Adaptive Eigenvalue Computation  Complexity Estimates
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 $\ell_2$, 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.
 Publication:

arXiv eprints
 Pub Date:
 November 2007
 arXiv:
 arXiv:0711.1070
 Bibcode:
 2007arXiv0711.1070D
 Keywords:

 Mathematics  Numerical Analysis;
 65N25;
 65J10;
 65N55
 EPrint:
 submitted to Math. Comp