Hostname: page-component-cd9895bd7-dzt6s Total loading time: 0 Render date: 2024-12-26T04:44:59.536Z Has data issue: false hasContentIssue false
  • English
  • Français

Global Astrometric Solutions with Sparse Matrix Techniques

Published online by Cambridge University Press:  12 April 2016

Richard L. Branham Jr.
Richard L. Branham Jr.*
Affiliation:
Instituto Argentino de Nivología y Glaciología (IANIGLA), C.C. 330, 5500 Mendoza, Argentina

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Modern astrometric techniques lead to large, linear systems solved by the precepts of least-squares. These systems are usually sparse, and one should take advantage of the sparsity to facilitate their solution. As long as the matrix A of the equations of condition possesses the weak Hall property, characteristic of linear systems derived from astrometric reductions, it is possible to find a sparse Cholesky factor. Before the equations of condition are accumulated, by use of the fast Givens transformation, a symbolic factorization of A using Tewarson’s length of intersection technique determines the ordering of the columns of A that result in low fill-in. The non-null elements are stored in a sparse, dynamic data structure by use of dynamic hashing. Numerical experimentation shows that this competes well with alternatives such as nested dissection, and large, but sparse, linear systems with several thousand unknowns can be solved in a reasonable amount of time, even on personal computers.

Type
Section 1. Celestial Reference System and Frame
Information
International Astronomical Union Colloquium , Volume 180: Towards Models and Constants for Sub-Microarcsecond Astrometry , March 2000 , pp. 127 - 131
Copyright
Copyright © US Naval Observatory 2000

References

Björck, A., 1996, Numerical Methods for Least Squares Problems, Philadelphia: SIAM, 162–163.Google Scholar
Branham, R.L. Jr., 1990, Scientific Data Analysis, New York: Springer, Sec. 3.3.1.CrossRefGoogle Scholar
Enbody, R.J. & Du, H.C., 1988, A CM Computing Surveys, 20, 85.Google Scholar
Gentleman, W.M., 1974, App. Stat., 23, 448.Google Scholar
George, A. & Liu, J.W., 1981, Computer Solution of Large Sparse Positive Definite Systems, Englewood Cliffs, New Jersey: Prentice-Hall.Google Scholar
Helmert, F.R., 1880, Die Mathematischen und Physikalishen Teorien der hoheren Geodäsie, 1 Teil, Leipzig: Teubner.Google Scholar
Knuth, D., 1973, The Art of Computer Programming, Vol. 3, Sorting and Searching, Reading, Mass.: Addison Wesley, Sec. 6.4, 5.2.1.Google Scholar
Larson, P.A., 1988, Comm. ACM, 31, 446.Google Scholar
Tewarson, R.P., 1973, Sparse Matrices, New York: Academic, Sec. 2.5, 3.2.Google Scholar