A generalization of the ABS algorithms and its application to some special real and integer matrix factorizations

• Published in: Iranian journal of numerical analysis and optimization Vol. 12; no. 2; pp. 301 - 314
• Main Authors: E. Golpar Raboky, N. Mahdavi-Amiri
• Format: Journal Article
• Language: English
• Published: Ferdowsi University of Mashhad 01.09.2022
• Subjects: abs algorithms; octant interlocking factorization; quadrant interlocking factorization
• ISSN: 2423-6977; 2423-6969
• DOI: 10.22067/ijnao.2021.70974.1043

In 1984, 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.