Due to the sheer size of sparse systems of linear equations arising from real-world applications in science and engineering, parallel computing as well as iterative methods are almost mandatory. For the iterative solution of large sparse nonsymmetric linear systems, a 1-norm quasi-minimal residual variant of the biconjugate gradient stabilized method (Bi-CGSTAB) is proposed. The algorithm is inspired by a recent transpose-free 1-norm quasi-minimal residual method (TFQMR/sub 1/) in that it applies the 1-norm quasi-minimal residual approach to Bi-CGSTAB in the same way as TFQMR/sub 1/ is derived from the conjugate gradient squared method (CGS). There is also an intimate connection to a method called QMRCGSTAB that is based on applying the (Euclidean norm) quasi-minimal residual approach to Bi-CGSTAB. Numerical examples are used to compare the convergence behavior of Bi-CGSTAB and its 1-norm quasi-minimal residual variant.
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机译：由于科学和工程中实际应用中产生的线性方程组稀疏系统的绝对规模，并行计算以及迭代方法几乎是必不可少的。针对大型稀疏非对称线性系统的迭代解，提出了双共轭梯度稳定方法（Bi-CGSTAB）的1-范数准最小残差。该算法的灵感来自于最近的无转置的1-范数准最小残差方法（TFQMR / sub 1 /），因为它以与TFQMR / sub相同的方式将1-范数准最小残差方法应用于Bi-CGSTAB。 1 /是从共轭梯度平方方法（CGS）得出的。还存在一种与称为QMRCGSTAB的方法的紧密联系，该方法基于对Bi-CGSTAB应用（欧几里得范数）准最小残差法。数值算例用于比较Bi-CGSTAB及其1模准最小残差变量的收敛行为。
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