Algorithms have two costs: arithmetic and communication. The latter represents the cost of moving data, either between levels of a memory hierarchy, or between processors over a network. Communication often dominates arithmetic and represents a rapidly increasing proportion of the total cost, so we seek algorithms that minimize communication. In recent work, lower bounds were presented on the amount of communication required for essentially all O(n^3)-like algorithms for linear algebra, including eigenvalue problems and the SVD. Conventional algorithms, including those currently implemented in (Sca)LAPACK, perform asymptotically more communication than these lower bounds require. In this paper we present parallel and sequential eigenvalue algorithms (for pencils, nonsymmetric matrices, and symmetric matrices) and SVD algorithms that do attain these lower bounds, and analyze their convergence and communication costs.
Title
Minimizing Communication for Eigenproblems and the Singular Value Decomposition
Published
2001-02-11
Full Collection Name
Electrical Engineering & Computer Sciences Technical Reports
Other Identifiers
EECS-2011-14
Type
Text
Extent
47 p
Archive
The Engineering Library
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