EIGENTEST: A Test Matrix Generator for Large-Scale Eigenproblems

Eigentest is a package that produces real test matrices with knowneigensystems. 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)'*b, inv(A - sI)*b, and inv(A - sI)*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 paper introduces the
eigenmat and describes implementations in Fortran~77, Fortran~95, C,
and Matlab.