ABS-Type Methods for Solving $m$ Linear Equations in $\frac{m}{k}$ Steps for $k=1,2,\cdots,m$

International Journal of Mathematical Modelling & Computations

مقاله 2، دوره 7، 3 (SUMMER) - شماره پیاپی 27، آبان 2017، صفحه 185-207   

نوع مقاله: Full Length Article

نویسندگان

Leila Asadbeigi¹؛ Majid Amirfakhrian^{* 2}

¹Hamadan Branch, Islamic Azad University

²IAUCTB

چکیده

‎The ABS methods‎, ‎introduced by Abaffy‎, ‎Broyden and Spedicato‎, ‎are‎
‎direct iteration methods for solving a linear system where the‎
‎$i$-th iteration satisfies the first $i$ equations‎, ‎therefore a‎ ‎system of $m$ equations is solved in at most $m$ steps‎. ‎In this‎
‎paper‎, ‎we introduce a class of ABS-type methods for solving a full row‎
‎rank linear equations‎, ‎where the $i$-th iteration solves the first‎
‎$3i$ equations‎. ‎We also extended this method for $k$ steps‎. ‎So‎,
‎termination is achieved in at most $\left[\frac{m+(k-1)}{k}\right]$‎
‎steps‎. ‎Morever in our new method in each iteration, we have the‎
‎the general solution of each iteration‎.

کلیدواژه‌ها

ABS methods‎؛ ‎rank $k$ update‎؛ ‎linear system‎؛ ‎general‎ ‎solution of a system‎؛ ‎general solution of an iteration