This is con rmed in the bottom table which consists

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Unformatted text preview: rs would lose one bit of precision for each increase in or . We could reduce this problem by using a di erent strategy to choose step sizes. For example, select 0 = 1, 1 = 1 , , h q Oh y R Oh q h q i h i q h 5 h =r ::: =0 1 2 3 4 = 0 0.0000 0.5000 0.3438 0.3701 0.3678 1 0.2500 0.3828 0.3668 0.3679 0.3679 2 0.3164 0.3708 0.3678 0.3679 0.3679 3 0.3436 0.3685 0.3679 0.3679 0.3679 4 0.3561 0.3680 0.3679 0.3679 0.3679 5 0.3621 0.3679 0.3679 0.3679 6 0.3650 0.3679 0.3679 7 0.3664 0.3679 8 0.3672 =0 1 2 3 4 = 0 3.6788e-01 -1.3212e-01 2.4129e-02 -2.2263e-03 1.0452e-04 1 1.1788e-01 -1.4933e-02 1.0682e-03 -4.1157e-05 8.3834e-07 2 5.1473e-02 -2.9321e-03 9.7508e-05 -1.7864e-06 1.7546e-08 3 2.4271e-02 -6.5990e-04 1.0625e-05 -9.5199e-08 4.6022e-10 4 1.1805e-02 -1.5701e-04 1.2449e-06 -5.5185e-09 1.3240e-11 5 5.8242e-03 -3.8318e-05 1.5078e-07 -3.3249e-10 6 2.8929e-03 -9.4664e-06 1.8557e-08 7 1.4417e-03 -2.3527e-06 8 7.1969e-04 =0 1 2 3 4 = 0 3.6788e-01 -1.3212e-01 2.4129e-02 -2.2263e-03 1.0452e-04 1 2.3576e-01 -5.9732e-02 8.5453e-03 -6.5851e-04 2.6827e-05 2 2.0589e-01 -4.6914e-02 6.2405e-03 -4.5731e-04 1.7967e-05 3 1.9416e-01 -4.2234e-02 5.4402e-03 -3.8993e-04 1.5080e-05 4 1.8888e-01 -4.0194e-02 5.0990e-03 -3.6166e-04 1.3883e-05 5 1.8637e-01 -3.9238e-02 4.9408e-03 -3.4864e-04 6 1.8515e-...
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