Use of Conjugate Gradient Methods for the Great-Circle Reduction

Details Use of Conjugate Gradient Methods for the Great-Circle Reduction Use of Conjugate Gradient Methods for the Great-Circle Reduction

Aug 1997

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1997esasp.402..819i&link_type=abstract

Proceedings of the ESA Symposium `Hipparcos - Venice '97', 13-16 May, Venice, Italy, ESA SP-402 (July 1997), p. 819-822

Astronomy and Astrophysics

Astronomy

Scientific paper

Over the past few years it has been demonstrated that iterative methods for finding the solution of linear systems of equations offer major advantages over the `direct' methods in various physical and numerical problems. We discuss here improvements in conjugate gradients algorithms applied to the reduction on the reference great circles for the Hipparcos or GAIA-like type of observations. We consider the CPU time and the storage requirements for various conjugate gradients methods. We recommend use of the stabilized version of the bi-conjugate-gradients algorithm with left Jacobi preconditioning. This algorithm requires 67 per cent greater storage than the simplest CG algorithm without preconditioning, but is typically three times faster and has a better convergence. Our results can be used in future space astrometric projects.

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