Nonlinear Theory and Its Applications, IEICE
Special Section on Recent Progress in Verified Numerical Computations
Accelerating interval matrix multiplication by mixed precision arithmetic
Katsuhisa OzakiTakeshi OgitaFlorian BüngerShin'ichi Oishi
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Volume 6 (2015) Issue 3 Pages 364-376

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Abstract

This paper is concerned with real interval arithmetic. We focus on interval matrix multiplication. Well-known algorithms for this purpose require the evaluation of several point matrix products to compute one interval matrix product. In order to save computing time we propose a method that modifies such known algorithm by partially using low-precision floating-point arithmetic. The modified algorithms work without significant loss of tightness of the computed interval matrix product but are about 30% faster than their corresponding original versions. The negligible loss of accuracy is rigorously estimated.

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© 2015 The Institute of Electronics, Information and Communication Engineers
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