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almost always faster in these experiments. From the wall-clock times reported, we can see that there is not any significant overhead. For loose outer tolerances (10−3), the inner-outer iteration uses 45% fewer iterations than the power method and for tight outer tolerances (10−7), it almost 30% fewer iterations. The results are consistently faster and involve no parameter search. Table 5.2 – Performance of the inner-outer iteration on various graphs. Total number of matrix- vector products and wall-clock time required for convergence to three different outer toler- ances τ, and the corresponding relative gains defined by (5.24). The parameters used here are α = 0.99, β = 0.5, η = 10−2 . For the first five graphs we used the Matlab mex codes, and for the final three large graphs we used the C++ codes where the graph is stored by out-edges and the times refer to the performance of an 8-core parallel code. tol. graph work power 10−3 ubc-cs-2006 ubc 242 in-2004 232 eu-2005 149 wb-edu 221 arabic-2005 213 sk-2005 156 uk-2007 145 10−5 ubc-cs-2006 ubc 676 in-2004 657 eu-2005 499 wb-edu 647 arabic-2005 638 sk-2005 523 uk-2007 531 10−7 ubc-cs-2006 ubc 1121 in-2004 1108 eu-2005 896 wb-edu 1096 arabic-2005 1083 sk-2005 951 uk-2007 964 (mults.) time in/out gain power (secs.) in/out 1.2 8.3 30.4 28.3 184.6 502.5 1595.9 2359.3 3.6 27.8 97.5 87.4 572.0 1670.0 5077.1 8661.9 6.8 49.0 179.8 148.6 1059.0 3012.9 9122.9 16016.7 gain 35.2% 38.4% 40.5% -5.3% 36.6% 35.5% 7.1% 15.8% 22.9% 26.2% 32.4% 2.1% 32.8% 28.4% 11.4% 15.3% 15.4% 21.6% 26.0% 7.1% 26.6% 23.9% 12.2% 13.7% 5.6 ⋅ numerical results 119 226 141 37.6% 141 41.7% 129 44.4% 150 -0.7% 130 41.2% 139 34.7% 144 7.7% 125 13.8% 432 24.7% 484 28.4% 428 34.9% 476 4.6% 417 35.5% 466 27.0% 460 12.0% 463 12.8% 815 17.3% 856 23.6% 795 28.2% 814 9.2% 777 29.1% 843 22.2% 828 12.9% 857 11.1% 1.9 13.6 51.1 26.9 291.2 779.2 1718.2 2802.0 4.7 37.7 144.3 89.3 850.6 2333.5 5729.0 10225.8 8.0 62.5 243.1 159.9 1442.9 3958.8 10393.3 18559.2 574 986PDF Image | Instagram Cheat Sheet
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