Given the following table of data. Assuming x lies between x, and X2 and the step his fixed, show that both 3-terms Newton forward interpolation formula and Lagrange interpolation formula provide the same value for f(x). (hint: use x, as the initial point) X2 X4 f₂ f₁ X f X1 f₁ X3 f3 X5 fs

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Given the following table of data. Assuming x lies between x and x2 and the step his
fixed, show that both 3-terms Newton forward interpolation formula and Lagrange
interpolation formula provide the same value for f(x). (hint: use x, as the initial point)
X2
X
X3
X4
X5
f
f₂
f3
f₁
fs
X1
f₁
Transcribed Image Text:Given the following table of data. Assuming x lies between x and x2 and the step his fixed, show that both 3-terms Newton forward interpolation formula and Lagrange interpolation formula provide the same value for f(x). (hint: use x, as the initial point) X2 X X3 X4 X5 f f₂ f3 f₁ fs X1 f₁
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