Numerical Methods Golden Section Search Method Example http

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Example. 2 2 2 The cross-sectional area A of a gutter with equal base and edge length of 2 is given by (trapezoidal area): Find the angle which maximizes the cross-sectional area of the gutter. Using an initial interval of find the solution after 2 iterations. Convergence achieved if “ interval length ” is within 5 forcollege. com ht

Solution The function to be maximized is Iteration 1: Given the values for the boundaries of we can calculate the initial intermediate points as follows: f 2 f 1 X 1=? XL 6 X 2 X 1 Xu XL=X 2 X 2=X 1 Xu forcollege. com ht

Solution Cont To check the stopping criteria the difference between and is calculated to be 7 forcollege. com ht

Solution Cont Iteration 2 XL 8 X 2 X 1 Xu forcollege. com ht

Theoretical Solution and Convergence Iteration 1 2 3 4 5 6 7 8 9 xl 0. 0000 0. 6002 0. 8295 0. 9712 1. 0253 xu 1. 5714 1. 2005 1. 1129 1. 0794 1. 0588 x 1 0. 9712 1. 2005 0. 9712 1. 0588 1. 1129 1. 0588 1. 0794 1. 0588 1. 0460 x 2 0. 6002 0. 9712 0. 8295 0. 9712 1. 0588 1. 0253 1. 0588 1. 0460 1. 0381 f(x 1) 5. 1657 5. 0784 5. 1657 5. 1955 5. 1740 5. 1955 5. 1908 5. 1955 5. 1961 f(x 2) 4. 1238 5. 1657 4. 9426 5. 1657 5. 1955 5. 1937 5. 1955 5. 1961 5. 1957 1. 5714 0. 9712 0. 6002 0. 3710 0. 2293 0. 1417 0. 0876 0. 0541 0. 0334 The theoretically optimal solution to the problem happens at exactly 60 degrees which is 1. 0472 radians and gives a maximum cross-sectional area of 5. 1962. 9 forcollege. com ht

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