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Table 8 Time 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

\(40 \times 40 \times 125\)

2.91E+02

3.62E+01

7.43E+01

8.57E+01

1.02E+02

1.08E+02

1.87E+01

2.58E+01

3.28E+01

3.81E+01

\(20 \times 20 \times 500\)

NA

1.87E+02

6.25E+02

4.58E+02

7.87E+02

NA

1.34E+02

1.46E+02

1.24E+02

1.84E+02

\(10 \times 10 \times 2000\)

NA

2.43E+03

NA

NA

NA

NA

9.32E+02

1.18E+03

9.09E+02

NA

  1. In the table, e.g. 5.14E−02 means \(5.14 \times 10^{-2}\) s, 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