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AITKEN'S METHODg(x) = e^-xp0 = 0

n pn (fxed point)0 2.00000001 0.69314722 1.43810243 1.21490204 1.31879555 1.27524386 1.29445247 1.28615508 1.28977259 1.2882016

10 1.288885011 1.288587912 1.288717113 1.288661014 1.288685415 1.288674816 1.288679417 1.288677418 1.288678219 1.288677920 1.288678021 1.288677922 1.288678023 1.2886780

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(Accelerating fxed p int iterati n!)

en lambda (bisection)- -

1.3068528 -0.7449552 0.57003760.2232004 0.29961580.1038934 0.46547170.0435517 0.41919580.0192086 0.44105210.0082973 0.43195900.0036175 0.43598170.0015709 0.43424640.0006833 0.43500340.0002970 0.43467470.0001292 0.43481770.0000562 0.43475560.0000244 0.43478260.0000106 0.43477080.0000046 0.43477600.0000020 0.43477370.0000009 0.43477470.0000004 0.43477430.0000002 0.43477450.0000001 0.43477440.0000000 0.43477440.0000000 0.4347744

2.30039370.4347086

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pn_ba (ait!en's) lambda (ait!en's) pn(fxed point "o ste#ens- - 2.000000000000- - 0.6931472

1.1676296 - 1.43810241.2663591 - 1.33612431.2857962 0.1968732 1.26720001.2881079 0.1189296 1.28931581.2885733 0.2013431 1.28840051.2886580 0.1818593 1.28867811.2886742 0.1917654 1.28867791.2886773 0.1877711 1.28867801.2886778 0.1895625 1.28867801.2886779 0.1887943 1.28867801.2886780 0.1891303 1.28867801.2886780 0.1889846 1.28867801.2886780 0.1890479 1.28867801.2886780 0.1890205 1.28867801.2886780 0.1890320 1.28867801.2886780 0.1890240 1.28867801.2886780 0.1890361 1.28867801.2886780 0.1890042 1.28867801.2886780 0.1897628 1.28867801.2886780 0.1842105 1.28867801.2886780 0.0000000 1.28867801.2886780 "#$%&0' 1.2886780

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pn_ba (ste#enson's)

1.1676296

1.2872092

1.2886777

1.2886780

1.2886780

"#$%&0'

"#$%&0'

"#$%&0'

"#$%&0'

"#$%&0'

"#$%&0'

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n a ! l te e01 """2 """3 """4 """5 """6 """7 """8 """9 """

10 """11 """12 """13 """14 """15 """16 """17 """18 """19 """20 """21 """22 """23 """24 """25 """

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a!*+pt tic c n!tant n a ! l te e a!*+pt tic c n!tant err r01

0.570038 20.299616 30.465472 4 0.0194370.419196 5 0.002312 0.118930.441052 6 0.000465 0.2013430.431959 7 8.46,-005 0.1818590.435982 8 1.62,-005 0.1917650.434246 9 3.05,-006 0.1877710.435003 10 5.78,-007 0.1895620.434675 11 1.09,-007 0.1887940.434818 12 2.06,-008 0.189130.434756 13 3.90,-009 0.1889850.434783 14 7.37,-010 0.1890480.434771 15 1.39,-010 0.1890210.434776 16 2.63,-011 0.1890320.434774 17 4.98,-012 0.1890240.434775 18 9.41,-013 0.1890360.434774 19 1.78,-013 0.1890040.434774 20 3.38,-014 0.1897630.434774 21 6.22,-015 0.1842110.434774 22 1.33,-015 0.2142860.434774 23 2.22,-016 0.166667

95092775 24 1.288678 5.8, 0150 25 0 0