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Assume the polynomial P5(x) interpolates a function f(x) at the six data points (xi, f(xi)) with a-coordinates x₁ = 0.0, 2 = 0.2, x3 = 0.4, 4 = 0.6, 50.8, 06 = 1.0. Assume that the interpolation error at x = 0.3 is f(0.3) - P(0.3)| 0.3 is f(0.3) P5(0.3)| = 0.01. Estimate the new interpolation error f(0.3) - P(0.3)| that would result if two additional interpolation points (x7, y7) = (0.1, f(0.1)) and (x8, ys) = (0.5, f(0.5)) are added. What assumptions have you made to produce this estimate?

Assume the polynomial P5(x) interpolates a function f(x) at the six data points (xi, f(xi)) with a-coordinates x₁ = 0.0, 2 = 0.2, x3 = 0.4, 4 = 0.6, 50.8, 06 = 1.0. Assume that the interpolation error at x = 0.3 is f(0.3) - P(0.3)| 0.3 is f(0.3) P5(0.3)| = 0.01. Estimate the new interpolation error f(0.3) - P(0.3)| that would result if two additional interpolation points (x7, y7) = (0.1, f(0.1)) and (x8, ys) = (0.5, f(0.5)) are added. What assumptions have you made to produce this estimate?

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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Assume the polynomial \( P_5(x) \) interpolates a function \( f(x) \) at the six data points \( (x_i, f(x_i)) \) with x-coordinates \( x_1 = 0.0, x_2 = 0.2, x_3 = 0.4, x_4 = 0.6, x_5 = 0.8, x_6 = 1.0 \). Assume that the interpolation error at \( x = 0.3 \) is \( |f(0.3) - P_5(0.3)| = 0.01 \). Estimate the new interpolation error \( |f(0.3) - P_7(0.3)| \) that would result if two additional interpolation points \( (x_7, y_7) = (0.1, f(0.1)) \) and \( (x_8, y_8) = (0.5, f(0.5)) \) are added. What assumptions have you made to produce this estimate?
Transcribed Image Text:Assume the polynomial \( P_5(x) \) interpolates a function \( f(x) \) at the six data points \( (x_i, f(x_i)) \) with x-coordinates \( x_1 = 0.0, x_2 = 0.2, x_3 = 0.4, x_4 = 0.6, x_5 = 0.8, x_6 = 1.0 \). Assume that the interpolation error at \( x = 0.3 \) is \( |f(0.3) - P_5(0.3)| = 0.01 \). Estimate the new interpolation error \( |f(0.3) - P_7(0.3)| \) that would result if two additional interpolation points \( (x_7, y_7) = (0.1, f(0.1)) \) and \( (x_8, y_8) = (0.5, f(0.5)) \) are added. What assumptions have you made to produce this estimate?
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