Consider the data 0.0 0.25 0.5 f(r) | 1.5 1.0 0.5 (a) Use the Lagrange interpolating polynomial that interpolates all the points to find an approximation of ( f(0.4). (b) Construct a Newton's divided difference polynomial that interpolates f(x) at these points and use it to approximate f(0.4). (c) Comment on your observation of the approximate solutions obtained in (i) and (ii) above.
Consider the data 0.0 0.25 0.5 f(r) | 1.5 1.0 0.5 (a) Use the Lagrange interpolating polynomial that interpolates all the points to find an approximation of ( f(0.4). (b) Construct a Newton's divided difference polynomial that interpolates f(x) at these points and use it to approximate f(0.4). (c) Comment on your observation of the approximate solutions obtained in (i) and (ii) above.
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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plz solve question (a),(b),(c) with explanation and get multiple upvotes.
Transcribed Image Text:find the attachment questions, please help me
Consider the data
0.0 0.25 0.5
f(r) | 1.5
1.0 0.5
(a) Use the Lagrange interpolating polynomial that interpolates all the points to find an approximation of
f(0.4).
(b) Construct a Newton's divided difference polynomial that interpolates f(x) at these points and use it to
approximate f(0.4).
(c) Comment on your observation of the approximate solutions obtained in (i) and (ii) above.
(d) Set up the explicit normal equations to be used to obtain a least squares function of the form y = aeb
where a and b are constants, that fits the data and use it to approximate the value of f(0.4).
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