283 RWTH Publication No: 47195        2007        IGPM283.pdf
TITLE Adaptive Eigenvalue Computation - Complexity Estimates
AUTHORS Wolfgang Dahmen, Thorsten Rohwedder, Reinhold Schneider, Andreas Zeiser
ABSTRACT This paper is concerned with the design and analysis of a fully adaptive eigenvalue solver for linear symmetric operators. After transforming the original problem into an equivalent one formulated on 2, the space of square summable sequences, the problem becomes sufficiently well conditioned so that a gradient type iteration can be shown to reduce the error by some fixed factor per step. It then remains to realize these (ideal) iterations within suitable dynamically updated error tolerances. It is shown under which circumstances the adaptive scheme exhibits in some sense asymptotically optimal complexity.
KEYWORDS adaptive eigenvalue solver, preconditioned infinite dimensional problem, Richardson iteration, convergence rates, complexity estimates
DOI 10.1007/s00211-008-0159-5
PUBLICATION Numerische Mathematik
110(3), 277-312 (2008)