QMR

CGS and QMR methods are easily broken off;

CGS和QMR方法易于中断；

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To the railway signal control system, the quadruple modular redundant ( QMR) architecture meet the higher safe requirement because of the busier railway transport and the higher train speed.

四模冗余结构满足铁路运输日益繁忙和列车速度不断提高对铁路信号控制系统更高的安全要求。

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When solving the nonsymmetric linear systems, the paper makes the total backward perturbation analysis to QMR method, and uses the total quasi-minimal backward perturbation ( TQMBACK) technique. So the restarted total quasi-minimal backward perturbation ( RTQMBACK) method is given.

同样地，对求解非对称线性方程组的QMR方法作出了向后扰动分析，结合总体向后扰动范数拟极小化的技巧，给出了求解非对称线性方程组的总体拟极小向后扰动（TQMBACK）方法。

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The transpose-free QMR ( TFQMR) algorithm is a Krylov subspace algorithm that can be used to obtain fast solutions for linear systems with very large and very sparse coefficient matrices.

TFQMR算法是一种Krylov子空间算法，常用来求解大型稀疏线性方程组。

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The algorithm uses the inexact search directions that are computed with only moderate accuracy by Krylov subspace methods like CG or QMR.

该算法使用的搜索方向仅需要达到一个相对的精度，这样的搜索方向可以通过Krylov子空间迭代法，比如CG或QMR得到。

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This article addresses the technical advantages of QMR safety system in aspects of agent structure of the system, operation principle, function of Integrated Safety Shutdown, and function of failure auto-diagnosis.

从系统的主体架构、工作原理、一体化停车功能和故障自诊断功能4个方面阐述了四重化冗余安全仪表系统的技术优势及其设计步骤；

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