Abstract
Strassen's algorithm multiplies two numerical matrices fast, but when applied to interval matrices, leads to excess width. We use Rump's interval arithmetic to propose an interval version of Strassen's algorithm whose only excess width is in second order terms.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Castrapel, R.: Analysis of Error Propagation in Strassen's M × M Algorithm Using Interval Arithmetic, Sun Microsystems Technical Report, 2001, http://www.sun.com/products-n-solutions/edu/events/archive/hpc/presentations/june01/rick castrapel.pdf.
Coppersmith, D. and Winograd, S.: Matrix Multiplication via Arithmetic Progression, Journal of Symbolic Computation 9(3) (1990), pp. 251–280.
Cormen, T. H., Leiserson, C. E., Rivest, R. L., and Stein, C.: Introduction to Algorithms, MIT Press, Cambridge, and Mc-Graw Hill Co., N.Y., 2001.
Hansen, E.: Sharpness in Interval Computations, Reliable Computing 3(1) (1997), pp. 7–29.
Jaulin, L., Kieffer, M., Didrit, O., and Walter, E.: Applied Interval Analysis: With Examples in Parameter and State Estimation, Robust Control and Robotics, Springer, London, 2001.
Rump, S. M.: Fast and Parallel Interval Arithmetic, BIT Numerical Mathematics 39(3) (1999), pp. 534–554.
Strassen, V.: Gaussian Elimination is Not Optimal, Numerische Mathematick 14(3) (1969), pp. 354–356.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Ceberio, M., Kreinovich, V. Fast Multiplication of Interval Matrices (Interval Version of Strassen's Algorithm). Reliable Computing 10, 241–243 (2004). https://doi.org/10.1023/B:REOM.0000032111.16328.b2
Issue Date:
DOI: https://doi.org/10.1023/B:REOM.0000032111.16328.b2