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http://hdl.handle.net/2183/22369 Parallel Sparse Modified Gram-Schmidt QR Decomposition
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Doallo R., Fraguela B.B., Touriño J., Zapata E.L. (1996) Parallel sparse modified Gram-Schmidt QR decomposition. In: Liddell H., Colbrook A., Hertzberger B., Sloot P. (eds) High-Performance Computing and Networking. HPCN-Europe 1996. Lecture Notes in Computer Science, vol 1067. Springer, Berlin, Heidelberg
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[Abstract] We present a parallel computational method for the QR decomposition with column pivoting of a sparse matrix by means of Modified Gram-Schmidt orthogonalization. Nonzero elements of the matrix M to be decomposed are stored in a one-dimensional doubly linked list data structure. We discuse a strategy to reduce fill-in in order to get memory savings and decrease the computation times. As an application of QR decomposition, we describe the least squares problem. This algorithm was designed for a message passing multiprocessor and has been evaluated on a Cray T3D, using the Harwell-Boeing sparse matrix collection.
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This is a post-peer-review, pre-copyedit version of an article published in Lecture Notes in Computer Science. The final authenticated version is available online at: https://doi.org/10.1007/3-540-61142-8_609