ACM Transactions on Mathematical Software (TOMS)
Implicit application of polynomial filters in a k-step Arnoldi method
SIAM Journal on Matrix Analysis and Applications
An Arnoldi code for computing selected eigenvalues of sparse, real, unsymmetric matrices
ACM Transactions on Mathematical Software (TOMS)
A Jacobi--Davidson Iteration Method for Linear EigenvalueProblems
SIAM Journal on Matrix Analysis and Applications
Implicitly Restarted GMRES and Arnoldi Methods for Nonsymmetric Systems of Equations
SIAM Journal on Matrix Analysis and Applications
An analysis of the Rayleigh—Ritz method for approximating eigenspaces
Mathematics of Computation
Thick-Restart Lanczos Method for Large Symmetric Eigenvalue Problems
SIAM Journal on Matrix Analysis and Applications
Convergence of Restarted Krylov Subspaces to Invariant Subspaces
SIAM Journal on Matrix Analysis and Applications
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This paper presents an invert-free Arnoldi method for extracting a few interior eigenpairs of large sparse matrices. It is derived by implicitly applying the Arnoldi process with the shifted and inverted operator (A-τ I)-1 in a shifted Krylov subspace (A-τ I)Km(A, v1). Due to a subtle relationship between the Krylov subspace Km(A, v1) and its shifted Krylov subspace, we avoid forming the shifted and inverted operator explicitly. Comparisons are drawn between the harmonic Arnoldi method and the invert-free Arnoldi method. Finally, numerical results are reported to show the efficiency of the new method.