New interpretation of related Huangʹs methods

The algebraic origin of Huangʹs method and its generalizations (called the ABS methods) for solving determined or underdetermined linear systems (Ax = b) is explained and formulated in detail. This arises from the formulation based upon the recursive computation of a right inverse of A. The general formulation obtained here, which depends on the arbitrary matrix, includes all the above-mentioned methods. Under a suitable choice of arbitrary matrix, the implicit QR factorization of A via Gram-Schmidt algorithms and the implicit LU factorization of A via Gaussian elimination techniques are recovered.