Reduction of Under-Determined Linear Systems by Sparce Block Matrix Technique

Niels Jacob Tarp-Johansen, Peter Noe Poulsen, Lars Damkilde

    Research output: Chapter in Book/Report/Conference proceedingArticle in proceedingsResearchpeer-review

    Abstract

    Under-determined linear equation systems occur in different engineering applications. In structural engineering they typically appear when applying the force method. As an example one could mention limit load analysis based on The Lower Bound Theorem. In this application there is a set of under-determined equilibrium equation restrictions in an LP-problem. A significant reduction of computer time spent on solving the LP-problem is achieved if the equilib rium equations are reduced before going into the optimization procedure. Experience has shown that for some structures one must apply full pivoting to ensure numerical stability of the aforementioned reduction. Moreover the coefficient matrix for the equilibrium equations is typically very sparse. The objective is to deal efficiently with the full pivoting reduction of sparse rectangular matrices using a dynamic storage scheme based on the block matrix concept.
    Original languageEnglish
    Title of host publicationNinth Nordic Seminar on Computational Mechanics
    Place of PublicationLyngby
    PublisherBKM, DTU
    Publication date1996
    Pages205-209
    Publication statusPublished - 1996
    Event9th Nordic Seminar on Computational Mechanics - Lyngby, Denmark
    Duration: 25 Oct 199626 Oct 1996
    Conference number: 9

    Conference

    Conference9th Nordic Seminar on Computational Mechanics
    Number9
    CountryDenmark
    CityLyngby
    Period25/10/199626/10/1996

    Cite this

    Tarp-Johansen, N. J., Poulsen, P. N., & Damkilde, L. (1996). Reduction of Under-Determined Linear Systems by Sparce Block Matrix Technique. In Ninth Nordic Seminar on Computational Mechanics (pp. 205-209). BKM, DTU.