Fast algorithms for floating-point interval matrix multiplication |
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| Authors: | Katsuhisa Ozaki Takeshi Ogita Siegfried M Rump Shin’ichi Oishi |
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| Institution: | a Department of Mathematical Sciences, College of Systems Engineering and Science, Shibaura Institute of Technology, 307 Fukasaku, Minuma-ku, Saitama-shi, Saitama 337-8570, Japanb Department of Mathematical Sciences, Tokyo Woman’s Christian University, 2-6-1 Zempukuji, Suginami-ku, Tokyo 167-8585, Japanc Faculty of Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjyuku-ku, Tokyo 169-8555, Japand JST (Japan Science and Technology Agency), CREST, Japane Institute for Reliable Computing, Hamburg University of Technology, Schwarzenbergstr. 95, 21071 Hamburg, Germany |
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| Abstract: | We discuss several methods for real interval matrix multiplication. First, earlier studies of fast algorithms for interval matrix multiplication are introduced: naive interval arithmetic, interval arithmetic by midpoint-radius form by Oishi-Rump and its fast variant by Ogita-Oishi. Next, three new and fast algorithms are developed. The proposed algorithms require one, two or three matrix products, respectively. The point is that our algorithms quickly predict which terms become dominant radii in interval computations. We propose a hybrid method to predict which algorithm is suitable for optimizing performance and width of the result. Numerical examples are presented to show the efficiency of the proposed algorithms. |
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| Keywords: | Matrix multiplication Interval arithmetic Verified numerical computations INTLAB |
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