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
    Solving large nonlinear systems of equations by an adaptive condensation process (1986)
    Springer
    Numerische Mathematik 50 (1986), S. 633-653 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65H10 ; 65H15 ; 65K10 ; 65N20 ; 65N30 ; CR: G1.5
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary We present an algorithm which efficiently solves large nonlinear systems of the form $$Au = F(u), u \in \mathbb{R}^n $$ whenever an (iterative) solver “A −1” for the symmetric positive definite matrixA is available andF'(u) is symmetric. Such problems arise from the discretization of nonlinear elliptic partial differential equations. By means of an adaptive decomposition process we split the original system into a low dimensional system — to be treated by any sophisticated solver — and a remaining high-dimensional system, which can easily be solved by fixed point iteration. Specifically we choose a Newton-type trust region algorithm for the treatment of the small system. We show global convergence under natural assumptions on the nonlinearity. The convergence results typical for trust-region algorithms carry over to the full iteration process. The only large systems to be solved are linear ones with the fixed matrixA. Thus existing software for positive definite sparse linear systems can be used.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01398377
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 2
    Book
    Book
    Software Engineering im Scientific Computing; Beiträge eines Workshops in Hamburg 6.-8. Juni 1995 (1996)
    Braunschweig u.a. :Vieweg,
    Details
    Title: Software Engineering im Scientific Computing; Beiträge eines Workshops in Hamburg 6.-8. Juni 1995
    Contributer: Mackens, Wolfgang , Rump, Siegfried M.
    Publisher: Braunschweig u.a. :Vieweg,
    Year of publication: 1996
    Pages: 315 S.
    Series Statement: Angewandte Mathematik/Informatik
    Type of Medium: Book
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    ZIB Catalog
    Zuse Institute Berlin get availability status
Close ⊗
This website uses cookies and the analysis tool Matomo. More information can be found here...