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[BE] Chapter 3.2, Problem 2E (a) Given the data points (1, 0), (2, In 2), (4, In 4), find the degree 2 interpolating polynomial. (b) Use the result of (a) to approximate In 3, (c) Use Theorem 3.3 to give an error bound for the approximation in part (b). (d) Compare the actual error to your error bound.

[BE] Chapter 3.2, Problem 2E (a) Given the data points (1, 0), (2, In 2), (4, In 4), find the degree 2 interpolating polynomial. (b) Use the result of (a) to approximate In 3, (c) Use Theorem 3.3 to give an error bound for the approximation in part (b). (d) Compare the actual error to your error bound.

Advanced Engineering Mathematics
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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I would like someone to explain what to do in b and c. Thank you.

 

[BE] Chapter 3.2, Problem 2E (a) Given the data points (1, 0), (2, In 2), (4, In 4), find the degree 2 interpolating polynomial. (b) Use the result of (a) to approximate In 3, (c) Use Theorem 3.3 to give an error bound for the approximation in part (b). (d) Compare the actual error to your error bound.
Transcribed Image Text:[BE] Chapter 3.2, Problem 2E (a) Given the data points (1, 0), (2, In 2), (4, In 4), find the degree 2 interpolating polynomial. (b) Use the result of (a) to approximate In 3, (c) Use Theorem 3.3 to give an error bound for the approximation in part (b). (d) Compare the actual error to your error bound.
Theorem 3.3 Assume that P(x) is the (degree n - 1 or less) interpolating polynomial fitting the n points (x₁, y₁), (In, Yn). The interpolation error is f(x) - P(x) = = .. (x − x1)(x − x₂) ··· (x · n! - xn) f(n) (c), where c lies between the smallest and largest of the numbers X, X1,..., n. (3.6)
Transcribed Image Text:Theorem 3.3 Assume that P(x) is the (degree n - 1 or less) interpolating polynomial fitting the n points (x₁, y₁), (In, Yn). The interpolation error is f(x) - P(x) = = .. (x − x1)(x − x₂) ··· (x · n! - xn) f(n) (c), where c lies between the smallest and largest of the numbers X, X1,..., n. (3.6)
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