A function y=f(x) is given by the following table. 12 84 21 343 4 Y 2.6 26 61 a) Explain and Construct the divided difference table for the above data and find f(19.75). b) Find a Lagrange interpolating polynomial which passes through the above points. c) Compute f(19.75) by Lagrange interpolating polynomial and compare your result with the value obtained in (a).

A function y=f(x) is given by the following table. 12 84 21 343 4 Y 2.6 26 61 a) Explain and Construct the divided difference table for the above data and find f(19.75). b) Find a Lagrange interpolating polynomial which passes through the above points. c) Compute f(19.75) by Lagrange interpolating polynomial and compare your result with the value obtained in (a).

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

A function y=f(x) is given by the following table.
12
21
343
4
2.6
26
61
84
a) Explain and Construct the divided difference table for the above data and find f(19.75).
b) Find a Lagrange interpolating polynomial which passes through the above points.
c) Compute f(19.75) by Lagrange interpolating polynomial and compare your result with the
value obtained in (a).

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