A refined shifted block inverse-free Krylov subspace method for symmetric generalized eigenvalue problems

作者：Wang, Xiang^*; Nie, Yong-ming

来源：Computers & Mathematics with Applications, 2013, 66(6): 1137-1146.

DOI：10.1016/j.camwa.2013.07.023

• Krylov subspace methods
• B-orthogonality
• Arnoldi process
• Ritz vector
• Refined Ritz vector
• Generalized eigenvalue problem

For computing the p smallest eigenvalues and their corresponding eigenvectors of symmetric generalized eigenproblems simultaneously, Quillen and Ye have introduced a block inverse-free preconditioned Krylov subspace method (Quillen and Ye, 2010)[14]. To accelerate convergence and compute interior eigenpairs, in this paper we present a refined shifted block inverse-free Krylov subspace algorithm based on the block Arnoldi process that generates a B-orthogonality basis of the matrix Krylov subspace. It is proved that this algorithm can guarantee the convergence if the corresponding Ritz values converge. Numerical experiments show that the refined algorithm is more efficient than the original approach.

• 出版日期2013-10
• 单位南昌大学; 南京大学