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)