A Filtered-Davidson Method for Large Symmetric Eigenvalue Problems

作者：Miao, Cun-Qiang^*

来源：East Asian Journal on Applied Mathematics, 2017, 7(1): 21-37.

DOI：10.4208/eajam.160816.131016a

• Symmetric eigenproblem
• filtering technique
• Chebyshev polynomials
• Krylov subspace
• Davidson-type method

For symmetric eigenvalue problems, we constructed a three-term recurrence polynomial filter by means of Chebyshev polynomials. The new filtering technique does not need to solve linear systems and only needs matrix-vector products. It is a memory conserving filtering technique for its three-term recurrence relation. As an application, we use this filtering strategy to the Davidson method and propose the filtered-Davidson method. Through choosing suitable shifts, this method can gain cubic convergence rate locally. Theory and numerical experiments show the efficiency of the new filtering technique.

• 出版日期2017-2
• 单位中国科学院; 中国科学院数学与系统科学研究院