Gerard L.G. Sleijpen, Peter Sonneveld and Martin B. van Gijzen, Bi ...

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1112 G.L.G. Sleijpen et al. / Applied Numerical Mathematics 60 (2010) 1100–1114
Fig. 1. Convergence of Bi-CGSTAB(4) and IDR(4) for SHERMAN4.
Table 1
Number of matrix–vector multiplications to solve the SHERMAN4 system
such that the scaled norm of the updated residual is less than 10 −8 .
Method Number of MVs ‖b − Ax‖/‖b‖
GMRES 120 9.8×10 −9
IDR(1) 179 6.6×10 −9
IDR(2) 161 8.3×10 −9
IDR(3) 153 8.7×10 −9
IDR(4) 146 3.0×10 −9
IDR(5) 150 1.2×10 −9
Bi-CGSTAB(1) 180 9.0×10 −9
Bi-CGSTAB(2) 162 8.6×10 −9
Bi-CGSTAB(3) 156 4.6×10 −9
Bi-CGSTAB(4) 150 1.8×10 −7
Bi-CGSTAB(5) 144 7.1×10 −9
Table 2
Number of matrix–vector multiplications to solve the ADD20 system such
that the scaled norm of the updated residual is less than 10 −8 .
Method Number of MVs ‖b − Ax‖/‖b‖
GMRES 295 1.0×10 −8
IDR(1) 672 9.0×10 −9
IDR(2) 581 9.9×10 −9
IDR(3) 588 4.8×10 −9
IDR(4) 480 5.3×10 −9
IDR(5) 444 9.4×10 −9
Bi-CGSTAB(1) 728 9.0×10 −9
Bi-CGSTAB(2) 648 9.8×10 −9
Bi-CGSTAB(3) 528 2.0×10 −7
Bi-CGSTAB(4) 545 7.1×10 −6
Bi-CGSTAB(5) 702 0.026