Subspace methods for sparse eigenvalue problems
Bernhard Steffen · JuSER (Forschungszentrum Jülich) · 2000
Subspace methods are the methods of choice for calculating a few eigenvalues and -vectors of a large matrix.They may also be considered for completely diagonalizing a matrix if it is either sparse or too large to be stored.A subspace method for a n × n matrix A consists of a scheme to extract approximations to some eigenvalues and -vectors of A from the action of A onto a subspace V ⊂ n and a method to update V. We will present extraction schemes for extremal (Ritz projection) as well as inner (residual minimization, harmonic Ritz projection) eigenvalues and discuss advanced update schemes.