This paper deals with a synthetic presentation of parallel iterative asynchronous algorithms and their extensions for the solution of large sparse linear or pseudo-linear algebraic systems eventually constrained. The behavior of these iterative parallel asynchronous algorithms is studied by three distinct methods : contraction property, partial ordering property linked to the discrete maximum principle and nested sets; the link between these three kinds of analysis is presented. Stopping tests of the iterations are presented both from computer science and from numerical analysis approach including in this last case approximate contraction property, partial ordering property linked to the discrete maximum principle and nested sets. The principle of implementation of these parallel asynchronous iterative methods is described for subdomain method without overlapping and for subdomain method with overlapping; the use of load balancing approach for asynchronous parallel algorithms is also discussed. Various applications modelled by linear equations or pseudo linear equations and solved by such parallel algorithms are presented as well as the uses of these methods in computer security and Boolean calculation. The efficiency of parallel iterative asynchronous algorithms is also discussed.

本文讨论了并行迭代异步算法的综合介绍，及其对最终受限的大型稀疏线性或伪线性代数系统解的扩展。通过三种不同的方法研究了这些迭代并行异步算法的行为：收缩特性，链接到离散最大原理的局部有序特性和嵌套集；以及 介绍了这三种分析之间的联系。从计算机科学和数值分析方法中都给出了迭代的停止测试，包括最后一种情况下的近似收缩特性，链接到离散最大原理的局部有序特性和嵌套集。对于不重叠的子域方法和重叠的子域方法，描述了这些并行异步迭代方法的实现原理。还讨论了将负载平衡方法用于异步并行算法。介绍了由线性方程或伪线性方程建模并由此类并行算法求解的各种应用，以及这些方法在计算机安全和布尔计算中的用途。还讨论了并行迭代异步算法的效率。介绍了由线性方程或伪线性方程建模并由此类并行算法求解的各种应用，以及这些方法在计算机安全和布尔计算中的用途。还讨论了并行迭代异步算法的效率。介绍了由线性方程或伪线性方程建模并由此类并行算法求解的各种应用，以及这些方法在计算机安全和布尔计算中的用途。还讨论了并行迭代异步算法的效率。