Preconditioning for linear systems arising in modeling and optimization

科学计算中的一个中心问题是求解大型线性方程组。线性方程几乎作为一个子问题出现在计算科学和工程的每一个分支中，包括固体力学、流体力学、电磁学、天体物理、化学、固体和高能物理，以及各种优化和统计问题。从设计汽车或飞机发动机，到在大公司安排工作人员的日程安排，再到开发下一代成像设备等各式各样的问题，都需要解线性方程。事实上，对于许多这样的问题，解线性方程是计算量最大的一步。

A central problem in scientific computing is the solution of large systems of linear equations. Linear equations arise as a subproblem in practically every branch of computational science and engineering, including solid mechanics, fluid mechanics, electromagnetics, astrophysics, chemistry, solid and high energy physics, as well as in all manner of optimization and statistical problems. Problems as disparate as designing automobile or aircraft engines, scheduling work crews at a large company, or developing next-generation imaging devices all require solving linear equations. Indeed, for many of these problems, solving linear equations is the most computationally intensive step.