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AEB 6184 – Production Gauss Seidel

AEB 6184 – Production Gauss Seidel. Elluminate - 2. Basic Idea. Using a first-order Taylor series expansion. General Function. Take a general function Suppose we want to solve for. General Function. First Order Setup. Applying the first-order Taylor series expansion

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AEB 6184 – Production Gauss Seidel

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  1. AEB 6184 – Production Gauss Seidel Elluminate - 2

  2. Basic Idea • Using a first-order Taylor series expansion

  3. General Function • Take a general function • Suppose we want to solve for

  4. General Function

  5. First Order Setup • Applying the first-order Taylor series expansion • To find the solution we substitute for the desired value of the function

  6. Iterations

  7. Two Equations – Two Unknowns • Building a two equation system • Extending the Taylor expansion

  8. Matrix Taylor Expansion • In Matrix form

  9. Jacobian • Jacobian

  10. Iteration

  11. Suppose we want to find the solution for f(x) =0.95 and g(x) = 0.75, starting from x1 = 0.50 and x2 = 0.50.

  12. Parameters of the Cobb-Douglas Function • Solving parameters

  13. X1=50, x2=65, P=3.00, w1=0.005, w2=0.004, Y=75.0

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