Test Matrices for the Nonsymmetric Eigenvalue Routines

Twenty-one different types of test matrices may be generated for the nonsymmetric eigenvalue routines. Table 5 shows the types available, along with the numbers used to refer to the matrix types. Except as noted, all matrices have 124#124 entries.

Table 5: Test matrices for the nonsymmetric eigenvalue problem

	Eigenvalue Distribution
Type	Arithmetic	Geometric	Clustered	Random	Other
Zero					1
Identity					2
125#125					3
Diagonal	4, 726#26, 8126#126	5	6
127#127	9	10	11	12
128#128	13	14	15	16, 1726#26, 18126#126
Random entries					19, 2026#26, 21126#126
26#26- matrix entries are 129#129
126#126- matrix entries are 130#130

Matrix types identified as ``Zero'', ``Identity'', ``Diagonal'', and ``Random entries'' should be self-explanatory. The other matrix types have the following meanings:

131#131:

Matrix with ones on the diagonal and the first subdiagonal, and zeros elsewhere

127#127:

Schur-form matrix 85#85 with 124#124 entries conjugated by a unitary (or real orthogonal) matrix 132#132

128#128:

Schur-form matrix 85#85 with 124#124 entries conjugated by an ill-conditioned matrix 98#98

For eigenvalue distributions other than ``Other'', the eigenvalues lie between 9#9 (the machine precision) and 133#133 in absolute value. The eigenvalue distributions have the following meanings:

Arithmetic:

Difference between adjacent eigenvalues is a constant

Geometric:

Ratio of adjacent eigenvalues is a constant

Clustered:

One eigenvalue is 133#133 and the rest are 9#9 in absolute value

Random:

Eigenvalues are logarithmically distributed