PROBLEM 3: BISECTION METHOD
3x^5 + 2x^2 + x-10
a=1
b=2
n a b c f(a) f(b) f(c) [f(a)][f(c)]_0
1 1 2 1.5 -4 96 18.78125 <
2 1 1.5 1.25 -4 18.7813 3.530273 <
3 1 1.25 1.125 -4 3.53027 -0.937653 >
4 1.125 1.25 1.1875 -0.937653 3.53027 1.091989 <
5 1.125 1.1875 1.15625 -0.937653 1.09199 0.029911 <
6 1.125 1.15625 1.140625 -0.937653 0.02991 -0.465229 >
7 1.140625 1.15625 1.148438 -0.465229 0.02991 -0.220555 >
8 1.148438 1.15625 1.152344 -0.220555 0.02991 -0.096053 >
9 1.152344 1.15625 1.154297 -0.096053 0.02991 -0.033255 >
10 1.154297 1.15625 1.155273 -0.033255 0.02991 -0.001718 >
11 1.155273 1.15625 1.155762 -0.001718 0.02991 0.014085 <
12 1.155273 1.155762 1.155518 -0.001718 0.01409 0.006181 <
13 1.155273 1.155518 1.155396 -0.001718 0.00618 0.002231 <
14 1.155273 1.155396 1.155334 -0.001718 0.00223 0.000256 <
15 1.155273 1.155334 1.155304 -0.001718 0.00026 -0.000731 >
16 1.155304 1.155334 1.155319 -0.000731 0.00026 -0.000237 >
17 1.155319 1.155334 1.155327 -0.000237 0.00026 9.535E-06 <
18 1.155319 1.155327 1.155323 -0.000237 9.54E-06 -0.000114 >
Relative Error Remarks
- CONTINUE
20 CONTINUE
11.11111111111 CONTINUE
5.263157894737 CONTINUE
2.702702702703 CONTINUE
1.369863013699 CONTINUE
0.680272108844 CONTINUE
0.338983050847 CONTINUE
0.169204737733 CONTINUE
0.084530853762 CONTINUE
0.042247570765 CONTINUE
0.021128248468 CONTINUE
0.010565240359 CONTINUE
0.005282899255 STOP
0.002641519402 STOP
0.001320742257 STOP
0.000660366768 STOP
0.000330184474 STOP
PROBLEM 4: BISECTION METHOD
x^2 - loge x = 12
a=1
b=1
n a b c f(a) f(b) f(c) [f(a)][f(c)]_0
1 2 6 4 -8.69314718 22.208240531 2.613705639 <
2 2 4 3 -8.69314718 2.6137056389 -4.098612289 >
3 3 4 3.5 -4.09861229 2.6137056389 -1.002762968 >
4 3.5 4 3.75 -1.00276297 2.6137056389 0.74074416 <
5 3.5 3.75 3.625 -1.00276297 0.74074416 -0.147229288 >
6 3.625 3.75 3.6875 -0.14722929 0.74074416 0.292707528 <
7 3.625 3.6875 3.65625 -0.14722929 0.2927075283 0.071726031 <
8 3.625 3.65625 3.640625 -0.14722929 0.0717260305 -0.03800498 >
9 3.640625 3.65625 3.648438 -0.03800498 0.0717260305 0.016797198 <
10 3.640625 3.648438 3.644531 -0.03800498 0.0167971977 -0.010619724 >
11 3.644531 3.648438 3.646484 -0.01061972 0.0167971977 0.003084779 <
12 3.644531 3.646484 3.645508 -0.01061972 0.0030847786 -0.003768462 >
13 3.645508 3.646484 3.645996 -0.00376846 0.0030847786 -0.000342089 >
14 3.645996 3.646484 3.64624 -0.00034209 0.0030847786 0.001371283 <
Relative Error Remarks
- CONTINUE
33.33333333333 CONTINUE
14.28571428571 CONTINUE
6.666666666667 CONTINUE
3.448275862069 CONTINUE
1.694915254237 CONTINUE
0.854700854701 CONTINUE
0.429184549356 CONTINUE
0.214132762313 CONTINUE
0.10718113612 CONTINUE
0.053561863953 CONTINUE
0.026788106081 CONTINUE
0.013392259274 CONTINUE
0.006695681286 STOP
PROBLEM 4: BISECTION METHOD
n a b c f(a) f(b) f(c) [f(a)][f(c)]_0
1 1 2 1.5 -1.123189 0.479759 -1.015806 >
2 1.5 2 1.75 -1.015806 0.479759 -0.479383 >
3 1.75 2 1.875 -0.479383 0.479759 -0.058267 >
4 1.875 2 1.9375 -0.058267 0.479759 0.195362 <
5 1.875 1.9375 1.90625 -0.058267 0.195362 0.064801 <
6 1.875 1.90625 1.890625 -0.058267 0.064801 0.002343 <
7 1.875 1.890625 1.882813 -0.058267 0.002343 -0.028192 >
8 1.882813 1.890625 1.886719 -0.028192 0.002343 -0.012982 >
9 1.886719 1.890625 1.888672 -0.012982 0.002343 -0.005334 >
10 1.888672 1.890625 1.889648 -0.005334 0.002343 -0.001499 >
11 1.889648 1.890625 1.890137 -0.001499 0.002343 0.000421 <
12 1.889648 1.890137 1.889893 -0.001499 0.000421 -0.000539 >
13 1.889893 1.890137 1.890015 -0.000539 0.000421 -5.93E-05 >
14 1.890015 1.890137 1.890076 -5.93E-05 0.000421 0.000181 <
15 1.890015 1.890076 1.890045 -5.93E-05 0.000181 6.072E-05 <
16 1.890015 1.890045 1.89003 -5.93E-05 6.072E-05 7E-07 <
17 1.890015 1.89003 1.890022 -5.93E-05 7E-07 -2.93E-05 >
18 1.890022 1.89003 1.890026 -2.93E-05 7E-07 -1.43E-05 >
METHOD
Relative Error Remarks
- CONTINUE
14.2857142857 CONTINUE
6.66666666667 CONTINUE
3.22580645161 CONTINUE
1.6393442623 CONTINUE
0.82644628099 CONTINUE
0.41493775934 CONTINUE
0.20703933747 CONTINUE
0.10341261634 CONTINUE
0.05167958656 CONTINUE
0.02583311806 CONTINUE
0.01291822762 CONTINUE
0.00645869664 STOP
0.00322924403 STOP
0.00161464809 STOP
0.00080733056 STOP
0.00040366691 STOP
0.00020183305 STOP
