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Unformatted text preview: 6‐ If no divergence problems are encountered, Newton‐Raphson converges faster than the bisection method. 7‐ The modified secant method is considered a bracketing method. 8‐ The modified secant method converges faster than the secant method. 9‐ The constant φ in the golden search method varies from one iteration to the next. 10‐ For a given function, a local maximum is smaller than a global maximum. 5 Louisiana State University CE 2720 (Fall 2009) Mid-Term Exam 1 (Practice) Formula Sheet: εa = x new − x old r r x100% x new r xr = xl + xu 2 φ = 1.618034 d = (φ − 1)( x u − x l ) x1 = x l + d x2 = xu − d – – If f(x1)>f(x2): – x1 becomes the new xu – x2 becomes the new x1 – xL remains the same If f(x1)<f(x2): – x1 becomes the new x2 – x2 becomes the new xL – xu remains the same ε a = (2 − φ) xu − xl 100% x opt 6...
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- Fall '08