GATE CE 2024 Set 1 — Question 32
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Engineering Mathematics → Numerical Solution of Equations → Newton Interpolation
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Question
Consider the data of given in the table.
The value of estimated using second-order Newton’s interpolation formula is ______________ (rounded off to 2 decimal places).
| 0 | 1 | 2 | |
|---|---|---|---|
| 1 | 2 | 3 | |
| 0 | 0.3010 | 0.4771 |
Correct answer
0.16 to 0.18
Solution
Newton's second-order forward interpolation formula is given by:
where .From the given data table:
Calculating the forward differences:
First differences:
Second difference:
For , we calculate :
Substituting these values into the formula:
Rounding off to 2 decimal places, we get .
where .From the given data table:
Calculating the forward differences:
First differences:
Second difference:
For , we calculate :
Substituting these values into the formula:
Rounding off to 2 decimal places, we get .
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