Condition

The Geometry of Numerical Algorithms

  • Peter Bürgisser
  • Felipe Cucker

Part of the Grundlehren der mathematischen Wissenschaften book series (GL, volume 349)

Table of contents

  1. Front Matter
    Pages I-XXXI
  2. Condition in Linear Algebra (Adagio)

    1. Front Matter
      Pages 1-1
    2. Peter Bürgisser, Felipe Cucker
      Pages 3-19
    3. Peter Bürgisser, Felipe Cucker
      Pages 21-58
    4. Peter Bürgisser, Felipe Cucker
      Pages 59-75
    5. Peter Bürgisser, Felipe Cucker
      Pages 77-100
    6. Peter Bürgisser, Felipe Cucker
      Pages 101-117
    7. Back Matter
      Pages 119-120
  3. Condition in Linear Optimization (Andante)

    1. Front Matter
      Pages 121-121
    2. Peter Bürgisser, Felipe Cucker
      Pages 123-145
    3. Peter Bürgisser, Felipe Cucker
      Pages 147-154
    4. Peter Bürgisser, Felipe Cucker
      Pages 155-171
    5. Peter Bürgisser, Felipe Cucker
      Pages 173-192
    6. Peter Bürgisser, Felipe Cucker
      Pages 193-199
    7. Peter Bürgisser, Felipe Cucker
      Pages 201-222
    8. Peter Bürgisser, Felipe Cucker
      Pages 223-232
    9. Peter Bürgisser, Felipe Cucker
      Pages 233-254
    10. Back Matter
      Pages 255-258
  4. Condition in Polynomial Equation Solving (Allegro con brio)

    1. Front Matter
      Pages 259-259
    2. Peter Bürgisser, Felipe Cucker
      Pages 261-282

About this book

Introduction

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.

Keywords

complexity condition numbers homotopy continuation linear optimization probabilistic analysis of algorithms

Authors and affiliations

  • Peter Bürgisser
    • 1
  • Felipe Cucker
    • 2
  1. 1.Technical University of Berlin Institute of MathematicsBerlinGermany
  2. 2.City University of Hong Kong Department of MathematicsHong KongHong Kong SAR

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-38896-5
  • Copyright Information Springer-Verlag Berlin Heidelberg 2013
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-642-38895-8
  • Online ISBN 978-3-642-38896-5
  • Series Print ISSN 0072-7830
  • Series Online ISSN 2196-9701
  • About this book