Read the following and answer accordingly: (a) Find an interpolating polynomial of appropriate degree using the Newton's divided-difference method for f(x) = sin(x). Consider the nodes [0,7/2,7]. Use the polynomial to find an approximate value of f(3π/2). Add a new node to the above nodes, and find the interpolating polynomial. (e) Write down the interpolation error term for the above polynomial, and identify the polynomial. Estimate the upper bound of the interpolation error between the given function f(x) = sin(x), and the interpolating polynomial with four nodes. (b) (c)
Read the following and answer accordingly: (a) Find an interpolating polynomial of appropriate degree using the Newton's divided-difference method for f(x) = sin(x). Consider the nodes [0,7/2,7]. Use the polynomial to find an approximate value of f(3π/2). Add a new node to the above nodes, and find the interpolating polynomial. (e) Write down the interpolation error term for the above polynomial, and identify the polynomial. Estimate the upper bound of the interpolation error between the given function f(x) = sin(x), and the interpolating polynomial with four nodes. (b) (c)
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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![1. Read the following and answer accordingly:
(a)
Find an interpolating polynomial of appropriate degree using the Newton's divided-difference method
for f(x) = sin(x). Consider the nodes [0,1/2,π].
(b)
(c)
(d)
(e)
Use the polynomial to find an approximate value of f(3π/2).
Add a new node to the above nodes, and find the interpolating polynomial.
Write down the interpolation error term for the above polynomial, and identify the polynomial.
Estimate the upper bound of the interpolation error between the given function f(x) = sin(x), and
the interpolating polynomial with four nodes.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F59f7d71d-2a82-433b-9b08-c8f37e3ceef9%2Ff838508e-f758-4132-8a87-af87dae3b838%2Fx73fa3kg_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1. Read the following and answer accordingly:
(a)
Find an interpolating polynomial of appropriate degree using the Newton's divided-difference method
for f(x) = sin(x). Consider the nodes [0,1/2,π].
(b)
(c)
(d)
(e)
Use the polynomial to find an approximate value of f(3π/2).
Add a new node to the above nodes, and find the interpolating polynomial.
Write down the interpolation error term for the above polynomial, and identify the polynomial.
Estimate the upper bound of the interpolation error between the given function f(x) = sin(x), and
the interpolating polynomial with four nodes.
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