Practical work #8.Lagrange’s Interpolation Formula

Practical work #8. Lagrange’s Interpolation Formula

Example 1. Using Lagrange’s interpolation formula, find y(10) from the following table:

Lagrange’s formula is

Putting x = 10, we get

Hence,

Example 2. Compute the value of f(x) for x = 2.5 from the following table:

using Lagrange’s interpolation method.

Lagrange’s formula is

Given x = 2.5, we get

Hence,

Example 3. Use Lagrange’s interpolation formula to fit a polynomial to the data:

Hence or otherwise find the value of u1.

Sol. Here,

Lagrange’s interpolation formula is

Hence, (1)

Given in (1), we get

PROBLEM SET

1. Apply Lagrange’s formula to find f (5) and f (6) given that

Explain why the result differs from those obtained by completing the series of powers of 2?

2. Values of f (x) for values of x are given as

Find f (6) and also the value of x for which f (x) is maximum or minimum.

3. Find by Lagrange’s formula, the value of

4. Using Lagrange’s formula, find the values of

5. Find the value of tan 33° by Lagrange’s formula if

6. Use Lagrange’s formula to find f (6) from the following table:

7. Apply Lagrange’s formula to find f (15), if

8. If y 0, y 1,..., y 9 are consecutive terms of a series, prove that

9. Using the following table, find f (x) as a polynomial in x:

10. Applying Lagrange’s formula, find a cubic polynomial which approximates the following data:

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