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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


next up previous contents
Next: Test Matrices for the Up: Testing the Nonsymmetric Eigenvalue Previous: The Nonsymmetric Eigenvalue Drivers   Contents
Susan Blackford 2001-08-13