Scientific Programming Using Excel for Beginners: Newton's Method

byRIZAuddin bin Saian

Faculty of Computer & Mathematical SciencesUniversiti Teknologi MARA (Perlis)

Venue: Lab 1, UiTM Perlis5 February 2016 (Friday)

3pm

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Scientific Programming Using Excel for Beginners: Newton's Method

Problem

• We want to find the root for .

xfy

xfy

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Scientific Programming Using Excel for Beginners: Newton's Method

Objective

• To approximate the root forusing 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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Scientific Programming Using Excel for Beginners: Newton's Method

Newton’s Method

nn

nn xfxfxx

'1

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Scientific Programming Using Excel for Beginners: Newton's Method

Equation of tangent line

nn

nn

n

nnn

nnnn

n

nnnnn

xfxfxx

xfxfxx

xxxfxfxxf

xxxfxfxf

'

'

'0intercept at the 0

'

1

1

1

1

11

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Scientific Programming Using Excel for Beginners: Newton's Method

Initial Guess of x

Actual root

xfy

X

Xx0

(Initial guess) 5/2/2016

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Scientific Programming Using Excel for Beginners: Newton's Method

Iteration 1

X

Tangent line at x0 = -1

0

001 ' xf

xfxx

X

xfy

x0 x1

Actual root

(Initial guess) 5/2/2016

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Scientific Programming Using Excel for Beginners: Newton's Method

Iteration 2

x1

Tangent line at x1

1

112 ' xf

xfxx

X X

xfy

x0

Actual root

(Initial guess) 5/2/2016

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Scientific Programming Using Excel for Beginners: Newton's Method

Example: Find the root.

Actual root

X

x0 = -1X

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13 xxxf

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Scientific Programming Using Excel for Beginners: Newton's Method

Initial guess of x 13 xxxf

13'

12

3

xxf

xxxf

1, of guess Initial

0 xx

131

'

2

3

1

xxxx

xfxfxxn

The estimated root,

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Scientific Programming Using Excel for Beginners: Newton's Method

Iteration 1i x xn+1

0 - 1 -1.5

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Scientific Programming Using Excel for Beginners: Newton's Method

Iteration 2i x xn+1

0 - 1 -1.5

1 -1.5 -1.347826087

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Scientific Programming Using Excel for Beginners: Newton's Method

Iteration 3i x xn+1

0 - 1 -1.5

1 -1.5 -1.347826087

2 -1.347826087 -1.325200399

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Scientific Programming Using Excel for Beginners: Newton's Method

Iteration 4i 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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Scientific Programming Using Excel for Beginners: Newton's Method

Iteration 5i 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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Scientific Programming Using Excel for Beginners: Newton's Method

Iteration 6i 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 5/2/2016

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Scientific Programming Using Excel for Beginners: Newton's Method

Iteration 6i 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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Scientific Programming Using Excel for Beginners: Newton's Method

Visual Basic for Application (VBA)Press Alt key and hold. Then, press F11 together to open the VBA Editor.

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Scientific Programming Using Excel for Beginners: Newton's Method

Add new Module5/2/2016

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Scientific Programming Using Excel for Beginners: Newton's Method

Define a function5/2/2016

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Scientific Programming Using Excel for Beginners: Newton's Method

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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Scientific Programming Using Excel for Beginners: Newton's Method

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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Scientific Programming Using Excel for Beginners: Newton's Method

Loop5/2/2016

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Scientific Programming Using Excel for Beginners: Newton's Method

Exercise 2

• Modify the Newton function in Ex. 1 to use loop to calculate the root using 4 iterations.

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Scientific Programming Using Excel for Beginners: Newton's Method

Exercise 2

• Modify the Newton function in Ex. 1 to use loop to calculate the root using 4 iterations.

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