An investigation into acceleration techniques for subspace iteration

The mathematical statement of the eigenproblem is deceptively simple and, although the basic theory has been well established for a long time, obtaining an accurate solution still remains far from trivial. The eigenproblem arises in many branches of science. In this study, however, it is considered only in the context of dynamic and buckling analysis.
The genesis of the eigenproblem in dynamic and buckling analysis is considered and a brief survey of popular solution techniques is presented. A most powerful solution technique, namely subspace iteration, which forms the kernal of this study is discussed in some detail.
Various ideas which may accelerate the subspace iteration method are investigated theoretically. These ideas are subsequently converted into algorithms, which are implemented in the form of FORTRAN computer programmes.
The validity and accuracy of the results obtained is tested against known solutions with a satisfactory outcome. The various modifications are then presented with a menu of problems for comparison purposes. This process identifies the 'best' modification and also yields new ideas and insights.
The subsequent investigations lead to the conception of the 'hybrid technique', which employs the best modification in conjunction with the original subspace iteration. .The convergence rate and solution time of the hybrid technique compare favourably with those of the original subspace iteration. . In fact, for the problem considered, the hybrid technique is always superior to the original subspace iteration.