Date
Thu, 09 Feb 2012
Time
14:00 - 15:00
Location
Rutherford Appleton Laboratory, nr Didcot
Speaker
Dr Yuji Nakatsukasa
Organisation
University of Manchester

Computing the eigenvalue decomposition of a symmetric matrix and the singular value decomposition of a general matrix are two of the central tasks in numerical linear algebra. There has been much recent work in the development of linear algebra algorithms that minimize communication cost. However, the reduction in communication cost sometimes comes at the expense of significantly more arithmetic and potential instability.

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In this talk I will describe algorithms for the two decompositions that have optimal communication cost and arithmetic cost within a small factor of those for the best known algorithms. The key idea is to use the best rational approximation of the sign function, which lets the algorithm converge in just two steps. The algorithms are backward stable and easily parallelizable. Preliminary numerical experiments demonstrate their efficiency.

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