subject: cvnm topic:newton’s forward,backward …srict.in/uploadedfiles/131916778953460000.pdf ·...
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![Page 1: SUBJECT: CVNM TOPIC:NEWTON’S FORWARD,BACKWARD …srict.in/UploadedFiles/131916778953460000.pdf · Illustration 2: Using Newton’s forward formula, find the value of f(218) if,](https://reader036.vdocument.in/reader036/viewer/2022080717/5f783fc90232e1624c42b7ad/html5/thumbnails/1.jpg)
SUBJECT: CVNMTOPIC:NEWTON’S FORWARD,BACKWARD
DIFFERENCE INTERPOLATION
![Page 2: SUBJECT: CVNM TOPIC:NEWTON’S FORWARD,BACKWARD …srict.in/UploadedFiles/131916778953460000.pdf · Illustration 2: Using Newton’s forward formula, find the value of f(218) if,](https://reader036.vdocument.in/reader036/viewer/2022080717/5f783fc90232e1624c42b7ad/html5/thumbnails/2.jpg)
NEWTON’S FORWARD DIFFERENCE INTERPOLATION FORMULA
Where -1<p<1
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FIRST FORWARD DIFFERENCES
![Page 4: SUBJECT: CVNM TOPIC:NEWTON’S FORWARD,BACKWARD …srict.in/UploadedFiles/131916778953460000.pdf · Illustration 2: Using Newton’s forward formula, find the value of f(218) if,](https://reader036.vdocument.in/reader036/viewer/2022080717/5f783fc90232e1624c42b7ad/html5/thumbnails/4.jpg)
SECOND FORWARD DIFFRENCE OPERATOR
![Page 5: SUBJECT: CVNM TOPIC:NEWTON’S FORWARD,BACKWARD …srict.in/UploadedFiles/131916778953460000.pdf · Illustration 2: Using Newton’s forward formula, find the value of f(218) if,](https://reader036.vdocument.in/reader036/viewer/2022080717/5f783fc90232e1624c42b7ad/html5/thumbnails/5.jpg)
TABLE
Argument
x
Entry
y = f(x)
First
Differences
∆
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0.7071 0.7660 0.8192 0.8660
0.7071
0.0589
0.7660 -0.0057
0.0532 -0.0007
0.8192 -0.0064
0.0468
0.8660
![Page 7: SUBJECT: CVNM TOPIC:NEWTON’S FORWARD,BACKWARD …srict.in/UploadedFiles/131916778953460000.pdf · Illustration 2: Using Newton’s forward formula, find the value of f(218) if,](https://reader036.vdocument.in/reader036/viewer/2022080717/5f783fc90232e1624c42b7ad/html5/thumbnails/7.jpg)
![Page 8: SUBJECT: CVNM TOPIC:NEWTON’S FORWARD,BACKWARD …srict.in/UploadedFiles/131916778953460000.pdf · Illustration 2: Using Newton’s forward formula, find the value of f(218) if,](https://reader036.vdocument.in/reader036/viewer/2022080717/5f783fc90232e1624c42b7ad/html5/thumbnails/8.jpg)
Illustration 2: Using Newton’s forward formula, find the value of f(218) if,
(JUNE 2014)
Solution : The table difference is
X 100 150 200 250 300 350 400
F(x) 10.63 13.03 15.04 16.81 18.42 19.90 21.27
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X f(x)
100 10.63
2.4
150 13.03 -0.39
2.01 0.15
200 15.04 -0.24 -0.07
1.77 0.08 0.02
250 16.81 -0.16 -0.05 0.02
1.61 0.03 0.04
300 18.42 -0.13 -0.01
1.48 0.02
350 19.90 -0.11
1.37
400 21.27
![Page 10: SUBJECT: CVNM TOPIC:NEWTON’S FORWARD,BACKWARD …srict.in/UploadedFiles/131916778953460000.pdf · Illustration 2: Using Newton’s forward formula, find the value of f(218) if,](https://reader036.vdocument.in/reader036/viewer/2022080717/5f783fc90232e1624c42b7ad/html5/thumbnails/10.jpg)
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Newton’s backward interpolation
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FIRST BACKWARD DIFFRENCES
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SECOND BACKWARD DIFFRENCE OPERATOR
![Page 14: SUBJECT: CVNM TOPIC:NEWTON’S FORWARD,BACKWARD …srict.in/UploadedFiles/131916778953460000.pdf · Illustration 2: Using Newton’s forward formula, find the value of f(218) if,](https://reader036.vdocument.in/reader036/viewer/2022080717/5f783fc90232e1624c42b7ad/html5/thumbnails/14.jpg)
TABLEArgument
x
Entry
y = f(x)
First Differences
𝛁
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