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Bisection method solved questions

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Sonia Pahuja

solutions of Laurence V. Fausett, Applied Numerical Analysis, Using MATLAB, Pearson,

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bisection_1 step a b m ym bound 1.0000 1.0000 2.0000 1.5000 0.2500 0.5000 2.0000 1.0000 1.5000 1.2500 -0.4375 0.2500 3.0000 1.2500 1.5000 1.3750 -0.1094 0.1250 4.0000 1.3750 1.5000 1.4375 0.0664 0.0625 5.0000 1.3750 1.4375 1.4063 -0.0225 0.0313 6.0000 1.4063 1.4375 1.4219 0.0217 0.0156 7.0000 1.4063 1.4219 1.4141 -0.0004 0.0078 zero not foundto desiredtolerence >> bisection_2 step a b m ym bound 1.0000 2.0000 3.0000 2.5000 1.2500 0.5000 2.0000 2.0000 2.5000 2.2500 0.0625 0.2500 3.0000 2.0000 2.2500 2.1250 -0.4844 0.1250 4.0000 2.1250 2.2500 2.1875 -0.2148 0.0625 5.0000 2.1875 2.2500 2.2188 -0.0771 0.0313 6.0000 2.2188 2.2500 2.2344 -0.0076 0.0156 7.0000 2.2344 2.2500 2.2422 0.0274 0.0078 8.0000 2.2344 2.2422 2.2383 0.0099 0.0039 zero not foundto desiredtolerence >>] bisection_3 step a b m ym bound 1.0000 2.0000 3.0000 2.5000 -0.7500 0.5000 2.0000 2.5000 3.0000 2.7500 0.5625 0.2500 3.0000 2.5000 2.7500 2.6250 -0.1094 0.1250 4.0000 2.6250 2.7500 2.6875 0.2227 0.0625
5.0000 2.6250 2.6875 2.6563 0.0557 0.0313 6.0000 2.6250 2.6563 2.6406 -0.0271 0.0156 zero not foundto desiredtolerence >>bisection_4 step a b m ym bound 1.0000 1.0000 2.0000 1.5000 0.3750 0.5000 2.0000 1.0000 1.5000 1.2500 -1.0469 0.2500 3.0000 1.2500 1.5000 1.3750 -0.4004 0.1250 4.0000 1.3750 1.5000 1.4375 -0.0295 0.0625 5.0000 1.4375 1.5000 1.4688 0.1684 0.0313 6.0000 1.4375 1.4688 1.4531 0.0684 0.0156 7.0000 1.4375 1.4531 1.4453 0.0192 0.0078 8.0000 1.4375 1.4453 1.4414 -0.0053 0.0039 9.0000 1.4414 1.4453 1.4434 0.0069 0.0020 10.0000 1.4414 1.4434 1.4424 0.0008 0.0010 zero not foundto desiredtolerence >> bisection_5 step a b m ym bound 1.0000 1.0000 2.0000 1.5000 -0.6250 0.5000 2.0000 1.5000 2.0000 1.7500 1.3594 0.2500 3.0000 1.5000 1.7500 1.6250 0.2910 0.1250 4.0000 1.5000 1.6250 1.5625 -0.1853 0.0625 5.0000 1.5625 1.6250 1.5938 0.0482 0.0313 6.0000 1.5625 1.5938 1.5781 -0.0697 0.0156 7.0000 1.5781 1.5938 1.5859 -0.0111 0.0078 zero not foundto desiredtolerance >> bisection_6
step a b m ym bound 1.0000 1.0000 2.0000 1.5000 -2.6250 0.5000 2.0000 1.5000 2.0000 1.7500 -0.6406 0.2500 3.0000 1.7500 2.0000 1.8750 0.5918 0.1250 4.0000 1.7500 1.8750 1.8125 -0.0457 0.0625 5.0000 1.8125 1.8750 1.8438 0.2677 0.0313 6.0000 1.8125 1.8438 1.8281 0.1097 0.0156 7.0000 1.8125 1.8281 1.8203 0.0317 0.0078 zero not foundto desiredtolerance >> bisection_7 step a b m ym bound 1.0000 0 1.0000 0.5000 -0.3875 0.5000 2.0000 0.5000 1.0000 0.7500 -0.1336 0.2500 3.0000 0.7500 1.0000 0.8750 0.1362 0.1250 4.0000 0.7500 0.8750 0.8125 -0.0142 0.0625 5.0000 0.8125 0.8750 0.8438 0.0568 0.0313 6.0000 0.8125 0.8438 0.8281 0.0203 0.0156 7.0000 0.8125 0.8281 0.8203 0.0028 0.0078 zero not foundto desiredtolerence >> bisection_8 step a b m ym bound 1.0000 0 1.0000 0.5000 -0.5875 0.5000 2.0000 0.5000 1.0000 0.7500 -0.3336 0.2500 3.0000 0.7500 1.0000 0.8750 -0.0638 0.1250 4.0000 0.8750 1.0000 0.9375 0.1225 0.0625 5.0000 0.8750 0.9375 0.9063 0.0245 0.0313 6.0000 0.8750 0.9063 0.8906 -0.0208 0.0156
7.0000 0.8906 0.9063 0.8984 0.0016 0.0078 zero not foundto desired tolerance bisection_9 step a b m ym bound 1.0000 0 1.0000 0.5000 0.0025 0.5000 2.0000 0 0.5000 0.2500 -0.0561 0.2500 3.0000 0.2500 0.5000 0.3750 -0.0402 0.1250 4.0000 0.3750 0.5000 0.4375 -0.0234 0.0625 5.0000 0.4375 0.5000 0.4688 -0.0117 0.0313 6.0000 0.4688 0.5000 0.4844 -0.0050 0.0156 7.0000 0.4844 0.5000 0.4922 -0.0013 0.0078 zero not foundto desiredtolerence >> bisection_10 step a b m ym bound 1.0000 0 1.0000 0.5000 -0.1875 0.5000 2.0000 0.5000 1.0000 0.7500 0.0664 0.2500 3.0000 0.5000 0.7500 0.6250 -0.0974 0.1250 4.0000 0.6250 0.7500 0.6875 -0.0266 0.0625 5.0000 0.6875 0.7500 0.7188 0.0169 0.0313 6.0000 0.6875 0.7188 0.7031 -0.0056 0.0156 7.0000 0.7031 0.7188 0.7109 0.0055 0.0078 zero not foundto desiredtolerence >> bisection_11 step a b m ym bound 1.0000 0 1.0000 0.5000 -2.3750 0.5000 2.0000 0 0.5000 0.2500 -0.2344 0.2500 3.0000 0 0.2500 0.1250 0.8770 0.1250
4.0000 0.1250 0.2500 0.1875 0.3191 0.0625 5.0000 0.1875 0.2500 0.2188 0.0417 0.0313 6.0000 0.2188 0.2500 0.2344 -0.0965 0.0156 7.0000 0.2188 0.2344 0.2266 -0.0274 0.0078 8.0000 0.2188 0.2266 0.2227 0.0071 0.0039 9.0000 0.2227 0.2266 0.2246 -0.0102 0.0020 10.0000 0.2227 0.2246 0.2236 -0.0015 0.0010 zero not foundto desiredtolerence >> bisection_11 step a b m ym bound 1.0000 2.0000 3.0000 2.5000 -4.8750 0.5000 2.0000 2.5000 3.0000 2.7500 -1.9531 0.2500 3.0000 2.7500 3.0000 2.8750 -0.1113 0.1250 4.0000 2.8750 3.0000 2.9375 0.9099 0.0625 5.0000 2.8750 2.9375 2.9063 0.3908 0.0313 6.0000 2.8750 2.9063 2.8906 0.1376 0.0156 7.0000 2.8750 2.8906 2.8828 0.0126 0.0078 8.0000 2.8750 2.8828 2.8789 -0.0495 0.0039 9.0000 2.8789 2.8828 2.8809 -0.0185 0.0020 10.0000 2.8809 2.8828 2.8818 -0.0029 0.0010 zero not foundto desired tolerance bisection_11 step a b m ym bound 1.0000 -3.0000 -4.0000 -3.5000 -9.3750 -0.5000 2.0000 -3.0000 -3.5000 -3.2500 -3.0781 -0.2500 3.0000 -3.0000 -3.2500 -3.1250 -0.3926 -0.1250 4.0000 -3.0000 -3.1250 -3.0625 0.8396 -0.0625
5.0000 -3.0625 -3.1250 -3.0938 0.2326 -0.0313 6.0000 -3.0938 -3.1250 -3.1094 -0.0777 -0.0156 7.0000 -3.0938 -3.1094 -3.1016 0.0780 -0.0078 8.0000 -3.1016 -3.1094 -3.1055 0.0003 -0.0039 zero not foundto desired tolerance bisection_12 one real and2 imaginary roots step a b m ym bound 1.0000 2.0000 3.0000 2.5000 -1.8750 0.5000 2.0000 2.5000 3.0000 2.7500 0.6719 0.2500 3.0000 2.5000 2.7500 2.6250 -0.6934 0.1250 4.0000 2.6250 2.7500 2.6875 -0.0344 0.0625 5.0000 2.6875 2.7500 2.7188 0.3127 0.0313 6.0000 2.6875 2.7188 2.7031 0.1377 0.0156 7.0000 2.6875 2.7031 2.6953 0.0512 0.0078 8.0000 2.6875 2.6953 2.6914 0.0083 0.0039 9.0000 2.6875 2.6914 2.6895 -0.0131 0.0020 10.0000 2.6895 2.6914 2.6904 -0.0024 0.0010 zero not foundto desiredtolerence >> bisection_13 step a b m ym bound 1.0000 0 1.0000 0.5000 -0.1250 0.5000 2.0000 0.5000 1.0000 0.7500 1.1094 0.2500 3.0000 0.5000 0.7500 0.6250 0.4160 0.1250 4.0000 0.5000 0.6250 0.5625 0.1272 0.0625 5.0000 0.5000 0.5625 0.5313 -0.0034 0.0313 6.0000 0.5313 0.5625 0.5469 0.0608 0.0156 7.0000 0.5313 0.5469 0.5391 0.0284 0.0078
8.0000 0.5313 0.5391 0.5352 0.0124 0.0039 9.0000 0.5313 0.5352 0.5332 0.0045 0.0020 10.0000 0.5313 0.5332 0.5322 0.0006 0.0010 zero not foundto desiredtolerence >> bisection_13 step a b m ym bound 1.0000 0 -1.0000 -0.5000 -0.3750 -0.5000 2.0000 -0.5000 -1.0000 -0.7500 0.2656 -0.2500 3.0000 -0.5000 -0.7500 -0.6250 -0.0723 -0.1250 4.0000 -0.6250 -0.7500 -0.6875 0.0930 -0.0625 5.0000 -0.6250 -0.6875 -0.6563 0.0094 -0.0313 6.0000 -0.6250 -0.6563 -0.6406 -0.0317 -0.0156 7.0000 -0.6406 -0.6563 -0.6484 -0.0112 -0.0078 8.0000 -0.6484 -0.6563 -0.6523 -0.0009 -0.0039 9.0000 -0.6523 -0.6563 -0.6543 0.0042 -0.0020 10.0000 -0.6523 -0.6543 -0.6533 0.0016 -0.0010 bisection_13 step a b m ym bound 1.0000 -2.0000 -3.0000 -2.5000 2.1250 -0.5000 2.0000 -2.5000 -3.0000 -2.7500 0.8906 -0.2500 3.0000 -2.7500 -3.0000 -2.8750 0.0332 -0.1250 4.0000 -2.8750 -3.0000 -2.9375 -0.4607 -0.0625 5.0000 -2.8750 -2.9375 -2.9063 -0.2082 -0.0313 6.0000 -2.8750 -2.9063 -2.8906 -0.0861 -0.0156 7.0000 -2.8750 -2.8906 -2.8828 -0.0261 -0.0078 8.0000 -2.8750 -2.8828 -2.8789 0.0036 -0.0039 9.0000 -2.8789 -2.8828 -2.8809 -0.0112 -0.0020 10.0000 -2.8789 -2.8809 -2.8799 -0.0038 -0.0010
zero not foundto desired tolerance bisection_14 step a b m ym bound 1.0000 0 1.0000 0.5000 -0.8750 0.5000 2.0000 0 0.5000 0.2500 0.0156 0.2500 3.0000 0.2500 0.5000 0.3750 -0.4473 0.1250 4.0000 0.2500 0.3750 0.3125 -0.2195 0.0625 5.0000 0.2500 0.3125 0.2813 -0.1028 0.0313 6.0000 0.2500 0.2813 0.2656 -0.0438 0.0156 7.0000 0.2500 0.2656 0.2578 -0.0141 0.0078 8.0000 0.2500 0.2578 0.2539 0.0007 0.0039 9.0000 0.2539 0.2578 0.2559 -0.0067 0.0020 10.0000 0.2539 0.2559 0.2549 -0.0030 0.0010 zero not foundto desiredtolerence >> bisection_14 step a b m ym bound 1.0000 1.0000 2.0000 1.5000 -1.6250 0.5000 2.0000 1.5000 2.0000 1.7500 -0.6406 0.2500 3.0000 1.7500 2.0000 1.8750 0.0918 0.1250 4.0000 1.7500 1.8750 1.8125 -0.2957 0.0625 5.0000 1.8125 1.8750 1.8438 -0.1073 0.0313 6.0000 1.8438 1.8750 1.8594 -0.0091 0.0156 7.0000 1.8594 1.8750 1.8672 0.0410 0.0078 8.0000 1.8594 1.8672 1.8633 0.0158 0.0039 9.0000 1.8594 1.8633 1.8613 0.0033 0.0020 10.0000 1.8594 1.8613 1.8604 -0.0029 0.0010 zero not foundto desired tolerance
bisection_14 step a b m ym bound 1.0000 -2.0000 -3.0000 -2.5000 -4.6250 -0.5000 2.0000 -2.0000 -2.5000 -2.2500 -1.3906 -0.2500 3.0000 -2.0000 -2.2500 -2.1250 -0.0957 -0.1250 4.0000 -2.0000 -2.1250 -2.0625 0.4763 -0.0625 5.0000 -2.0625 -2.1250 -2.0938 0.1964 -0.0313 6.0000 -2.0938 -2.1250 -2.1094 0.0519 -0.0156 7.0000 -2.1094 -2.1250 -2.1172 -0.0215 -0.0078 8.0000 -2.1094 -2.1172 -2.1133 0.0153 -0.0039 9.0000 -2.1133 -2.1172 -2.1152 -0.0031 -0.0020 10.0000 -2.1133 -2.1152 -2.1143 0.0061 -0.0010 zero not foundto desiredtolerence >> bisection_15 step a b m ym bound 1.0000 2.0000 3.0000 2.5000 -3.6250 0.5000 2.0000 2.5000 3.0000 2.7500 -0.7656 0.2500 3.0000 2.7500 3.0000 2.8750 0.9980 0.1250 4.0000 2.7500 2.8750 2.8125 0.0872 0.0625 5.0000 2.7500 2.8125 2.7813 -0.3464 0.0313 6.0000 2.7813 2.8125 2.7969 -0.1314 0.0156 7.0000 2.7969 2.8125 2.8047 -0.0226 0.0078 8.0000 2.8047 2.8125 2.8086 0.0322 0.0039 9.0000 2.8047 2.8086 2.8066 0.0048 0.0020 10.0000 2.8047 2.8066 2.8057 -0.0089 0.0010
zero not foundto desired tolerance bisection_16 step a b m ym bound 1.0000 0 1.0000 0.5000 -0.8750 0.5000 2.0000 0.5000 1.0000 0.7500 0.2969 0.2500 3.0000 0.5000 0.7500 0.6250 -0.2246 0.1250 4.0000 0.6250 0.7500 0.6875 0.0515 0.0625 5.0000 0.6250 0.6875 0.6563 -0.0826 0.0313 6.0000 0.6563 0.6875 0.6719 -0.0146 0.0156 7.0000 0.6719 0.6875 0.6797 0.0187 0.0078 8.0000 0.6719 0.6797 0.6758 0.0021 0.0039 9.0000 0.6719 0.6758 0.6738 -0.0062 0.0020 10.0000 0.6738 0.6758 0.6748 -0.0020 0.0010 zero not foundto desiredtolerence >> bisection_17 step a b m ym bound 1.0000 1.0000 2.0000 1.5000 -1.5000 0.5000 2.0000 1.0000 1.5000 1.2500 0.7813 0.2500 3.0000 1.2500 1.5000 1.3750 -0.3867 0.1250 4.0000 1.2500 1.3750 1.3125 0.1948 0.0625 5.0000 1.3125 1.3750 1.3438 -0.0971 0.0313 6.0000 1.3125 1.3438 1.3281 0.0486 0.0156 7.0000 1.3281 1.3438 1.3359 -0.0243 0.0078 8.0000 1.3281 1.3359 1.3320 0.0122 0.0039 9.0000 1.3320 1.3359 1.3340 -0.0061 0.0020 10.0000 1.3320 1.3340 1.3330 0.0030 0.0010
zero not foundto desiredtolerence >> bisection_17 step a b m ym bound 1.0000 2.0000 3.0000 2.5000 0 0.5000 bisectionhas converged bisection_17 0 bisection_18 step a b m ym bound 1.0000 0 1.0000 0.5000 -2.8750 0.5000 2.0000 0 0.5000 0.2500 1.4844 0.2500 3.0000 0.2500 0.5000 0.3750 -0.7324 0.1250 4.0000 0.2500 0.3750 0.3125 0.3689 0.0625 5.0000 0.3125 0.3750 0.3438 -0.1838 0.0313 6.0000 0.3125 0.3438 0.3281 0.0921 0.0156 7.0000 0.3281 0.3438 0.3359 -0.0460 0.0078 8.0000 0.3281 0.3359 0.3320 0.0230 0.0039 9.0000 0.3320 0.3359 0.3340 -0.0115 0.0020 10.0000 0.3320 0.3340 0.3330 0.0058 0.0010 zero not foundto desiredtolerence >> bisection_18 step a b m ym bound 1.0000 0 1.0000 0.5000 -2.8750 0.5000 2.0000 0 0.5000 0.2500 1.4844 0.2500 3.0000 0.2500 0.5000 0.3750 -0.7324 0.1250 4.0000 0.2500 0.3750 0.3125 0.3689 0.0625
5.0000 0.3125 0.3750 0.3438 -0.1838 0.0313 6.0000 0.3125 0.3438 0.3281 0.0921 0.0156 7.0000 0.3281 0.3438 0.3359 -0.0460 0.0078 8.0000 0.3281 0.3359 0.3320 0.0230 0.0039 9.0000 0.3320 0.3359 0.3340 -0.0115 0.0020 10.0000 0.3320 0.3340 0.3330 0.0058 0.0010 zero not foundto desiredtolerance bisection_18 step a b m ym bound 1.0000 -2.0000 -3.0000 -2.5000 -2.1250 -0.5000 2.0000 -2.0000 -2.5000 -2.2500 7.2656 -0.2500 3.0000 -2.2500 -2.5000 -2.3750 2.9199 -0.1250 4.0000 -2.3750 -2.5000 -2.4375 0.4871 -0.0625 5.0000 -2.4375 -2.5000 -2.4688 -0.7963 -0.0313 6.0000 -2.4375 -2.4688 -2.4531 -0.1490 -0.0156 7.0000 -2.4375 -2.4531 -2.4453 0.1704 -0.0078 8.0000 -2.4453 -2.4531 -2.4492 0.0111 -0.0039 9.0000 -2.4492 -2.4531 -2.4512 -0.0689 -0.0020 10.0000 -2.4492 -2.4512 -2.4502 -0.0289 -0.0010 zero not foundto desired tolerance bisection_18 step a b m ym bound 1.0000 2.0000 3.0000 2.5000 1.6250 0.5000 2.0000 2.0000 2.5000 2.2500 -5.3906 0.2500 3.0000 2.2500 2.5000 2.3750 -2.2012 0.1250 4.0000 2.3750 2.5000 2.4375 -0.3699 0.0625 5.0000 2.4375 2.5000 2.4688 0.6068 0.0313
6.0000 2.4375 2.4688 2.4531 0.1133 0.0156 7.0000 2.4375 2.4531 2.4453 -0.1295 0.0078 8.0000 2.4453 2.4531 2.4492 -0.0084 0.0039 9.0000 2.4492 2.4531 2.4512 0.0524 0.0020 10.0000 2.4492 2.4512 2.4502 0.0220 0.0010 zero not foundto desiredtolerence >> bisection_19 step a b m ym bound 1.0000 -1.0000 -2.0000 -1.5000 -1.6250 -0.5000 2.0000 -1.5000 -2.0000 -1.7500 1.5781 -0.2500 3.0000 -1.5000 -1.7500 -1.6250 0.0684 -0.1250 4.0000 -1.5000 -1.6250 -1.5625 -0.7561 -0.0625 5.0000 -1.5625 -1.6250 -1.5938 -0.3382 -0.0313 6.0000 -1.5938 -1.6250 -1.6094 -0.1335 -0.0156 7.0000 -1.6094 -1.6250 -1.6172 -0.0322 -0.0078 8.0000 -1.6172 -1.6250 -1.6211 0.0182 -0.0039 9.0000 -1.6172 -1.6211 -1.6191 -0.0070 -0.0020 10.0000 -1.6191 -1.6211 -1.6201 0.0056 -0.0010 zero not foundto desiredtolerence >> bisection_19 step a b m ym bound 1.0000 5.0000 6.0000 5.5000 -27.8750 0.5000 2.0000 5.5000 6.0000 5.7500 -12.9531 0.2500 3.0000 5.7500 6.0000 5.8750 -4.7363 0.1250 4.0000 5.8750 6.0000 5.9375 -0.4338 0.0625 5.0000 5.9375 6.0000 5.9688 1.7666 0.0313
6.0000 5.9375 5.9688 5.9531 0.6623 0.0156 7.0000 5.9375 5.9531 5.9453 0.1132 0.0078 8.0000 5.9375 5.9453 5.9414 -0.1606 0.0039 9.0000 5.9414 5.9453 5.9434 -0.0238 0.0020 10.0000 5.9434 5.9453 5.9443 0.0447 0.0010 zero not foundto desiredtolerence >> bisection_19 step a b m ym bound 1.0000 -3.0000 -4.0000 -3.5000 -3.1250 -0.5000 2.0000 -3.0000 -3.5000 -3.2500 1.1094 -0.2500 3.0000 -3.2500 -3.5000 -3.3750 -0.8340 -0.1250 4.0000 -3.2500 -3.3750 -3.3125 0.1804 -0.0625 5.0000 -3.3125 -3.3750 -3.3438 -0.3160 -0.0313 6.0000 -3.3125 -3.3438 -3.3281 -0.0651 -0.0156 7.0000 -3.3125 -3.3281 -3.3203 0.0583 -0.0078 8.0000 -3.3203 -3.3281 -3.3242 -0.0032 -0.0039 9.0000 -3.3203 -3.3242 -3.3223 0.0276 -0.0020 10.0000 -3.3223 -3.3242 -3.3232 0.0122 -0.0010 zero not foundto desiredtolerence >> bisection_20 step a b m ym bound 1.0000 3.0000 4.0000 3.5000 -0.8750 0.5000 2.0000 3.5000 4.0000 3.7500 -0.2031 0.2500 3.0000 3.7500 4.0000 3.8750 0.3262 0.1250 4.0000 3.7500 3.8750 3.8125 0.0442 0.0625 5.0000 3.7500 3.8125 3.7813 -0.0837 0.0313 6.0000 3.7813 3.8125 3.7969 -0.0208 0.0156
7.0000 3.7969 3.8125 3.8047 0.0114 0.0078 8.0000 3.7969 3.8047 3.8008 -0.0048 0.0039 9.0000 3.8008 3.8047 3.8027 0.0033 0.0020 10.0000 3.8008 3.8027 3.8018 -0.0007 0.0010 zero not foundto desiredtolerence >> bisection_20 step a b m ym bound 1.0000 0 1.0000 0.5000 -1.6250 0.5000 2.0000 0.5000 1.0000 0.7500 -0.0156 0.2500 3.0000 0.7500 1.0000 0.8750 0.5605 0.1250 4.0000 0.7500 0.8750 0.8125 0.2903 0.0625 5.0000 0.7500 0.8125 0.7813 0.1419 0.0313 6.0000 0.7500 0.7813 0.7656 0.0643 0.0156 7.0000 0.7500 0.7656 0.7578 0.0246 0.0078 8.0000 0.7500 0.7578 0.7539 0.0046 0.0039 9.0000 0.7500 0.7539 0.7520 -0.0055 0.0020 10.0000 0.7520 0.7539 0.7529 -0.0005 0.0010 zero not foundto desiredtolerence >>

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Bisection method solved questions

  • 1. bisection_1 step a b m ym bound 1.0000 1.0000 2.0000 1.5000 0.2500 0.5000 2.0000 1.0000 1.5000 1.2500 -0.4375 0.2500 3.0000 1.2500 1.5000 1.3750 -0.1094 0.1250 4.0000 1.3750 1.5000 1.4375 0.0664 0.0625 5.0000 1.3750 1.4375 1.4063 -0.0225 0.0313 6.0000 1.4063 1.4375 1.4219 0.0217 0.0156 7.0000 1.4063 1.4219 1.4141 -0.0004 0.0078 zero not foundto desiredtolerence >> bisection_2 step a b m ym bound 1.0000 2.0000 3.0000 2.5000 1.2500 0.5000 2.0000 2.0000 2.5000 2.2500 0.0625 0.2500 3.0000 2.0000 2.2500 2.1250 -0.4844 0.1250 4.0000 2.1250 2.2500 2.1875 -0.2148 0.0625 5.0000 2.1875 2.2500 2.2188 -0.0771 0.0313 6.0000 2.2188 2.2500 2.2344 -0.0076 0.0156 7.0000 2.2344 2.2500 2.2422 0.0274 0.0078 8.0000 2.2344 2.2422 2.2383 0.0099 0.0039 zero not foundto desiredtolerence >>] bisection_3 step a b m ym bound 1.0000 2.0000 3.0000 2.5000 -0.7500 0.5000 2.0000 2.5000 3.0000 2.7500 0.5625 0.2500 3.0000 2.5000 2.7500 2.6250 -0.1094 0.1250 4.0000 2.6250 2.7500 2.6875 0.2227 0.0625
  • 2. 5.0000 2.6250 2.6875 2.6563 0.0557 0.0313 6.0000 2.6250 2.6563 2.6406 -0.0271 0.0156 zero not foundto desiredtolerence >>bisection_4 step a b m ym bound 1.0000 1.0000 2.0000 1.5000 0.3750 0.5000 2.0000 1.0000 1.5000 1.2500 -1.0469 0.2500 3.0000 1.2500 1.5000 1.3750 -0.4004 0.1250 4.0000 1.3750 1.5000 1.4375 -0.0295 0.0625 5.0000 1.4375 1.5000 1.4688 0.1684 0.0313 6.0000 1.4375 1.4688 1.4531 0.0684 0.0156 7.0000 1.4375 1.4531 1.4453 0.0192 0.0078 8.0000 1.4375 1.4453 1.4414 -0.0053 0.0039 9.0000 1.4414 1.4453 1.4434 0.0069 0.0020 10.0000 1.4414 1.4434 1.4424 0.0008 0.0010 zero not foundto desiredtolerence >> bisection_5 step a b m ym bound 1.0000 1.0000 2.0000 1.5000 -0.6250 0.5000 2.0000 1.5000 2.0000 1.7500 1.3594 0.2500 3.0000 1.5000 1.7500 1.6250 0.2910 0.1250 4.0000 1.5000 1.6250 1.5625 -0.1853 0.0625 5.0000 1.5625 1.6250 1.5938 0.0482 0.0313 6.0000 1.5625 1.5938 1.5781 -0.0697 0.0156 7.0000 1.5781 1.5938 1.5859 -0.0111 0.0078 zero not foundto desiredtolerance >> bisection_6
  • 3. step a b m ym bound 1.0000 1.0000 2.0000 1.5000 -2.6250 0.5000 2.0000 1.5000 2.0000 1.7500 -0.6406 0.2500 3.0000 1.7500 2.0000 1.8750 0.5918 0.1250 4.0000 1.7500 1.8750 1.8125 -0.0457 0.0625 5.0000 1.8125 1.8750 1.8438 0.2677 0.0313 6.0000 1.8125 1.8438 1.8281 0.1097 0.0156 7.0000 1.8125 1.8281 1.8203 0.0317 0.0078 zero not foundto desiredtolerance >> bisection_7 step a b m ym bound 1.0000 0 1.0000 0.5000 -0.3875 0.5000 2.0000 0.5000 1.0000 0.7500 -0.1336 0.2500 3.0000 0.7500 1.0000 0.8750 0.1362 0.1250 4.0000 0.7500 0.8750 0.8125 -0.0142 0.0625 5.0000 0.8125 0.8750 0.8438 0.0568 0.0313 6.0000 0.8125 0.8438 0.8281 0.0203 0.0156 7.0000 0.8125 0.8281 0.8203 0.0028 0.0078 zero not foundto desiredtolerence >> bisection_8 step a b m ym bound 1.0000 0 1.0000 0.5000 -0.5875 0.5000 2.0000 0.5000 1.0000 0.7500 -0.3336 0.2500 3.0000 0.7500 1.0000 0.8750 -0.0638 0.1250 4.0000 0.8750 1.0000 0.9375 0.1225 0.0625 5.0000 0.8750 0.9375 0.9063 0.0245 0.0313 6.0000 0.8750 0.9063 0.8906 -0.0208 0.0156
  • 4. 7.0000 0.8906 0.9063 0.8984 0.0016 0.0078 zero not foundto desired tolerance bisection_9 step a b m ym bound 1.0000 0 1.0000 0.5000 0.0025 0.5000 2.0000 0 0.5000 0.2500 -0.0561 0.2500 3.0000 0.2500 0.5000 0.3750 -0.0402 0.1250 4.0000 0.3750 0.5000 0.4375 -0.0234 0.0625 5.0000 0.4375 0.5000 0.4688 -0.0117 0.0313 6.0000 0.4688 0.5000 0.4844 -0.0050 0.0156 7.0000 0.4844 0.5000 0.4922 -0.0013 0.0078 zero not foundto desiredtolerence >> bisection_10 step a b m ym bound 1.0000 0 1.0000 0.5000 -0.1875 0.5000 2.0000 0.5000 1.0000 0.7500 0.0664 0.2500 3.0000 0.5000 0.7500 0.6250 -0.0974 0.1250 4.0000 0.6250 0.7500 0.6875 -0.0266 0.0625 5.0000 0.6875 0.7500 0.7188 0.0169 0.0313 6.0000 0.6875 0.7188 0.7031 -0.0056 0.0156 7.0000 0.7031 0.7188 0.7109 0.0055 0.0078 zero not foundto desiredtolerence >> bisection_11 step a b m ym bound 1.0000 0 1.0000 0.5000 -2.3750 0.5000 2.0000 0 0.5000 0.2500 -0.2344 0.2500 3.0000 0 0.2500 0.1250 0.8770 0.1250
  • 5. 4.0000 0.1250 0.2500 0.1875 0.3191 0.0625 5.0000 0.1875 0.2500 0.2188 0.0417 0.0313 6.0000 0.2188 0.2500 0.2344 -0.0965 0.0156 7.0000 0.2188 0.2344 0.2266 -0.0274 0.0078 8.0000 0.2188 0.2266 0.2227 0.0071 0.0039 9.0000 0.2227 0.2266 0.2246 -0.0102 0.0020 10.0000 0.2227 0.2246 0.2236 -0.0015 0.0010 zero not foundto desiredtolerence >> bisection_11 step a b m ym bound 1.0000 2.0000 3.0000 2.5000 -4.8750 0.5000 2.0000 2.5000 3.0000 2.7500 -1.9531 0.2500 3.0000 2.7500 3.0000 2.8750 -0.1113 0.1250 4.0000 2.8750 3.0000 2.9375 0.9099 0.0625 5.0000 2.8750 2.9375 2.9063 0.3908 0.0313 6.0000 2.8750 2.9063 2.8906 0.1376 0.0156 7.0000 2.8750 2.8906 2.8828 0.0126 0.0078 8.0000 2.8750 2.8828 2.8789 -0.0495 0.0039 9.0000 2.8789 2.8828 2.8809 -0.0185 0.0020 10.0000 2.8809 2.8828 2.8818 -0.0029 0.0010 zero not foundto desired tolerance bisection_11 step a b m ym bound 1.0000 -3.0000 -4.0000 -3.5000 -9.3750 -0.5000 2.0000 -3.0000 -3.5000 -3.2500 -3.0781 -0.2500 3.0000 -3.0000 -3.2500 -3.1250 -0.3926 -0.1250 4.0000 -3.0000 -3.1250 -3.0625 0.8396 -0.0625
  • 6. 5.0000 -3.0625 -3.1250 -3.0938 0.2326 -0.0313 6.0000 -3.0938 -3.1250 -3.1094 -0.0777 -0.0156 7.0000 -3.0938 -3.1094 -3.1016 0.0780 -0.0078 8.0000 -3.1016 -3.1094 -3.1055 0.0003 -0.0039 zero not foundto desired tolerance bisection_12 one real and2 imaginary roots step a b m ym bound 1.0000 2.0000 3.0000 2.5000 -1.8750 0.5000 2.0000 2.5000 3.0000 2.7500 0.6719 0.2500 3.0000 2.5000 2.7500 2.6250 -0.6934 0.1250 4.0000 2.6250 2.7500 2.6875 -0.0344 0.0625 5.0000 2.6875 2.7500 2.7188 0.3127 0.0313 6.0000 2.6875 2.7188 2.7031 0.1377 0.0156 7.0000 2.6875 2.7031 2.6953 0.0512 0.0078 8.0000 2.6875 2.6953 2.6914 0.0083 0.0039 9.0000 2.6875 2.6914 2.6895 -0.0131 0.0020 10.0000 2.6895 2.6914 2.6904 -0.0024 0.0010 zero not foundto desiredtolerence >> bisection_13 step a b m ym bound 1.0000 0 1.0000 0.5000 -0.1250 0.5000 2.0000 0.5000 1.0000 0.7500 1.1094 0.2500 3.0000 0.5000 0.7500 0.6250 0.4160 0.1250 4.0000 0.5000 0.6250 0.5625 0.1272 0.0625 5.0000 0.5000 0.5625 0.5313 -0.0034 0.0313 6.0000 0.5313 0.5625 0.5469 0.0608 0.0156 7.0000 0.5313 0.5469 0.5391 0.0284 0.0078
  • 7. 8.0000 0.5313 0.5391 0.5352 0.0124 0.0039 9.0000 0.5313 0.5352 0.5332 0.0045 0.0020 10.0000 0.5313 0.5332 0.5322 0.0006 0.0010 zero not foundto desiredtolerence >> bisection_13 step a b m ym bound 1.0000 0 -1.0000 -0.5000 -0.3750 -0.5000 2.0000 -0.5000 -1.0000 -0.7500 0.2656 -0.2500 3.0000 -0.5000 -0.7500 -0.6250 -0.0723 -0.1250 4.0000 -0.6250 -0.7500 -0.6875 0.0930 -0.0625 5.0000 -0.6250 -0.6875 -0.6563 0.0094 -0.0313 6.0000 -0.6250 -0.6563 -0.6406 -0.0317 -0.0156 7.0000 -0.6406 -0.6563 -0.6484 -0.0112 -0.0078 8.0000 -0.6484 -0.6563 -0.6523 -0.0009 -0.0039 9.0000 -0.6523 -0.6563 -0.6543 0.0042 -0.0020 10.0000 -0.6523 -0.6543 -0.6533 0.0016 -0.0010 bisection_13 step a b m ym bound 1.0000 -2.0000 -3.0000 -2.5000 2.1250 -0.5000 2.0000 -2.5000 -3.0000 -2.7500 0.8906 -0.2500 3.0000 -2.7500 -3.0000 -2.8750 0.0332 -0.1250 4.0000 -2.8750 -3.0000 -2.9375 -0.4607 -0.0625 5.0000 -2.8750 -2.9375 -2.9063 -0.2082 -0.0313 6.0000 -2.8750 -2.9063 -2.8906 -0.0861 -0.0156 7.0000 -2.8750 -2.8906 -2.8828 -0.0261 -0.0078 8.0000 -2.8750 -2.8828 -2.8789 0.0036 -0.0039 9.0000 -2.8789 -2.8828 -2.8809 -0.0112 -0.0020 10.0000 -2.8789 -2.8809 -2.8799 -0.0038 -0.0010
  • 8. zero not foundto desired tolerance bisection_14 step a b m ym bound 1.0000 0 1.0000 0.5000 -0.8750 0.5000 2.0000 0 0.5000 0.2500 0.0156 0.2500 3.0000 0.2500 0.5000 0.3750 -0.4473 0.1250 4.0000 0.2500 0.3750 0.3125 -0.2195 0.0625 5.0000 0.2500 0.3125 0.2813 -0.1028 0.0313 6.0000 0.2500 0.2813 0.2656 -0.0438 0.0156 7.0000 0.2500 0.2656 0.2578 -0.0141 0.0078 8.0000 0.2500 0.2578 0.2539 0.0007 0.0039 9.0000 0.2539 0.2578 0.2559 -0.0067 0.0020 10.0000 0.2539 0.2559 0.2549 -0.0030 0.0010 zero not foundto desiredtolerence >> bisection_14 step a b m ym bound 1.0000 1.0000 2.0000 1.5000 -1.6250 0.5000 2.0000 1.5000 2.0000 1.7500 -0.6406 0.2500 3.0000 1.7500 2.0000 1.8750 0.0918 0.1250 4.0000 1.7500 1.8750 1.8125 -0.2957 0.0625 5.0000 1.8125 1.8750 1.8438 -0.1073 0.0313 6.0000 1.8438 1.8750 1.8594 -0.0091 0.0156 7.0000 1.8594 1.8750 1.8672 0.0410 0.0078 8.0000 1.8594 1.8672 1.8633 0.0158 0.0039 9.0000 1.8594 1.8633 1.8613 0.0033 0.0020 10.0000 1.8594 1.8613 1.8604 -0.0029 0.0010 zero not foundto desired tolerance
  • 9. bisection_14 step a b m ym bound 1.0000 -2.0000 -3.0000 -2.5000 -4.6250 -0.5000 2.0000 -2.0000 -2.5000 -2.2500 -1.3906 -0.2500 3.0000 -2.0000 -2.2500 -2.1250 -0.0957 -0.1250 4.0000 -2.0000 -2.1250 -2.0625 0.4763 -0.0625 5.0000 -2.0625 -2.1250 -2.0938 0.1964 -0.0313 6.0000 -2.0938 -2.1250 -2.1094 0.0519 -0.0156 7.0000 -2.1094 -2.1250 -2.1172 -0.0215 -0.0078 8.0000 -2.1094 -2.1172 -2.1133 0.0153 -0.0039 9.0000 -2.1133 -2.1172 -2.1152 -0.0031 -0.0020 10.0000 -2.1133 -2.1152 -2.1143 0.0061 -0.0010 zero not foundto desiredtolerence >> bisection_15 step a b m ym bound 1.0000 2.0000 3.0000 2.5000 -3.6250 0.5000 2.0000 2.5000 3.0000 2.7500 -0.7656 0.2500 3.0000 2.7500 3.0000 2.8750 0.9980 0.1250 4.0000 2.7500 2.8750 2.8125 0.0872 0.0625 5.0000 2.7500 2.8125 2.7813 -0.3464 0.0313 6.0000 2.7813 2.8125 2.7969 -0.1314 0.0156 7.0000 2.7969 2.8125 2.8047 -0.0226 0.0078 8.0000 2.8047 2.8125 2.8086 0.0322 0.0039 9.0000 2.8047 2.8086 2.8066 0.0048 0.0020 10.0000 2.8047 2.8066 2.8057 -0.0089 0.0010
  • 10. zero not foundto desired tolerance bisection_16 step a b m ym bound 1.0000 0 1.0000 0.5000 -0.8750 0.5000 2.0000 0.5000 1.0000 0.7500 0.2969 0.2500 3.0000 0.5000 0.7500 0.6250 -0.2246 0.1250 4.0000 0.6250 0.7500 0.6875 0.0515 0.0625 5.0000 0.6250 0.6875 0.6563 -0.0826 0.0313 6.0000 0.6563 0.6875 0.6719 -0.0146 0.0156 7.0000 0.6719 0.6875 0.6797 0.0187 0.0078 8.0000 0.6719 0.6797 0.6758 0.0021 0.0039 9.0000 0.6719 0.6758 0.6738 -0.0062 0.0020 10.0000 0.6738 0.6758 0.6748 -0.0020 0.0010 zero not foundto desiredtolerence >> bisection_17 step a b m ym bound 1.0000 1.0000 2.0000 1.5000 -1.5000 0.5000 2.0000 1.0000 1.5000 1.2500 0.7813 0.2500 3.0000 1.2500 1.5000 1.3750 -0.3867 0.1250 4.0000 1.2500 1.3750 1.3125 0.1948 0.0625 5.0000 1.3125 1.3750 1.3438 -0.0971 0.0313 6.0000 1.3125 1.3438 1.3281 0.0486 0.0156 7.0000 1.3281 1.3438 1.3359 -0.0243 0.0078 8.0000 1.3281 1.3359 1.3320 0.0122 0.0039 9.0000 1.3320 1.3359 1.3340 -0.0061 0.0020 10.0000 1.3320 1.3340 1.3330 0.0030 0.0010
  • 11. zero not foundto desiredtolerence >> bisection_17 step a b m ym bound 1.0000 2.0000 3.0000 2.5000 0 0.5000 bisectionhas converged bisection_17 0 bisection_18 step a b m ym bound 1.0000 0 1.0000 0.5000 -2.8750 0.5000 2.0000 0 0.5000 0.2500 1.4844 0.2500 3.0000 0.2500 0.5000 0.3750 -0.7324 0.1250 4.0000 0.2500 0.3750 0.3125 0.3689 0.0625 5.0000 0.3125 0.3750 0.3438 -0.1838 0.0313 6.0000 0.3125 0.3438 0.3281 0.0921 0.0156 7.0000 0.3281 0.3438 0.3359 -0.0460 0.0078 8.0000 0.3281 0.3359 0.3320 0.0230 0.0039 9.0000 0.3320 0.3359 0.3340 -0.0115 0.0020 10.0000 0.3320 0.3340 0.3330 0.0058 0.0010 zero not foundto desiredtolerence >> bisection_18 step a b m ym bound 1.0000 0 1.0000 0.5000 -2.8750 0.5000 2.0000 0 0.5000 0.2500 1.4844 0.2500 3.0000 0.2500 0.5000 0.3750 -0.7324 0.1250 4.0000 0.2500 0.3750 0.3125 0.3689 0.0625
  • 12. 5.0000 0.3125 0.3750 0.3438 -0.1838 0.0313 6.0000 0.3125 0.3438 0.3281 0.0921 0.0156 7.0000 0.3281 0.3438 0.3359 -0.0460 0.0078 8.0000 0.3281 0.3359 0.3320 0.0230 0.0039 9.0000 0.3320 0.3359 0.3340 -0.0115 0.0020 10.0000 0.3320 0.3340 0.3330 0.0058 0.0010 zero not foundto desiredtolerance bisection_18 step a b m ym bound 1.0000 -2.0000 -3.0000 -2.5000 -2.1250 -0.5000 2.0000 -2.0000 -2.5000 -2.2500 7.2656 -0.2500 3.0000 -2.2500 -2.5000 -2.3750 2.9199 -0.1250 4.0000 -2.3750 -2.5000 -2.4375 0.4871 -0.0625 5.0000 -2.4375 -2.5000 -2.4688 -0.7963 -0.0313 6.0000 -2.4375 -2.4688 -2.4531 -0.1490 -0.0156 7.0000 -2.4375 -2.4531 -2.4453 0.1704 -0.0078 8.0000 -2.4453 -2.4531 -2.4492 0.0111 -0.0039 9.0000 -2.4492 -2.4531 -2.4512 -0.0689 -0.0020 10.0000 -2.4492 -2.4512 -2.4502 -0.0289 -0.0010 zero not foundto desired tolerance bisection_18 step a b m ym bound 1.0000 2.0000 3.0000 2.5000 1.6250 0.5000 2.0000 2.0000 2.5000 2.2500 -5.3906 0.2500 3.0000 2.2500 2.5000 2.3750 -2.2012 0.1250 4.0000 2.3750 2.5000 2.4375 -0.3699 0.0625 5.0000 2.4375 2.5000 2.4688 0.6068 0.0313
  • 13. 6.0000 2.4375 2.4688 2.4531 0.1133 0.0156 7.0000 2.4375 2.4531 2.4453 -0.1295 0.0078 8.0000 2.4453 2.4531 2.4492 -0.0084 0.0039 9.0000 2.4492 2.4531 2.4512 0.0524 0.0020 10.0000 2.4492 2.4512 2.4502 0.0220 0.0010 zero not foundto desiredtolerence >> bisection_19 step a b m ym bound 1.0000 -1.0000 -2.0000 -1.5000 -1.6250 -0.5000 2.0000 -1.5000 -2.0000 -1.7500 1.5781 -0.2500 3.0000 -1.5000 -1.7500 -1.6250 0.0684 -0.1250 4.0000 -1.5000 -1.6250 -1.5625 -0.7561 -0.0625 5.0000 -1.5625 -1.6250 -1.5938 -0.3382 -0.0313 6.0000 -1.5938 -1.6250 -1.6094 -0.1335 -0.0156 7.0000 -1.6094 -1.6250 -1.6172 -0.0322 -0.0078 8.0000 -1.6172 -1.6250 -1.6211 0.0182 -0.0039 9.0000 -1.6172 -1.6211 -1.6191 -0.0070 -0.0020 10.0000 -1.6191 -1.6211 -1.6201 0.0056 -0.0010 zero not foundto desiredtolerence >> bisection_19 step a b m ym bound 1.0000 5.0000 6.0000 5.5000 -27.8750 0.5000 2.0000 5.5000 6.0000 5.7500 -12.9531 0.2500 3.0000 5.7500 6.0000 5.8750 -4.7363 0.1250 4.0000 5.8750 6.0000 5.9375 -0.4338 0.0625 5.0000 5.9375 6.0000 5.9688 1.7666 0.0313
  • 14. 6.0000 5.9375 5.9688 5.9531 0.6623 0.0156 7.0000 5.9375 5.9531 5.9453 0.1132 0.0078 8.0000 5.9375 5.9453 5.9414 -0.1606 0.0039 9.0000 5.9414 5.9453 5.9434 -0.0238 0.0020 10.0000 5.9434 5.9453 5.9443 0.0447 0.0010 zero not foundto desiredtolerence >> bisection_19 step a b m ym bound 1.0000 -3.0000 -4.0000 -3.5000 -3.1250 -0.5000 2.0000 -3.0000 -3.5000 -3.2500 1.1094 -0.2500 3.0000 -3.2500 -3.5000 -3.3750 -0.8340 -0.1250 4.0000 -3.2500 -3.3750 -3.3125 0.1804 -0.0625 5.0000 -3.3125 -3.3750 -3.3438 -0.3160 -0.0313 6.0000 -3.3125 -3.3438 -3.3281 -0.0651 -0.0156 7.0000 -3.3125 -3.3281 -3.3203 0.0583 -0.0078 8.0000 -3.3203 -3.3281 -3.3242 -0.0032 -0.0039 9.0000 -3.3203 -3.3242 -3.3223 0.0276 -0.0020 10.0000 -3.3223 -3.3242 -3.3232 0.0122 -0.0010 zero not foundto desiredtolerence >> bisection_20 step a b m ym bound 1.0000 3.0000 4.0000 3.5000 -0.8750 0.5000 2.0000 3.5000 4.0000 3.7500 -0.2031 0.2500 3.0000 3.7500 4.0000 3.8750 0.3262 0.1250 4.0000 3.7500 3.8750 3.8125 0.0442 0.0625 5.0000 3.7500 3.8125 3.7813 -0.0837 0.0313 6.0000 3.7813 3.8125 3.7969 -0.0208 0.0156
  • 15. 7.0000 3.7969 3.8125 3.8047 0.0114 0.0078 8.0000 3.7969 3.8047 3.8008 -0.0048 0.0039 9.0000 3.8008 3.8047 3.8027 0.0033 0.0020 10.0000 3.8008 3.8027 3.8018 -0.0007 0.0010 zero not foundto desiredtolerence >> bisection_20 step a b m ym bound 1.0000 0 1.0000 0.5000 -1.6250 0.5000 2.0000 0.5000 1.0000 0.7500 -0.0156 0.2500 3.0000 0.7500 1.0000 0.8750 0.5605 0.1250 4.0000 0.7500 0.8750 0.8125 0.2903 0.0625 5.0000 0.7500 0.8125 0.7813 0.1419 0.0313 6.0000 0.7500 0.7813 0.7656 0.0643 0.0156 7.0000 0.7500 0.7656 0.7578 0.0246 0.0078 8.0000 0.7500 0.7578 0.7539 0.0046 0.0039 9.0000 0.7500 0.7539 0.7520 -0.0055 0.0020 10.0000 0.7520 0.7539 0.7529 -0.0005 0.0010 zero not foundto desiredtolerence >>