E. Golpar Raboky - Department of Mathematics, University of Qom. Qom, Iran. Tel: +۹۸-۲۵-۳۲۱۰۳۷۹۱
N. Mahdavi-Amiri - Faculty of Mathematical Sciences, Sharif University of Technology, Tehran, Iran.

In ۱۹۸۴, Abaffy, Broyden, and Spediacto (ABS) introduced a class of the so-called ABS algorithms to solve systems of real linear equations. Later, the scaled ABS, the extended ABS, the block ABS, and the integer ABS algorithms were introduced leading to various well-known matrix factorizations. Here, we present a generalization of ABS algorithms containing all matrix factorizations such as triangular, W Z, and ZW . We discuss the octant interlocking factorization and make use of the generalized ABS algorithm as a more general approach for producing the octant interlocking factorization.

ABS algorithms, Quadrant interlocking factorization, Octant interlocking factorization