Based on some experimental data for f(r), we have to = 0.2, ƒ(10) = 1.36; x₁ = 0.4, ƒ(x₁) = 1.64; T₂ = 0.6, f(x₂) = 1.84. (a) Use above data and Newton's Divided-Difference formula to construct interpolating polynomial of degree 2 to interpolate f(r). Please write your polynomial in the form P₂ = ao + ª₁x + a₂x². (b) Construct the polynomial of degree one (P₁) and evaluate f(0.5). Suppose max(f"|) = 4 for x within [0.2, 0.6], using the error bound formula to estimate the maximum error |ƒ(1) - P₁(1).
Based on some experimental data for f(r), we have to = 0.2, ƒ(10) = 1.36; x₁ = 0.4, ƒ(x₁) = 1.64; T₂ = 0.6, f(x₂) = 1.84. (a) Use above data and Newton's Divided-Difference formula to construct interpolating polynomial of degree 2 to interpolate f(r). Please write your polynomial in the form P₂ = ao + ª₁x + a₂x². (b) Construct the polynomial of degree one (P₁) and evaluate f(0.5). Suppose max(f"|) = 4 for x within [0.2, 0.6], using the error bound formula to estimate the maximum error |ƒ(1) - P₁(1).
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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Please show all work when answering the following question.
This is a lecture problem that was unsolved
![Based on some experimental data for f(x), we have to
x₂ = 0.6, f(x₂) = 1.84.
(a) Use above data and Newton's Divided-Difference formula to construct interpolating polynomial of degree
2 to interpolate f(x). Please write your polynomial in the form P₂ = ao + a₁x + a₂x².
(b) Construct the polynomial of degree one (P₁) and evaluate f(0.5). Suppose max (f"|) = 4 for x within
[0.2, 0.6], using the error bound formula to estimate the maximum error f(x) - P₁(x)|.
=
0.2, f(ro) =
=
1.36; ₁= 0.4, f(x₁)
=
1.64;](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdb82eee3-c597-43b7-b98f-cffc18fbca72%2Fb8572aff-7f60-407e-81d3-2e26e403d74e%2F7dalgd_processed.png&w=3840&q=75)
Transcribed Image Text:Based on some experimental data for f(x), we have to
x₂ = 0.6, f(x₂) = 1.84.
(a) Use above data and Newton's Divided-Difference formula to construct interpolating polynomial of degree
2 to interpolate f(x). Please write your polynomial in the form P₂ = ao + a₁x + a₂x².
(b) Construct the polynomial of degree one (P₁) and evaluate f(0.5). Suppose max (f"|) = 4 for x within
[0.2, 0.6], using the error bound formula to estimate the maximum error f(x) - P₁(x)|.
=
0.2, f(ro) =
=
1.36; ₁= 0.4, f(x₁)
=
1.64;
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