4. (50 points) The goal of this simulation study is to study the relative performance of...

 

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4. (50 points) The goal of this simulation study is to study the relative performance of uniform search, golden section search, and parabolic interpolation (algorithms 1-3 from class notes). Fix m =1000, and generate 21,..., m ~ Uniform(-0,0), with 1, 10, 102,..., 107. We want to find 771 *= arg min f(8), where f(8)=x -31. im1 For each value of 0, apply the three algorithms using a reasonable convergence criterion of your choice. Repeat this across 100 independent samples of size m, and report a single table with (a) the average runtime and (b) the average iterations until convergence for each algorithm. Interpret your results. 4. (50 points) The goal of this simulation study is to study the relative performance of uniform search, golden section search, and parabolic interpolation (algorithms 1-3 from class notes). Fix m =1000, and generate 21,..., m ~ Uniform(-0,0), with 1, 10, 102,..., 107. We want to find 771 *= arg min f(8), where f(8)=x -31. im1 For each value of 0, apply the three algorithms using a reasonable convergence criterion of your choice. Repeat this across 100 independent samples of size m, and report a single table with (a) the average runtime and (b) the average iterations until convergence for each algorithm. Interpret your results.