Algorithm 879: EIGENTEST—a test matrix generator for large-scale eigenproblems

Eigentest is a package that produces real test matrices with known eigensystems. A test matrix, called an eigenmat, is generated in a factored form, in which the user can specify the eigenvalues and has some control over the condition of the eigenvalues and eigenvectors. An eigenmat A of order n requires only O(n) storage for its representation. Auxiliary programs permit the computation of (A − sI)b, (A − sI)Tb, (A − sI)−1 b, and (A − sI)−T b in O(n) operations. A special routine computes specified eigenvectors of an eigenmat and the condition of its eigenvalue. Thus eigenmats are suitable for testing algorithms based on Krylov sequences, as well as others based on matrix-vector products. This article introduces the eigenmat and describes implementations in Fortran 77, Fortran 95, C, and Matlab.