Abstract
The straightforward implementation of interval matrix product suffers from poor efficiency, far from the performances of highly optimized floating-point matrix products. In this paper, we show how to reduce the interval matrix multiplication to 9 floating-point matrix products - for performance issues - without sacrificing the quality of the result. Indeed, we show that, compared to the straightforward implementation, the overestimation factor is at most 1.18.
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References
Anderson, E., Bai, Z., Bischof, C., Blackford, S., Demmel, J., Dongarra, J., Du Croz, J., Greenbaum, A., Hammarling, S., McKenney, A., Sorensen, D.: LAPACK Users’ Guide, 3rd edn. Society for Industrial and Applied Mathematics, Philadelphia (1999)
Ceberio, M., Kreinovich, V.: Fast Multiplication of Interval Matrices (Interval Version of Strassen’s Algorithm). Reliable Computing 10(3), 241–243 (2004)
Jaulin, L., Kieffer, M., Didrit, O., Walter, E.: Applied Interval Analysis. Springer, Heidelberg (2001)
Knıuppel, O.: PROFIL/BIAS–A fast interval library. Computing 53(3–4), 277–287 (2006)
Moore, R.E., Kearfott, R.B., Cloud, M.J.: Introduction to Interval Analysis. SIAM, Philadelphia (2009)
Neumaier, A.: Interval Methods for Systems of Equations. Cambridge University Press (1990)
Nguyen, H.D.: Efficient implementation of interval matrix multiplication (extended version). Research report, INRIA, 04 (2010)
Rump, S.M.: INTLAB - INTerval LABoratory, http://www.ti3.tu-hamburg.de/rump/intlab
Rump, S.M.: Fast and parallel interval arithmetic. BIT 39(3), 534–554 (1999)
Rump, S.M.: Computer-assisted proofs and self-validating methods. In: Einarsson, B. (ed.) Handbook on Accuracy and Reliability in Scientific Computation, ch. 10, pp. 195–240. SIAM (2005)
Whaley, R.C., Petitet, A.: Minimizing development and maintenance costs in supporting persistently optimized BLAS. Software: Practice and Experience 35(2), 101–121 (2005), http://www.cs.utsa.edu/
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Diep, N.H. (2012). Efficient Implementation of Interval Matrix Multiplication. In: Jónasson, K. (eds) Applied Parallel and Scientific Computing. PARA 2010. Lecture Notes in Computer Science, vol 7134. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-28145-7_18
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DOI: https://doi.org/10.1007/978-3-642-28145-7_18
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-28144-0
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