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

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
>>