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Numerical Analysis | 10th Edition | ISBN: 9781305253667 | Authors: Richard L. Burden J. Douglas Faires, Annette M. Burden
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a. Use the following values and five-digit rounding arithmetic to constructtheHermite

Chapter 3, Problem 5

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QUESTION:

a. Use the following values and five-digit rounding arithmetic to constructtheHermite interpolating polynomial to approximate sin 0.34. X sin x D, sinx = cosx 0.30 0.29552 0.95534 0.32 0.31457 0.94924 0.35 0.34290 0.93937 b. Determine an error bound for the approximation in part (a) and compare it to the actual error. c. Add sin 0.33 = 0.32404 and cos 0.33 = 0.94604 to the data and redo the calculations.

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QUESTION:

a. Use the following values and five-digit rounding arithmetic to constructtheHermite interpolating polynomial to approximate sin 0.34. X sin x D, sinx = cosx 0.30 0.29552 0.95534 0.32 0.31457 0.94924 0.35 0.34290 0.93937 b. Determine an error bound for the approximation in part (a) and compare it to the actual error. c. Add sin 0.33 = 0.32404 and cos 0.33 = 0.94604 to the data and redo the calculations.

ANSWER:

Step 1 of 4

(a)

Construct a divided-difference table, with each of the interpolation points included twice; that  , and  .

Each of the divided difference  , where   and  , is set equal to  .

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