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Math / Numerical Analysis 10 / Chapter 3.1 / Problem 13

Numerical Analysis | 10th Edition | ISBN: 9781305253667 | Authors: Richard L. Burden J. Douglas Faires, Annette M. Burden

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Construct the Lagrange interpolating polynomials for the following functions and find a

Chapter 3, Problem 13

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QUESTION:

Construct the Lagrange interpolating polynomials for the following functions and find a bound for the absolute error on the interval [xq, x |. a. fix) e 2x cos 3x, xo = 0, X| - 0.3, X2 - 0.6, n 2 b. /(x) = sin(lnx), xq = 2.0, X| = 2.4, X2 = 2.6, = 2 c. /(x) = lnx, xo = 1, X| = 1.1, X2 = 1.3, X3 = 1.4, n = 3 d. /(x) = cosx -f sin x, Xq = 0, X| = 0.25, X2 = 0.5, X3 = 1.0, n = 3

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QUESTION:

Construct the Lagrange interpolating polynomials for the following functions and find a bound for the absolute error on the interval [xq, x |. a. fix) e 2x cos 3x, xo = 0, X| - 0.3, X2 - 0.6, n 2 b. /(x) = sin(lnx), xq = 2.0, X| = 2.4, X2 = 2.6, = 2 c. /(x) = lnx, xo = 1, X| = 1.1, X2 = 1.3, X3 = 1.4, n = 3 d. /(x) = cosx -f sin x, Xq = 0, X| = 0.25, X2 = 0.5, X3 = 1.0, n = 3

ANSWER:

Step 1 of 14

(a)

The second degree Lagrange interpolating polynomial is given as

where the polynomials , for are determined using (3.2) with as

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