Obtain the Lagrange interpolating polynomial using all the data points below: 2.0 2.5 -0.9589 x 0.5 1.0 1.5 f(x) 0.8415 0.9093 0.1411 -0.7568 The data points in #1 satisfy f(x) = sin 2x. Assuming that f(x) = sin 2x is the "theoretical function," plot f(x) = sin 2x against the Lagrange interpolating polynomials. Comment on the convergence of the Lagrange interpolating polynomial. (e.g. Is there a range within which it fits well with f(x) = sin 2x? Analyze briefly. 3 sentences max] Note: This is for students with gadgets.
Obtain the Lagrange interpolating polynomial using all the data points below: 2.0 2.5 -0.9589 x 0.5 1.0 1.5 f(x) 0.8415 0.9093 0.1411 -0.7568 The data points in #1 satisfy f(x) = sin 2x. Assuming that f(x) = sin 2x is the "theoretical function," plot f(x) = sin 2x against the Lagrange interpolating polynomials. Comment on the convergence of the Lagrange interpolating polynomial. (e.g. Is there a range within which it fits well with f(x) = sin 2x? Analyze briefly. 3 sentences max] Note: This is for students with gadgets.
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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Question
The data points in #1 satisfy f(x) = sin 2x. Assuming that f(x) = sin 2x is the
“theoretical function,” plot f(x) = sin 2x against the Lagrange interpolating
polynomials. Comment on the convergence of the Lagrange interpolating polynomial.
(e.g. Is there a range within which it fits well with f(x) = sin 2x? Analyze briefly. 3 sentences max)
Transcribed Image Text:Obtain the Lagrange interpolating polynomial using all the data points below:
1.5
f(x) 0.8415 | 0.9093 0.1411 -0.7568 | -0.9589
1.
0.5
1.0
2.0
2.5
The data points in #1 satisfy f (x) = sin 2x. Assuming that f (x) = sin 2x is the
"theoretical function," plot f (x) = sin 2x against the Lagrange interpolating
polynomials. Comment on the convergence of the Lagrange interpolating polynomial.
(e.g. Is there a range within which it fits well with f(x) = sin 2x? Analyze briefly. 3
sentences max) Note: This is for students with gadgets.
2.
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