Algorithmic and Computational Mathematics Assignment
- Subject Code :
AM41AC
- Country :
United Kingdom
TASK 1:
- Give the description of Simulated Annealing function optimisation method for minimising continuous functions. Include its concept, mathematical formulation, and algorithmic implementation. (4 marks)
- In what aspect(s) the method can be varied? How do variations influence its performance? What are the advantages and deficiencies of the variants of the method? (4 marks)
- Minimise the function for ???? = 2 using your implementation of the method. Analyse the results for various values of the parameters of the method. (4 marks)
- Quantitatively estimate the performance of the method. Explain the differences in performance depending on the parameters of the method. (4 marks)
- Plot the optimisation trajectory, analyse its dependence on the parameter of the method. (4 marks)
TASK2:
For the function defined in Coursework 1 and ???? = 2 :
- Construct a new function as the intersection of ????(????????) with the plane ????0 = ????1. Provide mathematical expression for this function and plot it. Analyse the function for its roots, extreme points and its behaviour at the limits (5 marks)
- Find the root(s) of the function using a numerical method of your choice. Compare to the analytical result. (5 marks)
- Integrate the function using a numerical method of your choice and analytically. Compare the results. (5 marks)
- How will the function change if constructed as the intersection with the plain containing a different line on the ????0 ? ????1 plane? (5 marks)