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Название:
N. N. Abdelmalek. On the solutions of the linear least squares problems and pseudo-inverses. Computing, 13(3-4):215-228, 1974.

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Цитата:

MR0395190 (52 #15988)
Abdelmalek, N. N.
On the solutions of the linear least squares problems and pseudo-inverses. (English. German summary)
Computing (Arch. Elektron. Rechnen) 13 (1974), no. 3-4, 215--228.
65F20

The author considers the problems of calculating the least-squares solution of $Ax=b$ and of computing the pseudoinverse of $A$, where $A$ is an $m\times n$ complex matrix of arbitrary rank. He begins by developing bounds for quantities in the Gauss elimination and Householder methods, allowing for the detection of actual zeros in the matrix factorizations. Under the assumption that the computed rank is exact, he develops a general analysis of the conditioning of such problems by extending the work of others [cf. G. W. Stewart, SIAM J. Appl. Math. 17 (1969), 33--45; MR0245583 (39 \#6889)]. Error estimates for the Gauss elimination and Householder methods are also derived. The paper concludes with a short numerical comparison involving both these methods as well as the methods of Givens, modified Gram-Schmidt, and classical Gram-Schmidt with reorthogonalization.

Reviewed by S. F. McCormick