Scientific Programming using Excel for Beginners: Newton's Method

Scientific Programming Using Excel
for Beginners: Newton's Method
by
RIZAuddin bin Saian
Faculty of Computer & Mathematical Sciences
Universiti Teknologi MARA (Perlis)
Venue: Lab 1, UiTM Perlis
5 February 2016 (Friday)
3pm

Scientific Programming Using Excel for Beginners: Newton's Method
Problem
• We want to find the root for .
 xfy 
 xfy 
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2
http://www.rizauddin.com

Objective
• To approximate the root for
using Newton’s method (Newton-Raphson
method)
– Perform Newton’s method by hand.
– Write a VBA code to perform the Newton’s
method.
 xfy 
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3

Newton’s Method
 
 n
n
nn
xf
xf
xx
'
1 
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4

Equation of tangent line
      
 
    
 
 
 
 n
n
nn
n
n
nn
nnnn
n
nnnnn
xf
xf
xx
xf
xf
xx
xxxfxf
xxf
xxxfxfxf
'
'
'0
interceptat the0
'
1
1
1
1
11










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Initial Guess of x
Actual root
 xfy 
X
X
x0
(Initial guess)
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6

Iteration 1
X
Tangent line at x0 = -1
 
 0
0
01
' xf
xf
xx 
X
 xfy 
x0x1
Actual root
(Initial guess)
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Iteration 2
x1
Tangent line at x1
 
 1
1
12
' xf
xf
xx 
X X
 xfy 
x0
Actual root
(Initial guess)
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Example: Find the root.
Actual root
X
x0 = -1
X
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9
  13
 xxxf

Initial guess of x
  13
 xxxf 
  13'
1
2
3


xxf
xxxf
1
,ofguessInitial
0 x
x
 
 
13
1
'
2
3
1




x
xx
x
xf
xf
xxn
The estimated root,
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Iteration 1
i x xn+1
0 - 1 -1.5
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Iteration 2
i x xn+1
0 - 1 -1.5
1 -1.5 -1.347826087
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Iteration 3
i x xn+1
0 - 1 -1.5
1 -1.5 -1.347826087
2 -1.347826087 -1.325200399
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13

Iteration 4
i x xn+1
0 - 1 -1.5
1 -1.5 -1.347826087
2 -1.347826087 -1.325200399
3 -1.325200399 -1.324718174
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Iteration 5
i x xn+1
0 - 1 -1.5
1 -1.5 -1.347826087
2 -1.347826087 -1.325200399
3 -1.325200399 -1.324718174
4 -1.324718174 -1.324717957
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15

Iteration 6
i x xn+1
0 - 1 -1.5
1 -1.5 -1.347826087
2 -1.347826087 -1.325200399
3 -1.325200399 -1.324718174
4 -1.324718174 -1.324717957
5 -1.324717957 -1.324717957
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Iteration 6
i x xn+1
0 - 1 -1.5
1 -1.5 -1.347826087
2 -1.347826087 -1.325200399
3 -1.325200399 -1.324718174
4 -1.324718174 -1.324717957
5 -1.324717957 -1.324717957
STOP!
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Visual Basic for Application (VBA)
Press Alt key and hold. Then, press F11 together to open the VBA Editor.
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Add new Module
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Define a function
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Exercise 1
• Define function Newton with parameter “x”
and return the estimation value for the root of
with x0=-1.  13
 xxxf
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Exercise 1
• Define function Newton with parameter “x”
and return the estimation value for the root of
with x0=-1.  13
 xxxf
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Loop
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Exercise 2
• Modify the Newton function in Ex. 1 to use
loop to calculate the root using 4 iterations.
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Exercise 2
• Modify the Newton function in Ex. 1 to use
loop to calculate the root using 4 iterations.
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THANK YOU
www.rizauddin.com
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26

Scientific Programming using Excel for Beginners: Newton's Method

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