Solution to HW3_S09

Solution to HW3_S09 - HW#3 EGM6341 Spring 2009 pp.117-127...

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Unformatted text preview: HW#3 EGM6341 Spring 2009 pp.117-127 of Atkinsons textbook #2 Bisection method Solutions: a) f(x) = exp(x)-3x 2 = 0-8-6-4-2 2 4-1 1 2 3 4 f x-10 10 20 30 40 50-1 1 2 3 exp(x) 3*x^2 x Finding r 1 n x0 x1 f0 f1 x2 f2 |x n-x n-1 | 1-1 1-2.6321206-0.5-0.14347 2-0.5 1-0.1434693-0.25 0.591301 2.500E-01 3-0.5-0.25-0.1434693 0.59130078-0.375 0.265414 1.250E-01 4-0.5-0.375-0.1434693 0.26541428-0.4375 0.07143 6.250E-02 5-0.5-0.4375-0.1434693 0.07142978-0.46875-0.0334 3.125E-02 6-0.4375-0.46875 0.0714298-0.0333957-0.453125 0.019672 1.563E-02 7-0.46875-0.453125-0.0333957 0.01967188-0.4609375-0.0067 7.813E-03 8-0.453125-0.4609375 0.0196719-0.006698-0.45703125 0.006528 3.906E-03 9-0.4609375-0.4570313-0.006698 0.00652786-0.45898438-7.5E-05 1.953E-03 10-0.4570313-0.4589844 0.0065279-7.485E-05-0.45800781 0.003229 9.766E-04 11-0.4589844-0.4580078-7.485E-05 0.00322907-0.45849609 0.001578 4.883E-04 12-0.4589844-0.4584961-7.485E-05 0.00157775-0.45874023 0.000752 2.441E-04 13-0.4589844-0.4587402-7.485E-05 0.00075161-0.45886230 0.000338 1.221E-04 14-0.4589844-0.4588623-7.485E-05 0.00033842-0.45892334 0.000132 6.104E-05 15-0.4589844-0.4589233-7.485E-05 0.00013179-0.45895386 2.85E-05 3.052E-05 16-0.4589844-0.4589539-7.485E-05 2.8474E-05-0.45896912-2.3E-05 1.526E-05 17-0.4589539-0.4589691 2.847E-05-2.319E-05-0.45896149 2.64E-06 7.629E-06 Finding r 2 n x0 x1 f0 f1 x2 f2 |x n-x n-1 | 1 1 1-0.2817182 0.5 0.898721 2 1 0.5-0.2817182 0.89872127 0.75 0.4295 2.500E-01 3 1 0.75-0.2817182 0.42950002 0.875 0.102 1.250E-01 4 1 0.875-0.2817182 0.10200029 0.9375-0.08313 6.250E-02 5 0.875 0.9375 0.1020003-0.0831293 0.90625 0.011157 3.125E-02 6 0.9375 0.90625-0.0831293 0.01115658 0.921875-0.03556 1.563E-02 7 0.90625 0.921875 0.0111566-0.0355608 0.9140625-0.0121 7.813E-03 8 0.90625 0.9140625 0.0111566-0.0120951 0.91015625-0.00044 3.906E-03 9 0.90625 0.91015625 0.0111566-0.0004425 0.908203125 0.005364 1.953E-03 10 0.9101563 0.90820313-0.0004425 0.00536378 0.909179688 0.002462 9.766E-04 11 0.9101563 0.90917969-0.0004425 0.00246234 0.909667969 0.00101 4.883E-04 12 0.9101563 0.90966797-0.0004425 0.00101036 0.909912109 0.000284 2.441E-04 13 0.9101563 0.90991211-0.0004425 0.00028405 0.91003418-7.9E-05 1.221E-04 14 0.9099121 0.91003418 0.0002841-7.918E-05 0.909973145 0.000102 6.104E-05 15 0.9100342 0.90997314-7.918E-05 0.00010245 0.910003662 1.16E-05 3.052E-05 16 0.9100342 0.91000366-7.918E-05 1.1636E-05 0.910018921-3.4E-05 1.526E-05 17 0.9100037 0.91001892 1.164E-05-3.377E-05 0.910011292-1.1E-05 7.629E-06 Finding r 3 n x0 x1 f0 f1 x2 f2 |x n-x n-1 | 1 1 4-0.2817182 6.59815003 2.5-6.56751 2 4 2.5 6.59815-6.567506 3.25-5.89716 7.500E-01 3 4 3.25 6.59815-5.8971601 3.625-1.89715 3.750E-01 4 4 3.625 6.59815-1.8971518 3.8125 1.657987 1.875E-01 5 3.625 3.8125-1.8971518 1.65798743 3.71875-0.27446 9.375E-02 6 3.8125 3.71875 1.6579874-0.2744588 3.765625 0.650897 4.688E-02 7 3.71875 3.765625-0.2744588 0.65089669 3.7421875 0.178278 2.344E-02 8 3.71875 3.7421875-0.2744588 0.17827846 3.73046875-0.05054 1.172E-021....
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Solution to HW3_S09 - HW#3 EGM6341 Spring 2009 pp.117-127...

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