Newton's Method
You can download the Newton's Method here. Put this file to your matlab directory. To execute the Newton's method, open your matlab program:
Using Toolbox Path Cache. Type "help toolbox_path_cache" for more
info.
To get started, select "MATLAB Help" from the Help menu.
>>
For instance, if you want to do example 2 on page 281, you can do:
>> f='sin(3*x)-cos(x)'
f =
sin(3*x)-cos(x)
>> Newton(f, 0.4, 4)
1.0000 0.3926 -0.0002
2.0000 0.3927 -0.0000
3.0000 0.3927 -0.0000
4.0000 0.3927 0.0000
If you are not satisfied with four decimal places, you do
>> format long
>> Newton(f, 0.4, 4)
1.00000000000000 0.39256474474919 -0.00020570078629
2.00000000000000 0.39269903816472 -0.00000006663898
3.00000000000000 0.39269908169872 -0.00000000000001
4.00000000000000 0.39269908169872 0.00000000000000
This solves the equation f=0 by four iterations with initial guess 0.4.
If you want to start with another initial guess, for ex: 0.2, you do
>> Newton(f, 0.2, 6)
1.00000000000000 0.35531753273452 -0.06228600122207
2.00000000000000 0.38994202442391 -0.00424837394140
3.00000000000000 0.39268101959338 -0.00002764947949
4.00000000000000 0.39269908091119 -0.00000000120550
5.00000000000000 0.39269908169872 0.00000000000000
6.00000000000000 0.39269908169872 0
If you want to continue example 3 on page 281, you do
>> clear
>> f='x^4-6*x^2+x+5'
f =
x^4-6*x^2+x+5
>> Newton(f,0,7)
1 -5 475
1.0e+002 *
0.02000000000000 -0.03917995444191 1.44621506056958
3.00000000000000 -3.16694805728908 42.24776570210613
4.00000000000000 -2.68712701380716 11.12677281628375
5.00000000000000 -2.43633031925806 2.18203602039247
6.00000000000000 -2.35729793861145 0.18020224687632
7.00000000000000 -2.34950003482378 0.00165807253059
>> Newton(f,-1,4)
1.00000000000000 -0.88888888888889 -0.00533455265966
2.00000000000000 -0.88828661401063 -0.00000045755408
3.00000000000000 -0.88828656234358 -0.00000000000000
4.00000000000000 -0.88828656234357 0
Play with it and have fun !