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代数方程组和计算复杂性理论(英文版)


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代数方程组和计算复杂性理论(英文版)
  • 书号:7030039440
    作者:王则柯等
  • 外文书名:
  • 装帧:
    开本:B5
  • 页数:252
    字数:200000
    语种:
  • 出版社:科学出版社
    出版时间:2006-07-29
  • 所属分类:Z89 文摘、索引
  • 定价: ¥70.00元
    售价: ¥55.30元
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Simplicial and continuation methods for approximating fixed points and solutions to systems of equations as well as their computational complexity problems are active topics ofrecent research.The starting point ofthe complexity theory in numerical methods in the elegant paper entitled "The fundamental theorem of algebra and complexity theory" by S.Smale.Since that,among others there are two main developments:complexity theories of simplical (or piecewise linear) homotopy methods and complexity theories of incremental algorithms or global Newton methods.This monograph provides a systemstical and self-contained presentation of the developments.Extra efforts have been paid upon its clarity.
Researchers and postgraduate students interested in computational mathematics and computer science.
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目录

  • Chpater 1
    Kuhn's algorithm for algebraic equations
    §1.Triangulation and labelling
    §2.Complementary pivoting algorithm
    §3.Convergence,I
    §4.Convergence,II
    Chapter 2
    Efficiency of Kuhn’S algorithm
    §1.Error estimate
    §2.Cost estimate
    §3.Monotonicity problem
    §4.Results on monotonicity
    Chapter 3
    Newton method and approximate zeros
    §1.Approximate zeros
    §2.Coefficients of polynomials
    §3. One step of Newton iteration
    §4.Conditions for approximate zeros
    Chapter 4
    A complexity comparison of Kuhn's algorithm and Newton method
    §1.Smale’S work on the complexity of Newton method
    §2.Set of bad polynomials and its volume estimate
    §3.Locate approximate zeros by Kuhn's algorithm
    §4.Some remarks
    Chapter 5
    Incremental algorithms and cost theory
    §1. Incremental algorithms Ih,f
    §2.Euler's algorithm is of efficiency k
    §3.Generalized approximate zeros
    §4.Ek iteration
    §5.Cost theory of Ek as an Euler's algorithm
    §6.Incremental algorithms of efficiency k
    Chapter 6
    Homotopy algorithms
    §1. Homotopies and Index Theorem
    §2. Degree and its invariance
    §3. Jacobian of polynomial mappings
    §4. Conditions for boundedness of solutions
    Chapter 7
    Probabilistic discussion on zeros of polynomial mappings
    §1. Number of zeros of polynomial mappings
    §2.Isolated zeros
    §3.Locating zeros of analytic functions in bounded regions
    Chapter 8
    Piecewise linear algorithms
    §1.Zeros of PL mapping and their indexes
    §2.PL approximations
    §3.PL homotopy algorithms work with probability one
    References
    Index
    Acknowledgments
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