[6] ['Brute force' calculation of Gaussian quadrature weights and nodes] Let (3) w₁ƒ(x1) +w2ƒ(x2) be a quadrature formula to approximate the integral ſ¹₁ ƒ(x). Determine the weights {w₁, w₂} and nodes {x₁, x2} such that (3) is exact (no error) for f(x) = 1, x, x², and x³. Then show that the formula is not exact for f(x) = x4 and conclude that the degree of exactness is N = 3. =
[6] ['Brute force' calculation of Gaussian quadrature weights and nodes] Let (3) w₁ƒ(x1) +w2ƒ(x2) be a quadrature formula to approximate the integral ſ¹₁ ƒ(x). Determine the weights {w₁, w₂} and nodes {x₁, x2} such that (3) is exact (no error) for f(x) = 1, x, x², and x³. Then show that the formula is not exact for f(x) = x4 and conclude that the degree of exactness is N = 3. =
Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
6th Edition
ISBN:9781337111348
Author:Bruce Crauder, Benny Evans, Alan Noell
Publisher:Bruce Crauder, Benny Evans, Alan Noell
ChapterA: Appendix
SectionA.2: Geometric Constructions
Problem 10P: A soda can has a volume of 25 cubic inches. Let x denote its radius and h its height, both in...
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