For computing the smallest eigenvalue and the corresponding eigenvector of a Hermitian matrix, by introducing a concept of perfect Krylov subspace, we propose a class of perfect Krylov subspace methods. For these methods, we prove their local, semilocal, and global convergence properties, and discuss their inexact implementations and preconditioning strategies. In addition, we use numerical experiments to demonstrate the convergence properties and exhibit the competitiveness of these methods with a few state-of-the art iteration methods such as Lanczos, rational Krylov sequence, and Jacobi-Davidson, when they are employed to solve large and sparse Hermitian eigenvalue problems.
Bai, Z.-Z., Miao, C.-Q.: On local quadratic convergence of inexact simplified Jacobi-Davidson method for interior eigenpairs of Hermitian eigenproblems. Appl. Math. Lett. 72, 23–28 (2017)MathSciNetCrossRefzbMATHGoogle Scholar
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1.State Key Laboratory of Scientific/Engineering Computing, Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijingPeople’s Republic of China
2.School of Mathematical SciencesUniversity of Chinese Academy of SciencesBeijingPeople’s Republic of China