f(x) -1 0 3 -1 (a) Write the polynomial interpolating f(x) at the first three nodes in Lagrange form. (b) Use divided differences to find the polynomial p(r) interpolating f(x) in Newton form. (c) Assuming all derivatives of f are available, give an expression of the interpolation error f(t) – p(t) for some t € [-1,2].
f(x) -1 0 3 -1 (a) Write the polynomial interpolating f(x) at the first three nodes in Lagrange form. (b) Use divided differences to find the polynomial p(r) interpolating f(x) in Newton form. (c) Assuming all derivatives of f are available, give an expression of the interpolation error f(t) – p(t) for some t € [-1,2].
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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![f(x) -1 0 3 -1
(a) Write the polynomial interpolating f(x) at the first three nodes in Lagrange form.
(b) Use divided differences to find the polynomial p(r) interpolating f(x) in Newton form.
(c) Assuming all derivatives of f are available, give an expression of the interpolation error
f(t) – p(t) for some t € [-1,2].](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F00c0432c-48ac-45e1-aa6d-a359c2a8b7b3%2F6d721636-79ae-4dff-b5ca-ee2f5f9ef5ad%2Fut2r0gn.png&w=3840&q=75)
Transcribed Image Text:f(x) -1 0 3 -1
(a) Write the polynomial interpolating f(x) at the first three nodes in Lagrange form.
(b) Use divided differences to find the polynomial p(r) interpolating f(x) in Newton form.
(c) Assuming all derivatives of f are available, give an expression of the interpolation error
f(t) – p(t) for some t € [-1,2].
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