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Using the Lagrange interpolating polynomials, estimate f(1.25). What is the actual error at this point? What is the maximum error? Analyze briefly. 2 sentences max.

Using the Lagrange interpolating polynomials, estimate f(1.25). What is the actual error at this point? What is the maximum error? Analyze briefly. 2 sentences max.

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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Using the Lagrange interpolating polynomials, estimate f(1.25). What is the actual error at this point? What is the maximum error? Analyze briefly. 2 sentences max.

Obtain the Lagrange interpolating polynomial using all the data points below: 1.5 1.0 f(x) | 0.8415 | 0.9093 | 0.1411 | -0.7568 | -0.9589 1. 0.5 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. 3. Using the Lagrange interpolating polynomials, estimate f(1.25). What is the actual error at this point? What is the maximum error? Analyze briefly. 2 sentences max.
Transcribed Image Text:Obtain the Lagrange interpolating polynomial using all the data points below: 1.5 1.0 f(x) | 0.8415 | 0.9093 | 0.1411 | -0.7568 | -0.9589 1. 0.5 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. 3. Using the Lagrange interpolating polynomials, estimate f(1.25). What is the actual error at this point? What is the maximum error? Analyze briefly. 2 sentences max.
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