Solving generalized least-squares problems with LSQR
Solving generalized least-squares problems with LSQR
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DOI：
10.1137/s0895479897321830
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发表时间：
1999-10-27
影响因子：
1.5
通讯作者：
Benbow, SJ
中科院分区：
文献类型：
--
作者：
Benbow, SJ
给出了广义最小二乘意义下求解增广线性方程组的一种迭代方法。该方法，LSQR（A（-1）），被证明是一个自然的扩展的LSQR算法的佩奇和桑德斯[ACM trans. Math. Software，8（1982），页。43-71]，具有广义正交性质，因此不需要A的Cholesky因子。相反，它只是假设有某种方法可以计算A（-1）对向量的影响。数值实验表明，当Schur补B（T）A（-1）B为病态时，新方法具有上级的数值性能.
An iterative method for solving augmented linear systems in a generalized least-squares sense is given. The method, LSQR(A(-1)), is shown to be a natural extension of the LSQR algorithm of Paige and Saunders [ACM Trans. Math. Software, 8 (1982), pp. 43-71], with generalized orthogonality properties so that the Cholesky factor of A is not required. Instead it is only assumed that some method of calculating the effect of A(-1) on a vector is available. Numerical experiments comparing LSQR(A(-1)) with similar preconditioned Krylov methods are described which demonstrate that the new method exhibits superior numerical properties when the Schur complement B(T)A(-1)B is ill conditioned.