A block Arnoldi-type contour integral spectral projection method for solving generalized eigenvalue problems

作者：Imakura, Akira^*; Du, Lei; Sakurai, Tetsuya

来源：Applied Mathematics Letters, 2014, 32: 22-27.

DOI：10.1016/j.aml.2014.02.007

• Generalized eigenvalue problems
• Contour integral spectral projection
• Krylov subspace
• Block Arnoldi method

For generalized eigenvalue problems, we consider computing all eigenvalues located in a certain region and their corresponding eigenvectors. Recently, contour integral spectral projection methods have been proposed for solving such problems. In this study, from the analysis of the relationship between the contour integral spectral projection and the Krylov subspace, we conclude that the Rayleigh-Ritz-type of the contour integral spectral projection method is mathematically equivalent to the Arnoldi method with the projected vectors obtained from the contour integration. By this Arnoldi-based interpretation, we then propose a block Arnoldi-type contour integral spectral projection method for solving the eigenvalue problem.

• 出版日期2014-6