New interpretation of related Huang’s methods. (English) Zbl 0886.65040
The general formulation of the ABS method for solving determined or underdetermined linear systems \(Ax=b\) is given first and it is shown that it is based on the recursive computation of a right inverse of \(A\). The method depends on an arbitrary matrix, and by the special selection of that matrix Gram-Schmidt algorithms and the implicit LU factorization of \(A\) via Gaussian elimination techniques are recovered.
Reviewer: F.Szidarovszky (Tucson)
MSC:
| 65F25 | Orthogonalization in numerical linear algebra |
| 65F05 | Direct numerical methods for linear systems and matrix inversion |
Keywords:
Huang’s method; ABS method; underdetermined linear systems; right inverse; matrix Gram-Schmidt algorithms; implicit LU factorization; Gaussian eliminationReferences:
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