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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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Main Authors: Bürgisser, Peter. (Author, http://id.loc.gov/vocabulary/relators/aut), Cucker, Felipe. (http://id.loc.gov/vocabulary/relators/aut)
Corporate Author: SpringerLink (Online service)
Language:English
Published: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2013.
Edition:1st ed. 2013.
Series:Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics, 349
Subjects:
Algorithms.
Computer science—Mathematics.
Probabilities.
Computer mathematics.
Mathematical optimization.
Mathematics of Computing.
Probability Theory and Stochastic Processes.
Computational Mathematics and Numerical Analysis.
Computational Science and Engineering.
Optimization.
Online Access:https://doi.org/10.1007/978-3-642-38896-5
Table of 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 .

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