Generalized method of least squares collocation

Ludmila Kubáčková; Lubomír Kubáček

Aplikace matematiky (1982)

  • Volume: 27, Issue: 6, page 446-456
  • ISSN: 0862-7940

Abstract

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Two general solutions of the collocation problem of physical geodesy are given. Their mutual equivalency and equivalency of them to the classical solution in the regular case are proved. The regularity means the non-singularity of the covariance matrix of those random variables by outcomes of which the measured values of the gravitational field are generated.

How to cite

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Kubáčková, Ludmila, and Kubáček, Lubomír. "Generalized method of least squares collocation." Aplikace matematiky 27.6 (1982): 446-456. <http://eudml.org/doc/15265>.

@article{Kubáčková1982,
abstract = {Two general solutions of the collocation problem of physical geodesy are given. Their mutual equivalency and equivalency of them to the classical solution in the regular case are proved. The regularity means the non-singularity of the covariance matrix of those random variables by outcomes of which the measured values of the gravitational field are generated.},
author = {Kubáčková, Ludmila, Kubáček, Lubomír},
journal = {Aplikace matematiky},
keywords = {least squares collocation; physical geodesy; gravitational field of the Earth; covariance matrix; least squares collocation; physical geodesy; gravitational field of the Earth; covariance matrix},
language = {eng},
number = {6},
pages = {446-456},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Generalized method of least squares collocation},
url = {http://eudml.org/doc/15265},
volume = {27},
year = {1982},
}

TY - JOUR
AU - Kubáčková, Ludmila
AU - Kubáček, Lubomír
TI - Generalized method of least squares collocation
JO - Aplikace matematiky
PY - 1982
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 27
IS - 6
SP - 446
EP - 456
AB - Two general solutions of the collocation problem of physical geodesy are given. Their mutual equivalency and equivalency of them to the classical solution in the regular case are proved. The regularity means the non-singularity of the covariance matrix of those random variables by outcomes of which the measured values of the gravitational field are generated.
LA - eng
KW - least squares collocation; physical geodesy; gravitational field of the Earth; covariance matrix; least squares collocation; physical geodesy; gravitational field of the Earth; covariance matrix
UR - http://eudml.org/doc/15265
ER -

References

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  1. Torben Krarup, A contribution to the mathematical foundation of physical geodesy, Geodaetisk Institut, Meddelelse No 44, København 1969. (1969) MR0250524
  2. Lubomír Kubáček, Universal model for adjusting observed values, Studia geoph. et geod. 20 (1976), 103-113. (1976) 
  3. Lubomír Kubáček, Lea Bartalošová, Ján Pecár, "Pandora-Box" matrix in the calculus of observations, Studia geoph. et geod. 21 (1977), 227-235. (1977) 
  4. Lubomír Kubáček, Ludmila Kubáčková, The present approach to the least-squares method, Studia geoph. et geod. 22 (1978), 140-147. (1978) 
  5. Lubomír Kubáček, Ludmila Kubáčková, Filtration and prediction of inhomogeneous geophysical potential fields, Studia geoph. et geod. 22 (1978), 330-335. (1978) 
  6. Alois Kufner, Geometrie Hilbertova prostoru, SNTL, Praha 1973. (1973) 
  7. Helmut Moritz, Least-squares collocation, DGK Bayer. Akad. d. Wiss., R. A. Nr. 75, München 1973. (1973) MR0456320
  8. Emanuel Parzen, Time series analysis papers, Holden-Day, S. Francisco 1967, (1967) MR0223042
  9. C. Radhakrishna Rao, Sujit Kumar Mitra, Generalized inverse of matrices and its application, J. Wiley, N. York 1971. (1971) MR0338013
  10. František Štulajter, The linear filtration and prediction of indirectly observed random processes, Kybernetika 12 (1976), 316-327. (1976) MR0446688

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