Robust expansion of subspaces in iterative projection methods for large eigenvalue problems
نویسندگان
چکیده
منابع مشابه
Iterative Projection Methods for Large–scale Nonlinear Eigenvalue Problems
In this presentation we review iterative projection methods for sparse nonlinear eigenvalue problems which have proven to be very efficient. Here the eigenvalue problem is projected to a subspace V of small dimension which yields approximate eigenpairs. If an error tolerance is not met then the search space V is expanded in an iterative way with the aim that some of the eigenvalues of the reduc...
متن کاملOn convergence of iterative projection methods for symmetric eigenvalue problems
We prove global convergence of particular iterative projection methods using the so-called shift-and-invert technique for solving symmetric generalized eigenvalue problems. In particular, we aim to provide a variant of the convergence theorem obtained by Crouzeix, Philippe, and Sadkane for the generalized Davidson method. Our result covers the Jacobi-Davidson and the rational Krylov methods wit...
متن کاملHarmonic projection methods for large non-symmetric eigenvalue problems
The problem of finding interior eigenvalues of a large nonsymmetric matrix is examined. A procedure for extracting approximate eigenpairs from a subspace is discussed. It is related to the Rayleigh–Ritz procedure, but is designed for finding interior eigenvalues. Harmonic Ritz values and other approximate eigenvalues are generated. This procedure can be applied to the Arnoldi method, to precond...
متن کاملProjection Methods for Nonlinear Sparse Eigenvalue Problems
This paper surveys numerical methods for general sparse nonlinear eigenvalue problems with special emphasis on iterative projection methods like Jacobi–Davidson, Arnoldi or rational Krylov methods and the automated multi–level substructuring. We do not review the rich literature on polynomial eigenproblems which take advantage of a linearization of the problem.
متن کاملIterative Methods for Neutron Transport Eigenvalue Problems
We discuss iterative methods for computing criticality in nuclear reactors. In general this requires the solution of a generalised eigenvalue problem for an unsymmetric integro-differential operator in 6 independent variables, modelling transport, scattering and fission, where the dependent variable is the neutron angular flux. In engineering practice this problem is often solved iteratively, u...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: PAMM
سال: 2007
ISSN: 1617-7061
DOI: 10.1002/pamm.200700542