Table 3: Properties of IULBF1, IULBF2, IULBF3, and IULBF4 preconditioners.

MethodIULBF1IULBF2IULBF3IULBF4

Density 𝑃 timeDensity 𝑃 time Density 𝑃 timeDensity 𝑃 time

hor-131 0.893352 34.422 1.104017 62.11 1.046628 26.219 1.889527 63.328
sherman2 1.434745 766.187 2.834069 1166.11 0.823720 562.094 1.335498 1263.34
cavity05 0.682030 1596.86 1.478304 1887.42 0.686106 803.25 1.538000 2071.98
cavity06 0.651693 663.953 1.549958 1870.22 0.657894 791.422 1.628745 1337.67
sherman4 1.270470 789.687 1.345483 870.672 1.386952 459.625 2.055203 622.031
epb0 0.850721 1077.48 0.853941 3577.97 1.009274 951.688 1.356775 2924.58
pde2961 1.278642 7344.64 1.357011 15909.7 1.309427 4634.16 2.180871 9440.33