Abstract
LSQR uses the Golub-Kahan bidiagonalization process to solve sparse least-squares problems with and without regularization. In some cases, projections of the right-hand side vector are required, rather than the least-squares solution itself. We show that projections may be obtained from the bidiagonalization as linear combinations of (the-oretically) orthogonal vectors. Even the least-squares solution may be obtained from orthogonal vectors, perhaps more accurately than the usual LSQR solution. (However, LSQR has proved equally good in all examples so far.)
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Partially supported by Department of Energy grant DE-FG03-92ER25117, National Science Foundation grants DMI-9204208 and DMI-9500668, and Office of Naval Research grants N00014-90-J-1242 and N00014-96-1-0274.
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Saunders, M.A. Computing projections with LSQR. Bit Numer Math 37, 96–104 (1997). https://doi.org/10.1007/BF02510175
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DOI: https://doi.org/10.1007/BF02510175