Roots of f(x)=x^2 - 2 (iterations achieve error < 10**-8) Bisection n u v p f(p) -------------------------------------------------------------------------- 0 1.00000000 2.00000000 1.50000000 0.25000000 1 1.00000000 1.50000000 1.25000000 -0.43750000 2 1.25000000 1.50000000 1.37500000 -0.10937500 3 1.37500000 1.50000000 1.43750000 0.06640625 4 1.37500000 1.43750000 1.40625000 -0.02246094 5 1.40625000 1.43750000 1.42187500 0.02172852 6 1.40625000 1.42187500 1.41406250 -0.00042725 7 1.41406250 1.42187500 1.41796875 0.01063538 8 1.41406250 1.41796875 1.41601562 0.00510025 9 1.41406250 1.41601562 1.41503906 0.00233555 10 1.41406250 1.41503906 1.41455078 0.00095391 11 1.41406250 1.41455078 1.41430664 0.00026327 12 1.41406250 1.41430664 1.41418457 -0.00008200 13 1.41418457 1.41430664 1.41424561 0.00009063 14 1.41418457 1.41424561 1.41421509 0.00000431 15 1.41418457 1.41421509 1.41419983 -0.00003884 16 1.41419983 1.41421509 1.41420746 -0.00001726 17 1.41420746 1.41421509 1.41421127 -0.00000647 18 1.41421127 1.41421509 1.41421318 -0.00000108 19 1.41421318 1.41421509 1.41421413 0.00000162 20 1.41421318 1.41421413 1.41421366 0.00000027 21 1.41421318 1.41421366 1.41421342 -0.00000041 22 1.41421342 1.41421366 1.41421354 -0.00000007 23 1.41421354 1.41421366 1.41421360 0.00000010 24 1.41421354 1.41421360 1.41421357 0.00000002 Regula Falsi n u v p AITKIN f(p) -------------------------------------------------------------------------- 0 1.00000000 2.00000000 1.33333333 -0.22222222 1 1.33333333 2.00000000 1.40000000 -0.04000000 2 1.40000000 2.00000000 1.41176471 1.41428571 -0.00692042 3 1.41176471 2.00000000 1.41379310 1.41421569 -0.00118906 4 1.41379310 2.00000000 1.41414141 1.41421362 -0.00020406 5 1.41414141 2.00000000 1.41420118 1.41421356 -0.00003501 6 1.41420118 2.00000000 1.41421144 1.41421356 -0.00000601 7 1.41421144 2.00000000 1.41421320 1.41421356 -0.00000103 8 1.41421320 2.00000000 1.41421350 1.41421356 -0.00000018 9 1.41421350 2.00000000 1.41421355 1.41421356 -0.00000003 10 1.41421355 2.00000000 1.41421356 1.41421356 -0.00000001 Newtons Method n p(n-1) p(n) f[p(n)] ---------------------------------------------------------------------- 1 1.50000000 1.41666667 0.00694444 2 1.41666667 1.41421569 0.00000601 3 1.41421569 1.41421356 0.00000000 Secant Method n p(n-2) p(n-1) p(n) f[p(n)] ---------------------------------------------------------------------- 2 1.50000000 1.25000000 1.40909091 -0.01446281 3 1.25000000 1.40909091 1.41452991 0.00089488 4 1.40909091 1.41452991 1.41421299 -0.00000162 5 1.41452991 1.41421299 1.41421356 0.00000000