------------------------ TERMINATION CRITERIA ------------------------- EDU> eta1 = 100*sqrt(eps), eta2 = 10000*eps eta1 = 1.4901e-006 eta2 = 2.2204e-012 ------------------- MATLAB TRANSCRIPT FOR PART C(a) ------------------- EDU> fname = 'expo'; dfname = 'expod'; hfname = 'expoh'; x0 = 100; EDU> newton Pure Newton minimization of function "expo", using gradient "expod" and Hessian "expoh": k x_k(1) f(x_k) e_1 e_2 0 1.0000e+002 2.6881e+043 1 9.9000e+001 9.8890e+042 1.0000e-002 9.9000e+001 2 9.8000e+001 3.6380e+042 1.0101e-002 9.8000e+001 3 9.7000e+001 1.3383e+042 1.0204e-002 9.7000e+001 4 9.6000e+001 4.9235e+041 1.0309e-002 9.6000e+001 5 9.5000e+001 1.8112e+041 1.0417e-002 9.5000e+001 6 9.4000e+001 6.6632e+040 1.0526e-002 9.4000e+001 7 9.3000e+001 2.4512e+040 1.0638e-002 9.3000e+001 8 9.2000e+001 9.0176e+039 1.0753e-002 9.2000e+001 9 9.1000e+001 3.3174e+039 1.0870e-002 9.1000e+001 10 9.0000e+001 1.2204e+039 1.0989e-002 9.0000e+001 11 8.9000e+001 4.4896e+038 1.1111e-002 8.9000e+001 12 8.8000e+001 1.6516e+038 1.1236e-002 8.8000e+001 13 8.7000e+001 6.0760e+037 1.1364e-002 8.7000e+001 14 8.6000e+001 2.2352e+037 1.1494e-002 8.6000e+001 15 8.5000e+001 8.2230e+036 1.1628e-002 8.5000e+001 16 8.4000e+001 3.0251e+036 1.1765e-002 8.4000e+001 17 8.3000e+001 1.1129e+036 1.1905e-002 8.3000e+001 18 8.2000e+001 4.0940e+035 1.2048e-002 8.2000e+001 19 8.1000e+001 1.5061e+035 1.2195e-002 8.1000e+001 20 8.0000e+001 5.5406e+034 1.2346e-002 8.0000e+001 21 7.9000e+001 2.0383e+034 1.2500e-002 7.9000e+001 22 7.8000e+001 7.4984e+033 1.2658e-002 7.8000e+001 23 7.7000e+001 2.7585e+033 1.2821e-002 7.7000e+001 24 7.6000e+001 1.0148e+033 1.2987e-002 7.6000e+001 25 7.5000e+001 3.7332e+032 1.3158e-002 7.5000e+001 26 7.4000e+001 1.3734e+032 1.3333e-002 7.4000e+001 27 7.3000e+001 5.0524e+031 1.3514e-002 7.3000e+001 28 7.2000e+001 1.8587e+031 1.3699e-002 7.2000e+001 29 7.1000e+001 6.8377e+030 1.3889e-002 7.1000e+001 30 7.0000e+001 2.5154e+030 1.4085e-002 7.0000e+001 31 6.9000e+001 9.2538e+029 1.4286e-002 6.9000e+001 32 6.8000e+001 3.4043e+029 1.4493e-002 6.8000e+001 33 6.7000e+001 1.2524e+029 1.4706e-002 6.7000e+001 34 6.6000e+001 4.6072e+028 1.4925e-002 6.6000e+001 35 6.5000e+001 1.6949e+028 1.5152e-002 6.5000e+001 36 6.4000e+001 6.2351e+027 1.5385e-002 6.4000e+001 37 6.3000e+001 2.2938e+027 1.5625e-002 6.3000e+001 38 6.2000e+001 8.4384e+026 1.5873e-002 6.2000e+001 39 6.1000e+001 3.1043e+026 1.6129e-002 6.1000e+001 40 6.0000e+001 1.1420e+026 1.6393e-002 6.0000e+001 41 5.9000e+001 4.2012e+025 1.6667e-002 5.9000e+001 42 5.8000e+001 1.5455e+025 1.6949e-002 5.8000e+001 43 5.7000e+001 5.6857e+024 1.7241e-002 5.7000e+001 44 5.6000e+001 2.0917e+024 1.7544e-002 5.6000e+001 45 5.5000e+001 7.6948e+023 1.7857e-002 5.5000e+001 46 5.4000e+001 2.8308e+023 1.8182e-002 5.4000e+001 47 5.3000e+001 1.0414e+023 1.8519e-002 5.3000e+001 48 5.2000e+001 3.8310e+022 1.8868e-002 5.2000e+001 49 5.1000e+001 1.4093e+022 1.9231e-002 5.1000e+001 50 5.0000e+001 5.1847e+021 1.9608e-002 5.0000e+001 51 4.9000e+001 1.9073e+021 2.0000e-002 4.9000e+001 52 4.8000e+001 7.0167e+020 2.0408e-002 4.8000e+001 53 4.7000e+001 2.5813e+020 2.0833e-002 4.7000e+001 54 4.6000e+001 9.4961e+019 2.1277e-002 4.6000e+001 55 4.5000e+001 3.4934e+019 2.1739e-002 4.5000e+001 56 4.4000e+001 1.2852e+019 2.2222e-002 4.4000e+001 57 4.3000e+001 4.7278e+018 2.2727e-002 4.3000e+001 58 4.2000e+001 1.7393e+018 2.3256e-002 4.2000e+001 59 4.1000e+001 6.3984e+017 2.3810e-002 4.1000e+001 60 4.0000e+001 2.3539e+017 2.4390e-002 4.0000e+001 61 3.9000e+001 8.6593e+016 2.5000e-002 3.9000e+001 62 3.8000e+001 3.1856e+016 2.5641e-002 3.8000e+001 63 3.7000e+001 1.1719e+016 2.6316e-002 3.7000e+001 64 3.6000e+001 4.3112e+015 2.7027e-002 3.6000e+001 65 3.5000e+001 1.5860e+015 2.7778e-002 3.5000e+001 66 3.4000e+001 5.8346e+014 2.8571e-002 3.4000e+001 67 3.3000e+001 2.1464e+014 2.9412e-002 3.3000e+001 68 3.2000e+001 7.8963e+013 3.0303e-002 3.2000e+001 69 3.1000e+001 2.9049e+013 3.1250e-002 3.1000e+001 70 3.0000e+001 1.0686e+013 3.2258e-002 3.0000e+001 71 2.9000e+001 3.9313e+012 3.3333e-002 2.9000e+001 72 2.8000e+001 1.4463e+012 3.4483e-002 2.8000e+001 73 2.7000e+001 5.3205e+011 3.5714e-002 2.7000e+001 74 2.6000e+001 1.9573e+011 3.7037e-002 2.6000e+001 75 2.5000e+001 7.2005e+010 3.8462e-002 2.5000e+001 76 2.4000e+001 2.6489e+010 4.0000e-002 2.4000e+001 77 2.3000e+001 9.7448e+009 4.1667e-002 2.3000e+001 78 2.2000e+001 3.5849e+009 4.3478e-002 2.2000e+001 79 2.1000e+001 1.3188e+009 4.5455e-002 2.1000e+001 80 2.0000e+001 4.8517e+008 4.7619e-002 2.0000e+001 81 1.9000e+001 1.7848e+008 5.0000e-002 1.9000e+001 82 1.8000e+001 6.5660e+007 5.2632e-002 1.8000e+001 83 1.7000e+001 2.4155e+007 5.5556e-002 1.7000e+001 84 1.6000e+001 8.8861e+006 5.8824e-002 1.6000e+001 85 1.5000e+001 3.2690e+006 6.2500e-002 1.5000e+001 86 1.4000e+001 1.2026e+006 6.6667e-002 1.4000e+001 87 1.3000e+001 4.4238e+005 7.1428e-002 1.3001e+001 88 1.2000e+001 1.6272e+005 7.6923e-002 1.2002e+001 89 1.1000e+001 5.9847e+004 8.3332e-002 1.1005e+001 90 1.0000e+001 2.2002e+004 9.0905e-002 1.0011e+001 91 9.0002e+000 8.0812e+003 9.9987e-002 9.0233e+000 92 8.0005e+000 2.9618e+003 1.1107e-001 8.0492e+000 93 7.0014e+000 1.0802e+003 1.2488e-001 7.1007e+000 94 6.0039e+000 3.8969e+002 1.4247e-001 6.1981e+000 95 5.0106e+000 1.3738e+002 1.6544e-001 5.3718e+000 96 4.0288e+000 4.6239e+001 1.9596e-001 4.6589e+000 97 3.0771e+000 1.4331e+001 2.3621e-001 4.0747e+000 98 2.2024e+000 4.0601e+000 2.8426e-001 3.4330e+000 99 1.5029e+000 1.4094e+000 3.1762e-001 1.8942e+000 100 1.1077e+000 1.0163e+000 2.6297e-001 3.3678e-001 101 1.0056e+000 1.0000e+000 9.2152e-002 1.5332e-002 102 1.0000e+000 1.0000e+000 5.5470e-003 4.2448e-005 103 1.0000e+000 1.0000e+000 1.5615e-005 3.3141e-010 104 1.0000e+000 1.0000e+000 1.2192e-010 0.0000e+000 Best point: x' = 9.9999999999999980e-001. Minimum value: expo(x) = 1.0000000000000000e+000. Number of Newton steps: 104. Termination criterion: e1 < eta1 and e2 < eta2. Flop count: 1565 total--average 15 per step. ------------------- MATLAB TRANSCRIPT FOR PART C(b) ------------------- EDU> fname='hw02cb'; dfname='hw02cbd'; hfname='hw02cbh'; x0=[1;1]; EDU> newton Pure Newton minimization of function "hw02cb", using gradient "hw02cbd" and Hessian "hw02cbh": k x_k(1) x_k(2) f(x_k) e_1 e_2 0 1.0000e+000 1.0000e+000 7.0000e+000 1 1.0000e+000 -5.0000e-001 2.5000e+000 1.5000e+000 1.8000e+000 2 1.3913e+000 -6.9565e-001 1.4092e+000 3.9130e-001 1.4723e+000 3 1.7459e+000 -9.4880e-001 1.0649e+000 3.6390e-001 8.5749e-001 4 1.9863e+000 -1.0482e+000 1.0025e+000 1.3765e-001 1.0122e-001 5 1.9987e+000 -1.0002e+000 1.0000e+000 4.5829e-002 5.0617e-003 6 2.0000e+000 -1.0000e+000 1.0000e+000 6.3308e-004 3.2034e-006 7 2.0000e+000 -1.0000e+000 1.0000e+000 1.6017e-006 5.5653e-012 8 2.0000e+000 -1.0000e+000 1.0000e+000 6.9567e-013 0.0000e+000 Best point: x' = 2.0000000000000000e+000 -1.0000000000000000e+000. Minimum value: hw02cb(x) = 1.0000000000000000e+000. Number of Newton steps: 8. Termination criterion: e1 < eta1 and e2 < eta2. Flop count: 815 total--average 102 per step. ------------------- MATLAB TRANSCRIPT FOR PART C(c) ------------------- EDU> fname='banana'; dfname='bananad'; hfname='bananah'; x0=[-1.2;1]; EDU> newton Pure Newton minimization of function "banana", using gradient "bananad" and Hessian "bananah": k x_k(1) x_k(2) f(x_k) e_1 e_2 0 -1.2000e+000 1.0000e+000 2.5200e+001 1 -1.1753e+000 1.3807e+000 5.7319e+000 3.8067e-001 9.5095e-001 2 7.6311e-001 -3.1750e+000 1.4128e+003! 3.2996e+000 1.6888e+000 3 7.6343e-001 5.8282e-001 1.0560e+000 1.1836e+000 3.4204e-001 4 1.0000e+000 9.4403e-001 1.3132e+000! 6.1974e-001 1.7046e+001 5 1.0000e+000 9.9999e-001 1.0000e+000 5.9282e-002 8.6086e-006 6 1.0000e+000 1.0000e+000 1.0000e+000 8.6087e-006 7.4110e-009 7 1.0000e+000 1.0000e+000 1.0000e+000 1.8537e-011 1.2434e-014 Best point: x' = 9.9999999999999380e-001 9.9999999999998760e-001. Minimum value: banana(x) = 1.0000000000000000e+000. Number of Newton steps: 7. Termination criterion: e1 < eta1 and e2 < eta2. Flop count: 620 total--average 89 per step.