Skip to main content
Log in

An iterative method for ill-posed problems with inequalities

  • Short Note
  • Published:
Zeitschrift für Operations Research Aims and scope Submit manuscript

Abstract

Ill-posed problems for integral and operator equations with nonnegativity and band inequality constraints arise in a wide range of applications. The effect and propagation of data perturbations in mathematical programming problems are highly dramatized in the area of ill-posed problems. In this note an iterative method for solving an ill-posed integral inequality and its moment discretization is described.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Bart, M.L.: A Fortran subroutine for solving Fredholm equations of the first kind by Nashed's method. Internal Report I 112, National Research Institute for Mathematical Sciences, CSIR, Pretoria, 1978.

    Google Scholar 

  • Cimmino, G.: Calcolo approssimato per le soluzioni dei sistemi di equazioni lineari. La Ricerca Scientifica, Roma, Serie II, 1938, 326–333.

    Google Scholar 

  • Dunn, J.C.: Global and asymptotic convergence rate estimates for a class of projected gradient processes. To appear.

  • Kammerer, W.J., andM.Z. Nashed: A generalization of a matrix iterative method of G. Cimmino to best approximate solution of linear integral equation of the first kind. Rend. Accad. dei Lincei48, 1970, 184–194.

    Google Scholar 

  • —: Iterative methods for best approximate solutions of linear operator equations of the first and second kinds. J. Math. Anal. Appl.40, 1972, 547–573.

    Google Scholar 

  • McCormick, S.F.: The methods of Kaczmarz and row orthogonalization for solving linear equations and least squares problems in Hilbert space. Indiana Univ. Math. J.26, 1977, 1137–1150.

    Google Scholar 

  • Nashed, M.Z.ed.: Generalized Inverses and Applications. New York 1976a.

  • —: On moment discretization and least-squares solutions of linear integral equations of the first kind. J. Math. Anal. Appl.53, 1976b, 359–366.

    Google Scholar 

  • -: Aspects of generalized inverses in analysis and regularization. Generalized Inverses and Applications. Ed. by M.Z. Nashed. New York 1976c, 193–244.

  • -: Continuous and semicontinuous analogues of iterative methods of Cimmino and Kaczmarz with applications to the inverse Radon transform. Mathematical Aspects of Computerized Tomography. Ed. by. G.T. Herman and F. Natterer. Berlin-Heidelberg-New York, to appear.

  • -: Regularization and approximation of ill-posed problems in system theory. Proceedings of the 1979 Conference on Information Sciences and Systems. Ed. by G.G.L. Meyer and C.R. Westgate. The Johns Hopkins University, 1979, 568–575.

  • -: Ill-posed problems and mathematical programming. Studies in Mathematical Programming. Ed. by A.V. Fiacco. To appear.

  • -: Ill-posed extremal problems. In preparation.

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Nashed, M.Z. An iterative method for ill-posed problems with inequalities. Zeitschrift für Operations Research 25, 101–105 (1981). https://doi.org/10.1007/BF01920052

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01920052

Keywords

Navigation