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.
This work was supported by the Spanish CICYT under contract TIC92-0942-C03 and by the TRACS Programme under the Human Capital and Mobility Programme of the European Union (grant number ERB-CHGE-CT92-0005)
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© 1996 Springer-Verlag Berlin Heidelberg
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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. https://doi.org/10.1007/3-540-61142-8_609
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DOI: https://doi.org/10.1007/3-540-61142-8_609
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