexity

Excellent pedagogical presentation

Explanation of Smale's 17th problem

Includes supplementary material: [...]

Inhaltsverzeichnis

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'sMethod.- 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¿.

Details

Erscheinungsjahr:	2013
Fachbereich:	Wahrscheinlichkeitstheorie
Genre:	Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Buch
Seiten:	588
Reihe:	Grundlehren der mathematischen Wissenschaften
Inhalt:	xxxi 554 S.
ISBN-13:	9783642388958
ISBN-10:	3642388957
Sprache:	Englisch
Ausstattung / Beilage:	HC runder Rücken kaschiert
Einband:	Gebunden
Autor:	Cucker, Felipe Bürgisser, Peter
Auflage:	2013
Hersteller:	Springer-Verlag GmbH Springer Berlin Heidelberg Grundlehren der mathematischen Wissenschaften
Maße:	241 x 160 x 36 mm
Von/Mit:	Felipe Cucker (u. a.)
Erscheinungsdatum:	23.08.2013
Gewicht:	1,039 kg

preigu-id: 105697426