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Test Matrices for the Symmetric Eigenvalue Routines

Except for the banded matrices, twenty-one different types of test matrices may be generated for the symmetric eigenvalue routines. Table 8 shows the types available, along with the numbers used to refer to the matrix types. Except as noted, all matrices have 124#124 entries. The expression 281#281 means a real diagonal matrix 282#282 with 124#124 entries conjugated by a unitary (or real orthogonal) matrix 132#132. The eigenvalue distributions have the same meanings as in the nonsymmetric case (see Section 7.3.2).

For banded matrices, fifteen different types of test matrices may be generated. These fifteen test matrices are the same as the first fifteen test matrices in Table 8.


Table 8: Test matrices for the symmetric eigenvalue problem
  Eigenvalue Distribution
Type Arithmetic Geometric Clustered Other
Zero   1
Identity   2
Diagonal 3 4, 626#26, 7126#126 5  
281#281 8, 1126#26, 12126#126, 9, 17175#175 10, 18175#175  
  16175#175, 19283#283, 20284#284      
Symmetric w/Random entries   13, 1426#26, 15126#126
Diag. Dominant   21    
26#26- matrix entries are 129#129
126#126- matrix entries are 130#130
285#285 - diagonal entries are positive
283#283 - matrix entries are 129#129 and diagonal entries are positive
175#175 - matrix entries are 130#130 and diagonal entries are positive



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