TY - JOUR

T1 - Fast algorithms for floating-point interval matrix multiplication

AU - Ozaki, Katsuhisa

AU - Ogita, Takeshi

AU - Rump, Siegfried M.

AU - Oishi, Shin'Ichi

N1 - Funding Information:
This research was supported by CREST program, Japan Science and Technology Agency (JST) .

PY - 2012/1

Y1 - 2012/1

N2 - 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 midpointradius form by OishiRump and its fast variant by OgitaOishi. 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.

AB - 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 midpointradius form by OishiRump and its fast variant by OgitaOishi. 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.

KW - INTLAB

KW - Interval arithmetic

KW - Matrix multiplication

KW - Verified numerical computations

UR - http://www.scopus.com/inward/record.url?scp=83655184732&partnerID=8YFLogxK

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U2 - 10.1016/j.cam.2011.10.011

DO - 10.1016/j.cam.2011.10.011

M3 - Article

AN - SCOPUS:83655184732

VL - 236

SP - 1795

EP - 1814

JO - Journal of Computational and Applied Mathematics

JF - Journal of Computational and Applied Mathematics

SN - 0377-0427

IS - 7

ER -