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Problem 1. Let xo = 0, x₁ = 1/2, and x2 = 1. Consider the degree n = 2 Lagrange interpolation problem. 1. Write down the Vandermonde matrix for this interpolation problem. 2. Compute the coefficients of the Lagrange basis functions Lo, L₁, and L₂2. 3. Graph the Lagrange basis functions together on the same axes. 4. Solve the Lagrange interpolation problem for f(x) = x², graph the interpolating polynomial, and find an upper bound on the error.

Problem 1. Let xo = 0, x₁ = 1/2, and x2 = 1. Consider the degree n = 2 Lagrange interpolation problem. 1. Write down the Vandermonde matrix for this interpolation problem. 2. Compute the coefficients of the Lagrange basis functions Lo, L₁, and L₂2. 3. Graph the Lagrange basis functions together on the same axes. 4. Solve the Lagrange interpolation problem for f(x) = x², graph the interpolating polynomial, and find an upper bound on the error.

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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Problem 1. Let xo = = 0, x₁ = 1/2, and x₂ : 1. Consider the degree n = = 2 Lagrange interpolation problem. = 1. Write down the Vandermonde matrix for this interpolation problem. 2. Compute the coefficients of the Lagrange basis functions Lo, L₁, and L₂. 3. Graph the Lagrange basis functions together on the same axes. 4. Solve the Lagrange interpolation problem for f(x) = x¹, graph the interpolating polynomial, and find an upper bound on the error.
Transcribed Image Text:Problem 1. Let xo = = 0, x₁ = 1/2, and x₂ : 1. Consider the degree n = = 2 Lagrange interpolation problem. = 1. Write down the Vandermonde matrix for this interpolation problem. 2. Compute the coefficients of the Lagrange basis functions Lo, L₁, and L₂. 3. Graph the Lagrange basis functions together on the same axes. 4. Solve the Lagrange interpolation problem for f(x) = x¹, graph the interpolating polynomial, and find an upper bound on the error.
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