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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