TY - JOUR
T1 - Algorithm 879: EIGENTEST—a test matrix generator for large-scale eigenproblems
JF - ACM Trans. Math. Softw.
Y1 - 2008
A1 - Lee,Che-Rung
A1 - Stewart, G.W.
KW - Eigensystem
KW - test matrix generation
AB - 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.
VL - 35
SN - 0098-3500
UR - http://doi.acm.org/10.1145/1377603.1377610
CP - 1
M3 - 10.1145/1377603.1377610
ER -