PROBLEM SET 2
ARELLANO REMUEL JOHN P .
21-03001
ECE 3102
REGULA
Fixed Point
FALSI
Iteration
f(x) = x^3+2x-1 0 = x^3+2x-1 The root is 0.4533976515.
g1(x) = (-2x+1)^1/3 -x^3=2x+1 The zero error is obtained after 18 iterations.
g2(x) = (-x^3+1)^2 -2x=-x^3+1
Iteration x g1(x) Error Iteration x g2(x) Error
0 0.5 0 0 0.5 0.4375
1 0 1 1 1 0.4375 0.458129883 0.04503064
2 1 -1 2 2 0.45812988 0.451923165 -0.01373401
3 -1 1.44224957 1.69336127 3 0.45192317 0.453850838 0.00424737
4 1.44224957 -1.23518492 2.16763858 4 0.45385084 0.45325777 -0.00130846
5 -1.23518492 1.51399783 1.81584326 5 0.45325777 0.453440771 0.00040358
6 1.51399783 -1.26577255 2.19610575 6 0.45344077 0.453384354 -0.00012444
7 -1.26577255 1.52284226 1.83119085 7 0.45338435 0.453401752 3.8371E-05
8 1.52284226 -1.26944207 2.1996154 8 0.45340175 0.453396387 -1.1832E-05
9 -1.26944207 1.52389642 1.83302385 9 0.45339639 0.453398041 3.6484E-06
10 1.52389642 -1.26987802 2.2000337 10 0.45339804 0.453397531 -1.125E-06
11 -1.26987802 1.52402156 1.83324151 11 0.45339753 0.453397689 3.469E-07
12 1.52402156 -1.26992975 2.20008335 12 0.45339769 0.45339764 -1.0697E-07
13 -1.26992975 1.52403641 1.83326733 13 0.45339764 0.453397655 3.2984E-08
14 1.52403641 -1.26993589 2.20008925 14 0.45339766 0.45339765 -1.0171E-08
15 -1.26993589 1.52403817 1.8332704 15 0.45339765 0.453397652 3.1362E-09
16 1.52403817 -1.26993662 2.20008995 16 0.45339765 0.453397651 -9.6706E-10
17 -1.26993662 1.52403838 1.83327076 17 0.45339765 0.453397652 2.982E-10
18 1.52403838 -1.26993671 2.20009003 18 0.45339765 0.453397652 -9.195E-11
19 -1.26993671 1.5240384 1.8332708 19 0.45339765 0.453397652 2.8353E-11
20 1.5240384 -1.26993672 2.20009004 20 0.45339765 0.453397652 -8.7429E-12
21 -1.26993672 1.52403841 1.83327081 21 0.45339765 0.453397652 2.696E-12
22 1.52403841 -1.26993672 2.20009004 22 0.45339765 0.453397652 -8.3132E-13
23 -1.26993672 1.52403841 1.83327081 23 0.45339765 0.453397652 2.5638E-13
24 1.52403841 -1.26993672 2.20009004 24 0.45339765 0.453397652 -7.9092E-14
25 -1.26993672 1.52403841 1.83327081 25 0.45339765 0.453397652 2.4364E-14
26 1.52403841 -1.26993672 2.20009004 26 0.45339765 0.453397652 -7.4685E-15
27 -1.26993672 1.52403841 1.83327081 27 0.45339765 0.453397652 2.2038E-15
28 1.52403841 -1.26993672 2.20009004 28 0.45339765 0.453397652 -6.1217E-16
29 -1.26993672 1.52403841 1.83327081 29 0.45339765 0.453397652 1.2243E-16
30 1.52403841 -1.26993672 2.20009004 30 0.45339765 0.453397652 0
