2. Consider the following interpolating points for the function f(x) = sin x: 1 1.3 1.6 f(x) 0 -0.80902 -0.95106 (a) Construct a linear Lagrange interpolating polynomial P₁(x) to approximate f(1.4)– Compute P₁(1.4) and error [ƒ(1.4) – P₁(1.4)|. - (b) Construct a quadratic Lagrange interpolating polynomial P₂ to approximate f(1.4). Compute P2(1.4) and error f(1.4) - P2(1.4). Is the approximation improved compared to (a)?
2. Consider the following interpolating points for the function f(x) = sin x: 1 1.3 1.6 f(x) 0 -0.80902 -0.95106 (a) Construct a linear Lagrange interpolating polynomial P₁(x) to approximate f(1.4)– Compute P₁(1.4) and error [ƒ(1.4) – P₁(1.4)|. - (b) Construct a quadratic Lagrange interpolating polynomial P₂ to approximate f(1.4). Compute P2(1.4) and error f(1.4) - P2(1.4). Is the approximation improved compared to (a)?
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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