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.
Asadbeigi, L., Amirfakhrian, M. (2017). 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, 7(3 (SUMMER)), 185-207.
MLA
Leila Asadbeigi; Majid Amirfakhrian. "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, 7, 3 (SUMMER), 2017, 185-207.
HARVARD
Asadbeigi, L., Amirfakhrian, M. (2017). '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, 7(3 (SUMMER)), pp. 185-207.
VANCOUVER
Asadbeigi, L., Amirfakhrian, M. 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, 2017; 7(3 (SUMMER)): 185-207.
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