Preconditioners for saddle point linear systems

鞍点线性系统在许多应用领域中具有重要的意义，求解方法的研究在过去的十年中得到了迅速发展。在约束优化和其他领域的问题往往需要解决这样的系统。相关应用的例子有流体动力学、曲面拟合和图像重建，还有很多。鞍点系统的有效数值解是这个建议的核心。我建议开发和研究方法的基础上，最近的新技术，我已经推导出与我的合作者，并扩展我的工作到新的方向。其他研究项目，这是在这个建议中所描述的是新的广义Krylov求解器的开发，条件数最小化和特征值灵敏度的问题的研究，和马尔可夫链的数值解，重点是谷歌的PageRank算法。

Saddle point linear systems are of great importance in many areas of applications, and research on solution methods has surged in the last decade. Problems in constrained optimization and other areas often require the solution of such systems. Examples of relevant applications are fluid dynamics, surface fitting and image reconstruction, and there are many more.The efficient numerical solution of saddle point systems stands at the centre of this proposal. I propose to develop and study methods based on recent novel techniques that I have derived with my collaborators, and extend my work into new directions.Other research projects that are described in this proposal are the development of new generalized Krylov solvers, the study of the problem of condition number minimization and eigenvalue sensitivity, and the numerical solution of Markov chains, with focus on Google's PageRank algorithm.