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0. (Multiply the linear factors together, but leave P(x) as a sum of 3 quadratics in the variable x.) DELIVERABLES: All your work in constructing the polynomial. b) Derive the quadrature formula of

0. (Multiply the linear factors together, but leave P(x) as a sum of 3 quadratics in the variable x.) DELIVERABLES: All your work in constructing the polynomial. b) Derive the quadrature formula of

Operations Research : Applications and Algorithms
Operations Research : Applications and Algorithms
4th Edition
ISBN:9780534380588
Author:Wayne L. Winston
Publisher:Wayne L. Winston
Chapter7: Transportation, Assignment, And Transshipment Problems
Section7.6: Transshipment Problems
Problem 4P
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a)Determine the Lagrange form of the interpolating polynomial P(x) that interpolates a function f(x) at x = 0, h and 3h, where h > 0. (Multiply the linear factors together, but leave P(x) as a sum of 3 quadratics in the variable x.) DELIVERABLES: All your work in constructing the polynomial.

b) Derive the quadrature formula of the form a0f(0) + a1f(h) + a2f(3h) for approximating I = R 3h 0 f(x)dx that results from approximating the integral I by I ≈ R 3h 0 P(x)dx.

Note: if you know only 3 function values of f(x) and they are at 3 unequally-spaced points 0, h and 3h, then this kind of quadrature formula can be used to approximate I. DELIVERABLES: All your work in deriving the quadrature formula.

(a) (2 points) Determine the Lagrange form of the interpolating polynomial P(x) that interpolates a function f(x) at x = 0, h and 3h, where h> 0. (Multiply the linear factors together, but leave P(x) as a sum of 3 quadratics in the variable x.) All your work in constructing the polynomial. DELIVERABLES: (b) (4 points) Derive the quadrature formula of the form aof (0) + a₁f(h) + a₂f (3h) for approximating I = f3h f(x)dx that results from approximating the integral I by I≈ f3h P(x) dx. 0 0 Note: if you know only 3 function values of f(x) and they are at 3 unequally-spaced points 0, h and 3h, then this kind of quadrature formula can be used to approximate I. DELIVERABLES: All your work in deriving the quadrature formula.
Transcribed Image Text:(a) (2 points) Determine the Lagrange form of the interpolating polynomial P(x) that interpolates a function f(x) at x = 0, h and 3h, where h> 0. (Multiply the linear factors together, but leave P(x) as a sum of 3 quadratics in the variable x.) All your work in constructing the polynomial. DELIVERABLES: (b) (4 points) Derive the quadrature formula of the form aof (0) + a₁f(h) + a₂f (3h) for approximating I = f3h f(x)dx that results from approximating the integral I by I≈ f3h P(x) dx. 0 0 Note: if you know only 3 function values of f(x) and they are at 3 unequally-spaced points 0, h and 3h, then this kind of quadrature formula can be used to approximate I. DELIVERABLES: All your work in deriving the quadrature formula.
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