Condition

The Geometry of Numerical Algorithms

Authors:

ISBN: 978-3-642-38895-8 (Print) 978-3-642-38896-5 (Online)

Table of contents (21 chapters)

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  1. Front Matter

    Pages I-XXXI

  2. Condition in Linear Algebra ()

    1. Front Matter

      Pages 1-1

    2. No Access

      Book Chapter

      Pages 3-19

      Normwise Condition of Linear Equation Solving

    3. No Access

      Book Chapter

      Pages 21-58

      Probabilistic Analysis

    4. No Access

      Book Chapter

      Pages 59-75

      Error Analysis of Triangular Linear Systems

    5. No Access

      Book Chapter

      Pages 77-100

      Probabilistic Analysis of Rectangular Matrices

    6. No Access

      Book Chapter

      Pages 101-117

      Condition Numbers and Iterative Algorithms

    7. Back Matter

      Pages 119-120

  3. Condition in Linear Optimization ()

    1. Front Matter

      Pages 121-121

    2. No Access

      Book Chapter

      Pages 123-145

      A Condition Number for Polyhedral Conic Systems

    3. No Access

      Book Chapter

      Pages 147-154

      The Ellipsoid Method

    4. No Access

      Book Chapter

      Pages 155-171

      Linear Programs and Their Solution Sets

    5. No Access

      Book Chapter

      Pages 173-192

      Interior-Point Methods

    6. No Access

      Book Chapter

      Pages 193-199

      The Linear Programming Feasibility Problem

    7. No Access

      Book Chapter

      Pages 201-222

      Condition and Linear Programming Optimization

    8. No Access

      Book Chapter

      Pages 223-232

      Average Analysis of the RCC Condition Number

    9. No Access

      Book Chapter

      Pages 233-254

      Probabilistic Analyses of the GCC Condition Number

    10. Back Matter

      Pages 255-258

  4. Condition in Polynomial Equation Solving ()

    1. Front Matter

      Pages 259-259

    2. No Access

      Book Chapter

      Pages 261-282

      A Geometric Framework for Condition Numbers

    3. No Access

      Book Chapter

      Pages 283-294

      Homotopy Continuation and Newton’s Method

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      Book Chapter

      Pages 295-329

      Homogeneous Polynomial Systems

    5. No Access

      Book Chapter

      Pages 331-365

      Smale’s 17th Problem: I

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      Book Chapter

      Pages 367-390

      Smale’s 17th Problem: II

    7. No Access

      Book Chapter

      Pages 391-417

      Real Polynomial Systems

    8. No Access

      Book Chapter

      Pages 419-437

      Probabilistic Analysis of Conic Condition Numbers: I. The Complex Case

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