Research Article

Preconditioning Complex Symmetric Linear Systems

Table 2

Numerical results for COCG and COCR preconditioned on the basis of the matrix ( + ) with complete Cholesky decomposition (), with incomplete Cholesky (IC), and with incomplete Cholesky with threshold (IC0). The reported numbers represent the iterations of the corresponding solver with the specified preconditioner. The dash indicates that it was not feasible to compute a particular test. The stopping tolerance was . The column “preconditioner” shows the time required to assemble the preconditioner. The time elapsed in the computation is expressed in seconds.

Test case Preconditioner COCG-MHSS COCR-MHSS
IC0 IC IC0 IC IC0 IC

T5k
 Iter. 25 148 25 25 148 25
 Time 0.21 0.01 0.25 0.51 0.3 0.48 0.52 0.32 0.42
T16k
 Iter. 24 78 24 24 75 24
 Time 25 0.031 22 34.7 0.48 23.4 36 0.64 23.9
T80k
 Iter. 22 22
 Time 5.3 11 11.2
T150k
 Iter. 638 32 634 32
 Time 0.03 3.0 11 5.6 11.2 5.8
T500k
 Iter.
 Time

S13k
 Iter. 5 5
 Time 0.66 0.88 0.85
S32k
 Iter.
 Time
S500k
 Iter.
 Time