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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.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.7: The Inverse Of A Matrix
Problem 32E
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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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