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

Iranian Journal of Numerical Analysis and Optimization

مقاله 3، دوره 12، شماره 2 - شماره پیاپی 22، آذر 2022، صفحه 301-314   

نوع مقاله: Research Article

شناسه دیجیتال (DOI): 10.22067/ijnao.2021.70974.1043

نویسندگان

E. Golpar Raboky^{* 1}؛ N. Mahdavi-Amiri²

¹Department of Mathematics, University of Qom. Qom, Iran. Tel: [phone]

²Faculty of Mathematical Sciences, Sharif University of Technology, Tehran, Iran.

چکیده

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.

کلیدواژه‌ها

ABS algorithms؛ Quadrant interlocking factorization؛ Octant interlocking factorization

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