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THE REGULARIZED MOORE-PENROSE PSEUDOINVERSION METHOD AS A TOOL FOR MEASUREMENT DATA PROCESSING

V. Dimova

First published: 2002DOI pendingView metrics

Abstract

The Moore-Penrose pseudoinversion method applied in solving systems of linear algebraic equations with incorrectly prescribed data lead to unstable solutions. This makes the method inapplicable in practice. The regularised version of that method is described which can be used as a basis for data processing in all branches of applied earth sciences.

Publication details

Title
THE REGULARIZED MOORE-PENROSE PSEUDOINVERSION METHOD AS A TOOL FOR MEASUREMENT DATA PROCESSING
Authors
V. Dimova
Proceedings
2nd International Scientific Conference - SGEM2002
Publisher
SGEM Scientific GeoConference
Year
2002
Pages
305-316
ISSN
Not available yet
ISBN
954-918181-2
Language
en
Publication type
Conference Paper
Proceedings contents
Open official contents
Keywords
References15
  1. 1. Hadamard J. Lectures on Cauchy’s Problem in Linear Partial Differential Equations, Yale University, New Haven, 1932

  2. Banach S. Th éorie des operations Lin éaires, Monografie Matematyczne, t.1. Warszawa, 1932

  3. Tikhonov A.N. On the stability of inverse problems, DAN SSSR, 39, No.5, 1943, pp.195-198 (in Russian)

  4. Tikhonov A.N. On the solution of ill-posed problems and the regularisation method, DAN SSSR, 151, No.3, 1963, pp.501-504 (in Russian)

  5. Tikhonov A.N. On the regularisation of ill-posed problems, DAN SSSR, 151, No.1, 1963, pp.49-52 (in Russian)

  6. Strang G. Linear algebra and its applications, NY, Academic Press, 1976

  7. Legendre A.M. Novelles methodes pour la determination des orbites des cometes, Courier, Paris, 1806

  8. Gauss C.F. Theoria motus corporum coelestium in sectionibus conicis solem ambientium, Hamburgi, 1809

  9. Voevodin V.V., Kuznetsov Y.A. Matrices and Calculations, Nauka, Moscow (in Russian)

  10. Moore E.N. On the reciprocal of the general algebraic matrix, Bull.Amer.Math.Soc., Vol.26, 1920, pp.394-395

  11. Penrose R.A. A generalised inverse for matrices, Proc. Camb. Phil. Soc., 51, No.3, 1055, pp.406-413

  12. Tikhonov A.N., A.C. Leonov, A.Y.Yagola Nonlinear ill-posed problems, Nauka, Moscow, 1995 (in Russian)

  13. Kliot-Dashinskiy M.I. Algebra of Matrices and Vectors, Leningrad University Publ.House, Leningrad, 1974 (in Russian)

  14. Ortega J.M., W.G.Poole An Introduction to Numerical Methods for Differential Equations, Pitman Publishing Inc., L., 1981

  15. Leonov A.S., A.G.Yagola Can an ill-posed problem be solved if the data error is unknown? Physics Bull. , Moscow University, Vol.50, No.4, 1995, pp.25-28 MONITORING OF CHANGES IN MEASUREMENTS OF OBJECTS FROM PHOTOGRAPHS Doc.Ing., CSc. Lacezar Licev, Katedra informatiky-456, VŠB-TU, Ostrava, Czech Republic

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