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

AN - SCOPUS:0029425535

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