Newtons Method Explanation
28
Explanation of Newton’s method Dr. Ammar Hasan
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Transcript of Newtons Method Explanation
Explanation of Newton’s method
Dr. Ammar Hasan
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-4 -3 -2 -1 0 1 2 3 4
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5
10
Function (Blue line)
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-4 -3 -2 -1 0 1 2 3 4
0
5
10
Function (Blue line) xk (Black cross)
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-4 -3 -2 -1 0 1 2 3 4
0
5
10
Function (Blue line)
Quadratic approximation (Red line)
xk (Black cross)
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30
-4 -3 -2 -1 0 1 2 3 4
0
5
10
Function (Blue line)
Quadratic approximation (Red line)
xk (Black cross)
sk (Green Asterisk)
Initial point x = -2,
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iteration 1
-4 -3 -2 -1 0 1 2 3 4
0
5
10
Function (Blue line)
Quadratic approximation (Red line)
xk (Black cross)
sk (Green Asterisk)
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iteration 2
-4 -3 -2 -1 0 1 2 3 4
0
5
10
Function (Blue line)
Quadratic approximation (Red line)
xk (Black cross)
sk (Green Asterisk)
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iteration 3
-4 -3 -2 -1 0 1 2 3 4
0
5
10
Function (Blue line)
Quadratic approximation (Red line)
xk (Black cross)
sk (Green Asterisk)
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iteration 4
-4 -3 -2 -1 0 1 2 3 4
0
5
10
Function (Blue line)
Quadratic approximation (Red line)
xk (Black cross)
sk (Green Asterisk)
Initial point x = -0.5Initial point x = -0.5
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iteration 1
-4 -3 -2 -1 0 1 2 3 4
0
5
10
Function (Blue line)
Quadratic approximation (Red line)
xk (Black cross)
sk (Green Asterisk)
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iteration 2
-4 -3 -2 -1 0 1 2 3 4
0
5
10
Function (Blue line)
Quadratic approximation (Red line)
xk (Black cross)
sk (Green Asterisk)
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iteration 3
-4 -3 -2 -1 0 1 2 3 4
0
5
10
Function (Blue line)
Quadratic approximation (Red line)
xk (Black cross)
sk (Green Asterisk)
Initial point x = 0.6Initial point x = 0.6
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Initial point x = 0.6, iteration 1
-4 -3 -2 -1 0 1 2 3 4
0
5
10
Function (Blue line)
Quadratic approximation (Red line)
xk (Black cross)
sk (Green Asterisk)
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Initial point x = 0.6, iteration 2
-4 -3 -2 -1 0 1 2 3 4
0
5
10
Function (Blue line)
Quadratic approximation (Red line)
xk (Black cross)
sk (Green Asterisk)
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25
30
iteration 3
-4 -3 -2 -1 0 1 2 3 4
0
5
10
Function (Blue line)
Quadratic approximation (Red line)
xk (Black cross)
sk (Green Asterisk)
15
20
25
30
iteration 4
-4 -3 -2 -1 0 1 2 3 4
0
5
10
Function (Blue line)
Quadratic approximation (Red line)
xk (Black cross)
sk (Green Asterisk)
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20
25
30
iteration 5
-4 -3 -2 -1 0 1 2 3 4
0
5
10
Function (Blue line)
Quadratic approximation (Red line)
xk (Black cross)
sk (Green Asterisk)
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iteration 6
-4 -3 -2 -1 0 1 2 3 4
0
5
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Function (Blue line)
Quadratic approximation (Red line)
xk (Black cross)
sk (Green Asterisk)
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iteration 7
-4 -3 -2 -1 0 1 2 3 4
0
5
10
Function (Blue line)
Quadratic approximation (Red line)
xk (Black cross)
sk (Green Asterisk)
Function of two variables
Initial point x = [0.7;0.7]Initial point x = [0.7;0.7]
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-3 -2 -1 0 1 2 3-3
-2
-1
-3 -2 -1 0 1 2 3-3
-2
-1
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-3 -2 -1 0 1 2 3-3
-2
-1
-3 -2 -1 0 1 2 3-3
-2
-1
0
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3
0
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-3 -2 -1 0 1 2 3-3
-2
-1
-3 -2 -1 0 1 2 3-3
-2
-1
0
1
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3
0
1
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-3 -2 -1 0 1 2 3-3
-2
-1
-3 -2 -1 0 1 2 3-3
-2
-1
0
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3
0
1
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3
-3 -2 -1 0 1 2 3-3
-2
-1
-3 -2 -1 0 1 2 3-3
-2
-1
