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Randomization, Relaxation, and Complexity in Polynomial Equation Solving
 
Edited by: Leonid Gurvits Los Alamos National Laboratory, Los Alamos, NM
Philippe Pébay Sandia National Laboratories, Livermore, CA
J. Maurice Rojas Texas A&M University, College Station, TX
David Thompson Sandia National Laboratories, Livermore, CA
Randomization, Relaxation, and Complexity in Polynomial Equation Solving
eBook ISBN:  978-0-8218-8235-1
Product Code:  CONM/556.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
Randomization, Relaxation, and Complexity in Polynomial Equation Solving
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Randomization, Relaxation, and Complexity in Polynomial Equation Solving
Edited by: Leonid Gurvits Los Alamos National Laboratory, Los Alamos, NM
Philippe Pébay Sandia National Laboratories, Livermore, CA
J. Maurice Rojas Texas A&M University, College Station, TX
David Thompson Sandia National Laboratories, Livermore, CA
eBook ISBN:  978-0-8218-8235-1
Product Code:  CONM/556.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
  • Book Details
     
     
    Contemporary Mathematics
    Volume: 5562011; 217 pp
    MSC: Primary 11; 12; 14; 52; 65

    This volume corresponds to the Banff International Research Station Workshop on Randomization, Relaxation, and Complexity, held from February 28–March 5, 2010 in Banff, Alberta, Canada.

    This volume contains a sample of advanced algorithmic techniques underpinning the solution of systems of polynomial equations. The papers are written by leading experts in algorithmic algebraic geometry and touch upon core topics such as homotopy methods for approximating complex solutions, robust floating point methods for clusters of roots, and speed-ups for counting real solutions. Vital related topics such as circuit complexity, random polynomials over local fields, tropical geometry, and the theory of fewnomials, amoebae, and coamoebae are treated as well. Recent advances on Smale's 17th Problem, which deals with numerical algorithms that approximate a single complex solution in average-case polynomial time, are also surveyed.

    Readership

    Graduate students and research mathematicians interested in algorithms in algebraic geometry.

  • Table of Contents
     
     
    • Articles
    • Martin Avendaño and Ashraf Ibrahim — Multivariate ultrametric root counting
    • Daniel J. Bates, Jonathan D. Hauenstein and Andrew J. Sommese — A parallel endgame
    • Carlos Beltrán and Luis Miguel Pardo — Efficient polynomial system solving by numerical methods
    • Bruno Grenet, Erich L. Kaltofen, Pascal Koiran and Natacha Portier — Symmetric determinantal representation of formulas and weakly skew circuits
    • Tsung-Lin Lee and Tien-Yien Li — Mixed volume computation in solving polynomial systems
    • Anton Leykin — A search for an optimal start system for numerical homotopy continuation
    • Mounir Nisse — Complex tropical localization, and coamoebas of complex algebraic hypersurfaces
    • Osbert Bastani, Christopher J. Hillar, Dimitar Popov and J. Maurice Rojas — Randomization, sums of squares, near-circuits, and faster real root counting
    • Korben Rusek, Jeanette Shakalli and Frank Sottile — Dense fewnomials
    • Zhonggang Zeng — The numerical greatest common divisor of univariate polynomials
  • Additional Material
     
     
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 5562011; 217 pp
MSC: Primary 11; 12; 14; 52; 65

This volume corresponds to the Banff International Research Station Workshop on Randomization, Relaxation, and Complexity, held from February 28–March 5, 2010 in Banff, Alberta, Canada.

This volume contains a sample of advanced algorithmic techniques underpinning the solution of systems of polynomial equations. The papers are written by leading experts in algorithmic algebraic geometry and touch upon core topics such as homotopy methods for approximating complex solutions, robust floating point methods for clusters of roots, and speed-ups for counting real solutions. Vital related topics such as circuit complexity, random polynomials over local fields, tropical geometry, and the theory of fewnomials, amoebae, and coamoebae are treated as well. Recent advances on Smale's 17th Problem, which deals with numerical algorithms that approximate a single complex solution in average-case polynomial time, are also surveyed.

Readership

Graduate students and research mathematicians interested in algorithms in algebraic geometry.

  • Articles
  • Martin Avendaño and Ashraf Ibrahim — Multivariate ultrametric root counting
  • Daniel J. Bates, Jonathan D. Hauenstein and Andrew J. Sommese — A parallel endgame
  • Carlos Beltrán and Luis Miguel Pardo — Efficient polynomial system solving by numerical methods
  • Bruno Grenet, Erich L. Kaltofen, Pascal Koiran and Natacha Portier — Symmetric determinantal representation of formulas and weakly skew circuits
  • Tsung-Lin Lee and Tien-Yien Li — Mixed volume computation in solving polynomial systems
  • Anton Leykin — A search for an optimal start system for numerical homotopy continuation
  • Mounir Nisse — Complex tropical localization, and coamoebas of complex algebraic hypersurfaces
  • Osbert Bastani, Christopher J. Hillar, Dimitar Popov and J. Maurice Rojas — Randomization, sums of squares, near-circuits, and faster real root counting
  • Korben Rusek, Jeanette Shakalli and Frank Sottile — Dense fewnomials
  • Zhonggang Zeng — The numerical greatest common divisor of univariate polynomials
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.