Question
Asked Nov 22, 2019
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From Numerical Analysis 8th edition by Richard Burden. This is #1 from Section 8.1

 

1. Compute the linear least squares polynomial for the data of Example 2 (repeated below).
Yi
2
1
0.00
1.0000
2
0.25 1.2840
3 0.50 1.6487
4 0.75 2.1170
5 1.00 2.7183
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1. Compute the linear least squares polynomial for the data of Example 2 (repeated below). Yi 2 1 0.00 1.0000 2 0.25 1.2840 3 0.50 1.6487 4 0.75 2.1170 5 1.00 2.7183

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Expert Answer

Step 1

1 0
1
1 0.25
1.2840
0.5
b
1 0.75
1
=1.6487
2.1170
1
1
2.7183
Consider the residual vector r as,
1
1
0
1 0.25
р
1.2840
r=1.6487
1
0.5
1 0.75
2.1170
2.7183
1
1-p
1.2840- р - 0.25g
1.6487- p-0.5q
2.1170- р - 0.75q
2.7183- р -9
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1 0 1 1 0.25 1.2840 0.5 b 1 0.75 1 =1.6487 2.1170 1 1 2.7183 Consider the residual vector r as, 1 1 0 1 0.25 р 1.2840 r=1.6487 1 0.5 1 0.75 2.1170 2.7183 1 1-p 1.2840- р - 0.25g 1.6487- p-0.5q 2.1170- р - 0.75q 2.7183- р -9

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Step 2

f F(1-p) +(1.2840-p-0.25g+
(1.6487-p-0.5q) +(2.1170-p-0.75q)
+(2.7183-p-g)
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f F(1-p) +(1.2840-p-0.25g+ (1.6487-p-0.5q) +(2.1170-p-0.75q) +(2.7183-p-g)

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Step 3

Differentiate the function f partially with resp...

of
— 8.7681-5р- 2.5q %3D 0
др
5.4515-2.5p-1.875q = 0
8.7681
5
The sy stem obtained is
2.5
р
2.5 1.875
5.4515
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of — 8.7681-5р- 2.5q %3D 0 др 5.4515-2.5p-1.875q = 0 8.7681 5 The sy stem obtained is 2.5 р 2.5 1.875 5.4515

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