Astronomical data reduction with total least squares

New Astronomy Reviews

Volumn 45, Issue 11-12, 2001, Pages 649-661

  Branham Jr , Richard L ^a  

^a INSTITUTO ARGENTINO DE NIVOLOGÍA   (Argentina)

Author keywords

Data reduction; Errors in variables; Generalized least squares; Total least squares

Indexed keywords

EID: 0012908170     PISSN: 13876473     EISSN: None     Source Type: Journal    
DOI: 10.1016/S1387-6473(01)00136-1     Document Type: Review

References (46)

1. Björck, A., 1996. In: Numerical Methods for Least Squares Problems. SIAM, Philadelphia, pp. 162-163.
2. Björck, A., 1997. Newton and Rayleigh quotient methods for total least squares problems. In: Van Huffel, S. (Ed.), Recent Advances in Total Least Squares and Errors-in Variables Modeling. SIAM, Philadelphia, pp. 149-160.
3. Branham, Jr. R.L., 1989. A program for total (orthogonal) least squares in compact storage mode. Comput. Phys. 3, 42-46.
4. Branham, Jr. R.L., 1990. In: Scientific Data Analysis. Springer, New York, pp. 178-179, Sec. 1.5.
5. Branham, Jr. R.L., 1995. Multivariate orthogonal regression in astronomy. Celest. Mech. 61, 239-251.
6. Branham, Jr. R.L., 1998. Total least squares: an ideal mathematical tool for Galactic kinematics. Ap&SS 257, 107-121.
7. Branham, Jr. R.L., 1999. A covariance matrix for total least squares with heteroscedastic data. AJ 117, 1942-1948.
8. Branham, Jr. R.L., 2000a. Global astrometric solutions with sparse matrix techniques. In: Johnston, K.J., McCarthy, D.D., Luzum, B.J., Kaplan (, G.H. (Eds.), Towards Models and Constants for Sub-Microarcsecond Astrometry. U.S. Naval Observatory, Washington, DC, pp. 127-131.
9. Branham, Jr. R.L., 2000b. The parameters of Galactic kinematics determined from total least squares. RMxAA 36, 97-112.
10. Branham, R.L. Jr., 2000c. The Sun's distance from the Galactic plane, Ap&SS, submitted.
11. Brouwer, D., Clemence, G.M., 1961. In: Methods of Celestial Mechanics. Academic, New York, p. 237, 241.
12. Brown, D., 1955. A matrix treatment of the general problem of least squares considering correlated observations, Ballistic Research Lab. Report No. 937, Aberdeen, Md.
13. Chauvenet, W., 1960. A Manual of Spherical and Practical Astronomy, Vol. 2, Dover, New York, Appendix.
14. Cohen, C.J., Hubbard, E.C., Oesterwinter, C., 1967. New orbit for Pluto and analysis of differential correction. AJ 72, 973-988.
15. Eichhorn, H., 1993. Generalized least-squares adjustment, a timely but much neglected tool. Celest. Mech. 56, 337-351.
16. ESA, 1997. The Hipparcos and Tycho Catalogues, ESA SP-1200.
17. Feigelson, E.D., Babu, G.J., 1992. Linear regression in Astronomy II. AJ 397, 55-67.
18. Gauss, K.F., 1963. Theory of the Motion of the Heavenly Bodies Moving about the Sun in Conic Sections Dover, New York, Secs. 175-186.
19. Golub, G.H., Van Loan, C.F., 1980. An analysis of the total least squares problem. SIAM J. Numer. Anal. 17, 883-893.
20. Golub, G.H., Hoffman, A., Stewart, G.W., 1987. A generalization of the Eckart-Young-Mirsky matrix approximation theorem. Linear Alg. Appl. 88-89, 317-327.
21. Gum, C.S., Kerr, F.J., Westerhout, G., 1960. A 21-cm determination of the principal plane of the Galaxy. MNRAS 121, 132-149.
22. Isobe, T., Feigelson, E.D., Akritas, M.G., Babu, G.J., 1990. Linear regression in astronomy. ApJ 364, 104-113.
23. Jefferys, W.H., 1980. On the method of least squares. AJ 85, 177-181.
24. Jefferys, W.H., 1981. On the method of least squares II. AJ 86, 149-155.
25. Laplace, P.S., 1966. Celestial Mechanics, Chelsea, New York, Book 3, Chapter 5, Sec. 39.
26. Legendre, A.M., 1805. Nouvelles Méthodes pour la Détermination des Orbites des Comètes, Courcier, Paris, Appendix.
27. McArthur, B., Jefferys, W., McCartney, J., 1994. GaussFit, a system for least squares and robust estimation. Bull. AAS 26, 900.
28. Miller, B.P., Dunn, H.E., 1988. Orthogonal least-squares line fit with variable scaling. Comput. Phys. 2, 59-61.
29. Murtagh, F., 1989. Linear regression with errors in both variables. In: Jaschek, C., Murtagh, F. (Eds.), Bias and Uncertainties in Astronomy. Cambridge University Press, Cambridge, pp. 385-391.
30. Newcomb, S., 1960. A Compendium of Spherical Astronomy, Dover, New York, Chapter 3.
31. Pearson, K., 1901. On lines and planes of closest fit to points in space. Philos. Mag. 2, 559-572.
32. Pont, F., Mayor, M., Burki, G., 1994. New radial velocities for classical cepheids. Local galactic rotation revisited. A&A 285, 415-439.
33. Press, W.H., Teukolsky, S.A., Vettering, W.T., Flannery, B.P., 1992. In: Numerical Recipes in C: the Art of Scientific Computing, 2nd Edition, Sec. 15.3. Cambridge University Press, Cambridge.
34. Reed, B.C., 1989. Linear least-squares fit with errors in both coordinates II: Comments of parameter variances. Am. J. Phys. 60 (1), 59-62.
35. Scarborough, J.B., 1966. In: Numerical Mathematical Analysis, 6th Edition. Johns Hopkins, Baltimore, pp. 551-553.
36. Smart, W.M., 1967. Stellar Kinematics. Wiley, New York, Sec. 8.42.
37. Smith, Jr. H., Eichhorn, H., 1996. MNRAS 281, 211-218.
38. Starr, R., Heindel, W.A., Crannell, C.J., Thomas, R.J., Batchelor, D.A., Megun, A., 1988. Energetics and dynamics of simple impulsive solar flares. ApJ 329, 967-981.
39. Stephan, J.B., Bassani, L., Caroli, E., DiCocco, G., 1987. Statistical significance of the relationship between X-ray luminosity and variability timescale in active galactic nuclei. Nature 328, 784-785.
40. Strömberg, G., 1940. Accidental and systematic errors in spectroscopic absolute magnitudes for dwarf G0-K2 stars. ApJ 92, 156-169.
41. Trumpler, R.J., Weaver, H., 1962. Statistical Astronomy, Dover, New York, p. 184, pp. 422-423.
42. Van Huffel, S., Vandewalle, J., 1988. Analysis and solution of the nongeneric total least squares problem. SIAM J. Matrix Anal. Appl. 9, 360-372.
43. Van Huffel, S., Vandewalle, J., 1989. Analysis and properties of the generalized total least squares problem AX≈B when some or all columns in A are subject to error. SIAM J. Matrix Anal. Appl 10, 294-315.
44. Van Huffel, S., Vandewalle, J., 1991. The Total Least Squares Problem: Computational Aspects and Analysis. SIAM, Philadelphia, Sec. 3.6.2., 3.6.3.
45. York, D., 1966. Least squares fitting of a straight line. Canad. J. Phys. 44, 1079-1086.
46. Zadunaisky, P.E., Pereyra, V., 1965. On the convergence and precision of a process of successive differential corrections, Instituto de Calculo, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Publ. No. 5.