Use the data given in Table 13.20 to estimate the gradient of the unknown function f (x)

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Use the data given in Table 13.20 to estimate the gradient of the unknown function f (x) at each node point using the following approaches.

a. Elementary approximation.

b. Central-difference method of order 2.

c. Central-difference method of order 4.

You are given that f (x) = 1 + x² cos x. Comment on your answers.
Table 13.20 Samples of an unknown function f(x) at various node points {Xn} Xn f(xn) - 2 -1.9 -1.8 -1.7 -1.6

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 1.0000 1.0100 1.0392 1.0860

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Introduction To Actuarial And Financial Mathematical Methods

ISBN: 9780128001561

1st Edition

Authors: Stephen Garrett

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Question Posted: Dec 11, 2023 07:00 AM

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Use the data given in Table 13.20 to estimate the gradient of the unknown function f (x)

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a Note that the data fixes the step size at h xnxn1 01 The elementary approach approximates the derivative at each xn using C Dhf xn This expression c...View the full answer

Introduction To Actuarial And Financial Mathematical Methods

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