This paper discussed QR factorization algorithms for a special type of matrix arising from the application of the Tikhnov's regularization method to an ill-conditioned least squares problem. The matrix involved is half dense and half sparse. Householder transformation and the hybrid algorithm were implemented on iPSC/2 and iPSC/860 hypercubes. For a highly over-determined system, the row-oriented hybrid algorithm is faster than the column-oriented Householder transformation. The efficiency of the algorithms has been improved by overlapping communications with computations. BLAS routines are also used on iPSC/860 to enhance the performance of the algorithms.
QR Factorization for The Regularized Least Squares Problem on HypercubesParallel Computing
Citation InformationZhu, J. (1993). QR Factorization for The Regularized Least Squares Problem on Hypercubes. Parallel Computing, 19(8), 939-948, doi: 10.1016/0167-8191(93)90076-W.