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Table 7 Numbers of GCR iterations to convergence on ill-posed problems

From: Newton–Raphson preconditioner for Krylov type solvers on GPU devices

 

DIAG

SSOR

BFGS–DIAG

BFGS–SSOR

m = 3

m = 5

m = 7

m = 10

m = 3

m = 5

m = 7

m = 10

\(40 \times 40 \times 125\)

3930

341

878

900

964

891

165

210

248

267

\(20 \times 20 \times 500\)

NA

1817

7709

4994

7690

NA

1188

1187

926

1256

\(10 \times 10 \times 2000\)

NA

25,209

NA

NA

NA

NA

8736

9954

7088

NA

  1. In the table, NA denotes the preconditioned GCR doesn’t converge within 300,000 iterations, and m denotes the number of previous iterations to be taken into consideration