Preconditioners for least squares problems by LU factorization.
Preconditioners for least squares problems by LU factorization.
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发表时间：
1999
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通讯作者：
Å. Björck;Jinyun Yuan
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文献类型：
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作者：
Å. Björck;Jinyun Yuan
. Iterative methods are often suitable for solving least-squares problems min k Ax (cid:0) b k2 , where A 2 R m(cid:2)n is large and sparse. The use of the conjugate gradient method with a nonsingular square submatrix A1 2 R n(cid:2)n of A as preconditioner was first suggested by L¨auchli in 1961. This conjugate gradient method has recently been extended by Yuan to generalized least-squares problems. In this paper we consider the problem of finding a suitable submatrix A1 and its LU factorization for a sparse rectangular matrix A . We give three algorithms based on the sparse LU factorization algorithm by Gilbert and Peierls. Numerical results are given, which indicate that our preconditioners can be effective.
