Abstract
The effect of reordering strategies on the rounding errors is considered for the factorization and solution of sparse symmetric systems. On the one hand, a reduction of rounding errors can be expected, because the number of floating point operations decreases. On the other hand, the clustering of neighboring parameters and therefore the fixing of the sequence of parameter elimination may result in numerical instabilities. These effects are demonstrated for sparse covariance matrices in Wiener filtering. In particular Cholesky factorization and profile reordering in conjunction with envelope storage schemes are examined.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Dahmen W, Reusken A (2008) Numerics for engineers and natural scientists (German). Springer, Berlin, Heidelberg
Ernst A (2009) Implementation of efficient algorithms to reorder, solve and invert sparse normal equation systems with geodetic applications (German). Master’s thesis, Unitversity Bonn, Institute of Geodesy and Geoinformation
Gaspari G, Cohn S, (1999) Construction of correlation functions in two and three dimensions. Q J Roy Meteorol Soc 125(554):723–757
Gaspari G, Cohn S, Guo J, Pawson S (2006) Construction and application of covariance functions with variable length-fields. Q J Roy Meteorol Soc, 132:1815–1838
Gibbs N, Poole W, Stockmeyer P (1976) An algorithm for reducing the bandwidth and profile of a sparse matrix. SIAM J Numer Anal 13:236–250
IEEE Computer Society (2008) IEEE standard for floating point arithmetic. Technical report, The Institute of Electrical and Electronics Engineers, Inc
Kreyszig E (1993) Advanced engineering mathematics, 7th edn. Wiley, New York
Meissl P (1980) A priori prediction of roundoff error accumulation in the solution of a super-large geodetic normal equation system. NOAA/National Ocean Survey’s National Geodetic Survey (NGS), Rockville, Md., Professional Paper 12
Moreaux G (2008) Compactly supported radial covariance functions. J Geodesy 82(7):431–443
Sansò F, Schuh W-D (1987) Finite covariance functions. Bulletin Géodésique 61:331–347
Schuh W-D (1991) Numerical behaviour of covariance matrices and their influence on iterative solution techniques. In: Rapp R, Sansò F (eds) Determination of the Geoid – Present and Future, IAG Proceedings, vol 106. Springer, Heidelberg, 432–441
Snay R (1976) Reducing the profile of sparse symmetric matrices. NOAA Technical Memorandum, NOS NGS-4
Stewart G (1973) Introduction to matrix computations. Academic press, New York, San Fancisco, London
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Ernst, A., Schuh, WD. (2012). The Effect of Reordering Strategies on Rounding Errors in Large, Sparse Equation Systems. In: Sneeuw, N., Novák, P., Crespi, M., Sansò, F. (eds) VII Hotine-Marussi Symposium on Mathematical Geodesy. International Association of Geodesy Symposia, vol 137. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22078-4_15
Download citation
DOI: https://doi.org/10.1007/978-3-642-22078-4_15
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-22077-7
Online ISBN: 978-3-642-22078-4
eBook Packages: Earth and Environmental ScienceEarth and Environmental Science (R0)