Library

X
feed icon rss

Your email was sent successfully. Check your inbox.

An error occurred while sending the email. Please try again.

Proceed reservation?

Export
  • 1
    Electronic Resource
    Electronic Resource
    Nonlinear reduction for solving deficient polynomial systems by continuation methods (1992)
    Springer
    Numerische Mathematik 63 (1992), S. 263-282 
    Details
    ISSN: 0945-3245
    Keywords: 65H10 ; 68Q40
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary Neither continuation methods, nor symbolic elimination methods can be directly applied to compute all finite solutions to polynomial systems, because the amount of computational time is mostly not proportional to the dimension of the system and to the number of finite solutions. The notion of S-polynomials is used to developed a reduction algorithm to lower the total degree of the deficient polynomial system, so that computing the solutions at infinity can be avoided. Applying the reduction algorithm before solving the system with continuation methods, yields a reliable solution method.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01385861
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 2
    Electronic Resource
    Electronic Resource
    Symbolic homotopy construction (1993)
    Springer
    Applicable algebra in engineering, communication and computing 4 (1993), S. 169-183 
    Details
    ISSN: 1432-0622
    Keywords: Bézout number ; BKK bound ; Homotopy continuation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics , Technology
    Notes: Abstract The classical Theorem of Bézout yields an upper bound for the number of finite solutions to a given polynomial system, but is very often too large to be useful for the construction of a start system, for the solution of a polynomial system by means of homotopy continuation. The BKK bound gives a much lower upper bound for the number of solutions, but unfortunately, constructing a start system based on this bound seems as hard as solving the original given polynomial system. This paper presents a way for computing an upper bound together with the construction of a start system. The first computation is performed symbolically. Due to this symbolic computation, the constructed start system can be solved numerically more efficiently. The paper generalizes current approaches for homotopy construction towards the BKK bound.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01202036
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 3
    Electronic Resource
    Electronic Resource
    Polyhedral end games for polynomial continuation (1998)
    Springer
    Numerical algorithms 18 (1998), S. 91-108 
    Details
    ISSN: 1572-9265
    Keywords: homotopy continuation ; polynomial systems ; Newton polytopes ; Bernshtein bound ; cycle number ; 14Q99 ; 52A39 ; 52B20 ; 65H10
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract Bernshtein’s theorem provides a generically exact upper bound on the number of isolated solutions a sparse polynomial system can have in (ℂ*)n, with ℂ* = ℂ\{0}. When a sparse polynomial system has fewer than this number of isolated solutions some face system must have solutions in (ℂ*)n. In this paper we address the process of recovering a certificate of deficiency from a diverging solution path. This certificate takes the form of a face system along with approximations of its solutions. We apply extrapolation to estimate the cycle number and the face normal. Applications illustrate the practical usefulness of our approach.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1019163811284
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 4
    facet.materialart.
    Unknown
    Symmetric Newton Polytopes for Solving Sparse Polynomial Systems. (1994)
    Details
    Publication Date: 2014-02-26
    Description: The aim of this paper is to compute all isolated solutions to symmetric polynomial systems. Recently, it has been proved that modelling the sparse structure of the system by its Newton polytopes leads to a computational breakthrough in solving the system. In this paper, it will be shown how the Lifting Algorithm, proposed by Huber and Sturmfels, can be applied to symmetric Newton polytopes. This symmetric version of the Lifting Algorithm enables the efficient construction of the symmetric subdivision, giving rise to a symmetric homotopy, so that only the generating solutions have to be computed. Efficiency is obtained by combination with the product homotopy. Applications illustrate the practical significance of the presented approach.
    Keywords: ddc:000
    Language: English
    Type: reportzib , doc-type:preprint
    Format: application/postscript
    Format: application/pdf
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    OPUS
Close ⊗
This website uses cookies and the analysis tool Matomo. More information can be found here...