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Generalized inverses and resolution in the solution of linear equations

Verallgemeinerte Inverse und Auflösung bei der Lösung von linearen Gleichungen

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Abstract

A new generalized inverse of a singular and/or rectangular matrix is constructed by utilizing the Moore-Penrose generalized inverse. If this new inverse is used for solving a system of linear equations then it yields a solution vector with good resolution and small errors. Such solutions are particularly useful in remote sensing of atmospheric temperature profiles by satellites.

Zusammenfassung

Eine neue verallgemeinerte Inverse einer singulären und/oder rechteckigen Matrix wurde konstruiert unter Verwendung der Moore-Penrose verallgemeinerten Inversen. Wenn diese neue Inverse zur Lösung eines Systems von linearen Gleichungen angewandt wird, liefert sie einen Lösungsvektor mit guter Auflösung und kleinen Fehlern. Solche Lösungen sind besonders nützlich für die Ferndeutung von atmosphärischen Temperaturen via Satelliten.

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References

  1. Penrose, R.: On the best approximate solutions of linear matrix equations. Proc. of Cambridge Philo. Soc.52, 17–19 (1956).

    Google Scholar 

  2. Conrath, B. J.: Vertical resolution of temperature profiles obtained from remote radiation measurements. J. Atmospheric Sc.29, 1262–1271 (1972).

    Google Scholar 

  3. Tewarson, R. P.: On computing generalized inverses. Computing4, 139–152 (1969).

    Google Scholar 

  4. Fleming, H. E., and W. L. Smith: Inversion techniques for remote sensing of atmospheric temperature profiles. Proceedings of the fifth symposium on temperature, its measurement and control in science and industry, Washington D. C. 1972.

  5. Tewarson, R. P.: Solution of linear equations in remote sensing and picture reconstruction. Computing10, 221–230 (1973).

    Google Scholar 

  6. Tewarson, R. P., and P. Narain: Solution of linear equations resulting from satellite remote soundings. J. Math. Anal. and Appl. (1974 forthcoming).

  7. Scheffe, H.: The Analysis of Variance. New York: Wiley. 1959.

    Google Scholar 

  8. Faddeev, D. K., and V. N. Vaddeeva: Computational Methods of Linear Algebra. San Francisco, Calif. (1963).

  9. Backus, G. E.: Inference from inadequate and inaccurate data I, II and III. Proc. Nat. Acad. Sci.65, 1–7, 281–289 (1970).

    Google Scholar 

  10. Gordon, R., R. Bender, and G. T. Herman: Algebraic reconstruction techniques (ART) for three dimensional electron microscopy and x-ray photography. J. Theor. Bio.29, 471–481 (1970).

    Google Scholar 

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Authors and Affiliations

  1. Department of Applied Mathematics and Statistics, State University of New York at Stony Brook, 11790, Stony Brook, NY, USA

    R. P. Tewarson &  P. Narain

Authors
  1. R. P. Tewarson
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  2. P. Narain
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Tewarson, R.P., Narain, P. Generalized inverses and resolution in the solution of linear equations. Computing 13, 81–88 (1974). https://doi.org/10.1007/BF02268393

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  • DOI: https://doi.org/10.1007/BF02268393

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