3. General Use of ARPACK
Society for Industrial and Applied Mathematics eBooks · 1998
This chapter will describe the complete structure of the reverse communication interface to the ARPACK codes. Numerous computational modes are available, including several shift-invert strategies designed to accelerate convergence. Two of the more sophisticated modes will be described in detail. The remaining ones are quite similar in principle, but require slightly different tasks to be performed with the reverse communication interface. This chapter is structured as follows. The naming conventions used in ARPACK and the data types and precisions available are described in section 3.1. Spectral transformations are discussed in section 3.2. Spectral transformations are usually extremely effective, but there are a number of problem-dependent issues that determine which one to use. In section 3.3 we describe the reverse communication interface needed to exercise the various shift-invert options. Each shift-invert option is specified as a computational mode, and all of these are summarized in the remaining sections. There is a subsection for each problem type and hence these sections are quite similar and repetitive. Once the basic idea is understood, it is probably best to turn directly to the subsection that describes the problem setting that is most interesting to you. Perhaps the easiest way to rapidly become acquainted with the modes of ARPACK is to run the example driver routines (see Appendix A) that have been supplied for each of the modes. These may be used as templates and adapted to solve specific problems. 3.1 Naming Conventions, Precisions, and Types ARPACK has two interface routines that must be invoked by the user. They are __aupd that implements the IRAM and __eupd to postprocess the results of __aupd. The user may request an orthogonal basis for a selected invariant subspace or eigenvectors corresponding to selected eigenvalues with __eupd. If a spectral transformation is used, __eupd transforms the computed eigenvalues for the problem .