Minimax method for the inversion of Fredholm equations of the first kind and the determination of linear relaxation spectra

Yu G. Yanovsky, Yu A. Basistov, Dennis A. Siginer

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    Abstract

    A new theory based on an extensively modified version of the minimax method is proposed to estimate the cause from the result, that is the characteristic functions of viscoelastic media from experimentally obtained material functions through the solution of Fredholm integral equations of the first kind. The method does not require the assumption of a priori error bounds as in other smoothing techniques. The algorithm is applied to several hypothetical test problems to show the excellent performance of the method in extreme severe conditions. The shortcomings of the Tikhonov's regularization and other smoothing techniques are discussed. It is shown that the solution via these methods may not represent the real solution in any norm. The new method is applied to linear viscoelasticity to obtain the relaxation spectrum from experimental material functions. The relaxation spectra of some materials obtained via the proposed algorithm and experiments run in a rotary viscometer, are presented.

    Original languageEnglish
    Title of host publicationDevelopments and Applications of Non-Newtonian Flows
    PublisherASME
    Pages39-52
    Number of pages14
    Volume231
    Publication statusPublished - 1995
    EventProceedings of the 1995 ASME International Mechanical Engineering Congress and Exposition - San Francisco, CA, USA
    Duration: Nov 12 1995Nov 17 1995

    Other

    OtherProceedings of the 1995 ASME International Mechanical Engineering Congress and Exposition
    CitySan Francisco, CA, USA
    Period11/12/9511/17/95

    Fingerprint

    Viscometers
    Viscoelasticity
    Integral equations
    Experiments

    All Science Journal Classification (ASJC) codes

    • Engineering(all)

    Cite this

    Yanovsky, Y. G., Basistov, Y. A., & Siginer, D. A. (1995). Minimax method for the inversion of Fredholm equations of the first kind and the determination of linear relaxation spectra. In Developments and Applications of Non-Newtonian Flows (Vol. 231, pp. 39-52). ASME.
    Yanovsky, Yu G. ; Basistov, Yu A. ; Siginer, Dennis A. / Minimax method for the inversion of Fredholm equations of the first kind and the determination of linear relaxation spectra. Developments and Applications of Non-Newtonian Flows. Vol. 231 ASME, 1995. pp. 39-52
    @inproceedings{1060136f51c840bd86a9e8bd31be6d8b,
    title = "Minimax method for the inversion of Fredholm equations of the first kind and the determination of linear relaxation spectra",
    abstract = "A new theory based on an extensively modified version of the minimax method is proposed to estimate the cause from the result, that is the characteristic functions of viscoelastic media from experimentally obtained material functions through the solution of Fredholm integral equations of the first kind. The method does not require the assumption of a priori error bounds as in other smoothing techniques. The algorithm is applied to several hypothetical test problems to show the excellent performance of the method in extreme severe conditions. The shortcomings of the Tikhonov's regularization and other smoothing techniques are discussed. It is shown that the solution via these methods may not represent the real solution in any norm. The new method is applied to linear viscoelasticity to obtain the relaxation spectrum from experimental material functions. The relaxation spectra of some materials obtained via the proposed algorithm and experiments run in a rotary viscometer, are presented.",
    author = "Yanovsky, {Yu G.} and Basistov, {Yu A.} and Siginer, {Dennis A.}",
    year = "1995",
    language = "English",
    volume = "231",
    pages = "39--52",
    booktitle = "Developments and Applications of Non-Newtonian Flows",
    publisher = "ASME",

    }

    Yanovsky, YG, Basistov, YA & Siginer, DA 1995, Minimax method for the inversion of Fredholm equations of the first kind and the determination of linear relaxation spectra. in Developments and Applications of Non-Newtonian Flows. vol. 231, ASME, pp. 39-52, Proceedings of the 1995 ASME International Mechanical Engineering Congress and Exposition, San Francisco, CA, USA, 11/12/95.

    Minimax method for the inversion of Fredholm equations of the first kind and the determination of linear relaxation spectra. / Yanovsky, Yu G.; Basistov, Yu A.; Siginer, Dennis A.

    Developments and Applications of Non-Newtonian Flows. Vol. 231 ASME, 1995. p. 39-52.

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    TY - GEN

    T1 - Minimax method for the inversion of Fredholm equations of the first kind and the determination of linear relaxation spectra

    AU - Yanovsky, Yu G.

    AU - Basistov, Yu A.

    AU - Siginer, Dennis A.

    PY - 1995

    Y1 - 1995

    N2 - A new theory based on an extensively modified version of the minimax method is proposed to estimate the cause from the result, that is the characteristic functions of viscoelastic media from experimentally obtained material functions through the solution of Fredholm integral equations of the first kind. The method does not require the assumption of a priori error bounds as in other smoothing techniques. The algorithm is applied to several hypothetical test problems to show the excellent performance of the method in extreme severe conditions. The shortcomings of the Tikhonov's regularization and other smoothing techniques are discussed. It is shown that the solution via these methods may not represent the real solution in any norm. The new method is applied to linear viscoelasticity to obtain the relaxation spectrum from experimental material functions. The relaxation spectra of some materials obtained via the proposed algorithm and experiments run in a rotary viscometer, are presented.

    AB - A new theory based on an extensively modified version of the minimax method is proposed to estimate the cause from the result, that is the characteristic functions of viscoelastic media from experimentally obtained material functions through the solution of Fredholm integral equations of the first kind. The method does not require the assumption of a priori error bounds as in other smoothing techniques. The algorithm is applied to several hypothetical test problems to show the excellent performance of the method in extreme severe conditions. The shortcomings of the Tikhonov's regularization and other smoothing techniques are discussed. It is shown that the solution via these methods may not represent the real solution in any norm. The new method is applied to linear viscoelasticity to obtain the relaxation spectrum from experimental material functions. The relaxation spectra of some materials obtained via the proposed algorithm and experiments run in a rotary viscometer, are presented.

    UR - http://www.scopus.com/inward/record.url?scp=0029425535&partnerID=8YFLogxK

    UR - http://www.scopus.com/inward/citedby.url?scp=0029425535&partnerID=8YFLogxK

    M3 - Conference contribution

    VL - 231

    SP - 39

    EP - 52

    BT - Developments and Applications of Non-Newtonian Flows

    PB - ASME

    ER -

    Yanovsky YG, Basistov YA, Siginer DA. Minimax method for the inversion of Fredholm equations of the first kind and the determination of linear relaxation spectra. In Developments and Applications of Non-Newtonian Flows. Vol. 231. ASME. 1995. p. 39-52