Preconditioning for linear systems arising in modeling and optimization

建模和优化中出现的线性系统的预处理

• 批准号: 341718-2007
• 负责人: Vavasis, Stephen
• 金额: $ 1.89万
• 依托单位: University of Waterloo
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2008
• 资助国家: 加拿大
• 起止时间: 2008-01-01 至 2009-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=399568
• 关键词: Preconditioning; linear; systems; arising; modeling

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.

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