The implicitlualgorithm of the (basic) ABS class corresponds to the parameter choices H-1= I, z(i) = w(i) = e(i). The algorithm can be considered as the ABS version of the classic lu factorization algorithm. In this...
详细信息
The implicitlualgorithm of the (basic) ABS class corresponds to the parameter choices H-1= I, z(i) = w(i) = e(i). The algorithm can be considered as the ABS version of the classic lu factorization algorithm. In this paper we consider the generalization where the initial matrix H-1 is arbitrary except for a certain condition. We prove that every algorithm in the ABS class is equivalent, in the sense of generating the same set of search directions, to a generalized implicit lu algorithm, with suitable initial matrix, that can be interpreted as a right preconditioning matrix. We discuss some consequences of this result, including a straightforward derivation of Bienayme's (1853) classical result on the equivalence of the Gram-Schmidt orthogonalization procedure with Gaussian elimination on the normal equations.
暂无评论