Additive preconditioning and aggregation in matrix computations

作者：Pan Victor Y^*; Ivolgin Dmitriy; Murphy Brian; Rosholt Rhys Eric; Taj Eddin Islam; Tang Yuqing; Yan Xiaodong

来源：Computers & Mathematics with Applications, 2008, 55(8): 1870-1886.

DOI：10.1016/j.camwa.2004.03.022

• matrix computations
• additive preconditioning
• aggregation
• MSAs

We combine our novel SVD-free additive preconditioning with aggregation and other relevant techniques to facilitate the solution of a linear system of equations and other fundamental matrix computations. Our analysis and experiments show the power of our algorithms, guide us in selecting most effective policies of preconditioning and aggregation, and provide some new insights into these and related subjects. Compared to the popular SVD-based multiplicative preconditioners, our additive preconditioners are generated more readily and for a much larger class of matrices. Furthermore, they better preserve matrix structure and sparseness and have a wider range of applications (e.g., they facilitate the solution of a consistent singular linear system of equations and of the eigenproblem).

• 出版日期2008-4