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Let f(æ) = VE = ai. For æo = 2.6, #1 = 3.4, x2 = 3.9, 23 = 4, æ4 = 4.5, %3D • What is the maximum possible absolute error if we use the Lagrange polynomial of degree at most two that interpolates f(x) at the three points æ0, #1, and æ2 to approximate f(3.7)?

Let f(æ) = VE = ai. For æo = 2.6, #1 = 3.4, x2 = 3.9, 23 = 4, æ4 = 4.5, %3D • What is the maximum possible absolute error if we use the Lagrange polynomial of degree at most two that interpolates f(x) at the three points æ0, #1, and æ2 to approximate f(3.7)?

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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Let f(æ) = Væ = x3. For xo = 2.6, x1 = 3.4, x2 = 3.9, 23 = 4, x4 = 4.5, What is the maximum possible absolute error if we use the Lagrange polynomial of degree at most two that interpolates f(x) at the three points æ0, x1, and æ2 to approximate f(3.7)? • What is the maximum possible absolute error if we use the Hermite polynomial of degree at most seven that interpolates f(x) at the four points æ1, x2, x3, and x4 to approximate f(3.7)?
Transcribed Image Text:Let f(æ) = Væ = x3. For xo = 2.6, x1 = 3.4, x2 = 3.9, 23 = 4, x4 = 4.5, What is the maximum possible absolute error if we use the Lagrange polynomial of degree at most two that interpolates f(x) at the three points æ0, x1, and æ2 to approximate f(3.7)? • What is the maximum possible absolute error if we use the Hermite polynomial of degree at most seven that interpolates f(x) at the four points æ1, x2, x3, and x4 to approximate f(3.7)?
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