Deflating Eigenvalues for Linear Equations in QCD

将发展有效的收缩迭代法来求解多右端线性方程组。一种技术涉及一个放气GMRES方法，既解决了线性方程组和计算特征向量。这些特征向量然后被用来帮助解决随后的右手边。将分析和评估这种技术的效率。对于非重启迭代方法，如BiCGStab和QMR，将使用左右特征向量开发比最小残差更好的投影。同时解决方案的多移位系统也将进行分析。 线性方程组出现在许多科学领域，这些系统通常具有多个右侧和轻微变化的参数。一个重要的例子是计算一组相互作用，其中包括同时产生的夸克-反夸克对。这些所谓的不连通图对理解强相互作用（QCD）物理学的进展构成了重大障碍，强相互作用是我们了解宇宙如何构建的基础理论。此外，在QCD中对夸克的新型更真实的模拟对科学计算提出了很大的需求。这个国际数学/物理项目的目标是在QCD和其他科学领域的线性方程的迭代解方面取得重大进展。基本的算法改进将被提出和评估，这将推动这些领域的进展。

Efficient deflated iterative methods will be developed for solving linear equations with multiple right hand sides. One technique involves a deflated GMRES method that both solves the linear equations and computes eigenvectors. These eigenvectors then are used to assist in the solution of subsequent right-hand sides. This technique will be analyzed and evaluated for efficiency. For nonrestarted iterative methods such as BiCGStab and QMR, a better projection than minimum residual will be developed using both right and left eigenvectors. Simultaneous solution of multiply shifted systems will also be analyzed. Systems of linear equations arise in many areas of science, and it is common for these systems to have multiple right-hand sides and slightly changed parameters. One important example is the calculation of a set of interactions which involve simultaneously created quark-antiquark pairs. These co-called disconnected diagrams present a significant obstacle to progress in understanding the physics of the strong interaction (QCD), a theory which is fundamental to our knowledge of how the universe is built. In addition, new types of more realistic simulations of quarks in QCD are making a large demand on scientific computing. The goal of this interdisplinary math/physics project is to make a major advance in the iterative solution of linear equations in QCD and other scientific areas. Basic algorithmic improvements will be proposed and evaluated which will advance progress in these fields.