HP MLIB User's Guide Vol. 2 7th Ed.

Chapter 15 Sparse Eigenvalues and Eigenvectors 1003
Overview
15 Sparse Eigenvalues and Eigenvectors
Overview
This chapter describes state-of-the-art software for solving sparse symmetric
and generalized symmetric eigenvalue problems. This package of subprograms
provides efficient use of the Hewlett-Packard architecture in conjunction with
powerful techniques for using the sparsity of the problem to reduce the cost of
solution. Accuracy is assured through appropriate numerical techniques.
This chapter explains how to use sparse eigenvalue subprograms to solve
sparse eigenvalue problems where the matrix or matrices are symmetric.
Subprograms are provided to:
• Solve ordinary symmetric sparse eigenvalue problems of the form Ax=λx
• Solve certain generalized symmetric sparse eigenvalue problems of the form
Ax=λBx
This sparse matrix eigenvalue software is designed so that it is possible to call
a single subprogram to solve a sparse symmetric eigenvalue problem. However,
this requires a particular format for the sparse matrix. This package provides
other approaches that provide a very general interface to alternative
representations of the sparse matrix. These optional approaches, however,
require the user to call a sequence of subprograms.
Chapter objectives
After you read this chapter you will:
• Understand what a sparse matrix is
• Understand how to use these subprograms to compute some of the
eigenvalues and eigenvectors of sparse symmetric matrices