Let S (2) = [* dt, Vr E [0, 1]. Consider the table f (Ik) 1 0.25 0.2763263902 0.5 0.5204998778 3 0.75 0.7111556337 4 1 0.8427007929 (a.) Find the best Lagrange interpolation polynomial that approximate f (0.4).

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Let
f (x) =
e* dt,
Vr E [0, 1].
Consider the table
f (Ik)
k Ik
0 0
1 0.25 0.2763263902
0.5 0.5204998778
3 0.75 0.7111556337
4
1
0.8427007929
(a.) Find the best Lagrange interpolation polynomial that approximate f (0.4).
(b.) Use the divided difference formula to approximate f (0.6).
(c.) Find the natural cubic spline that interpolates f at these points.
Transcribed Image Text:Let f (x) = e* dt, Vr E [0, 1]. Consider the table f (Ik) k Ik 0 0 1 0.25 0.2763263902 0.5 0.5204998778 3 0.75 0.7111556337 4 1 0.8427007929 (a.) Find the best Lagrange interpolation polynomial that approximate f (0.4). (b.) Use the divided difference formula to approximate f (0.6). (c.) Find the natural cubic spline that interpolates f at these points.
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