New interpretation of related Huang's methods

✍ Scribed by M. Ballalij; H. Sadok

• Publisher: Elsevier Science
• Year: 1998
• Tongue: English
• Weight: 574 KB
• Volume: 269
• Category: Article
• ISSN: 0024-3795
• DOI: 10.1016/s0024-3795(97)00064-5

✦ Synopsis

The algebraic origin of Huang's 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.