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
UR - http://www.scopus.com/inward/citedby.url?scp=83655184732&partnerID=8YFLogxK
U2 - 10.1016/j.cam.2011.10.011
DO - 10.1016/j.cam.2011.10.011
M3 - Article
AN - SCOPUS:83655184732
SN - 0377-0427
VL - 236
SP - 1795
EP - 1814
JO - Journal of Computational and Applied Mathematics
JF - Journal of Computational and Applied Mathematics
IS - 7
ER -