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Table 3 Error in solutions

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

  DIAG SSOR BFGS–DIAG BFGS–SSOR BFGS
m = 3 m = 5 m = 7 m = 10 m = 3 m = 5 m = 7 m = 10
GR_30_30 1.14E−08 9.28E−09 5.06E−09 4.13E−09 4.52E−09 5.22E−09 3.46E−09 2.12E−09 2.12E−09 2.12E−09 1.60E−04
BCSSTK14 1.44E−12 NA 1.01E−10 6.29E−12 1.42E−12 1.85E−12 5.59E−12 1.19E−11 1.37E−12 1.83E−12 5.90E−09
BCSSTK15 NA NA 6.69E−11 1.10E−10 1.03E−10 NA 1.05E−11 9.53E−12 1.22E−11 NA 1.51E−08
RDB450 NA NA 1.34E−08 1.44E−08 1.22E−08 NA 9.93E−09 1.12E−08 1.52E−08 1.27E−08 NA
  1. In the table, e.g. 1.14E−08 means that the error defined as \(\Vert \mathbf {x}_{true}-\mathbf {x}_{GCR} \Vert _2\) is \(1.14 \times 10^{-8}\), where \(\mathbf {x}_{true}\) is the solution by the LU factorization, and \(\mathbf {x}_{GCR}\) is the solution by the preconditioned GCR. NA denotes the preconditioned GCR doesn’t converge within 150,000 iterations, and m denotes the number of previous iterations to be taken into consideration