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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