For the given problem: xe [-1.1] and ye [-1.1] = 0.001 And given algorithms: f(x, y)=sin(x-0.7)...

 

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For the given problem: xe [-1.1] and ye [-1.1] = 0.001 And given algorithms: f(x, y)=sin(x-0.7) + sin (y-0.7) Powell's method: Steepest descent gradient method 1. Calculate first two iterations of one assigned algorithm on paper. Please note that in the R space a single iteration consists of two steps - one for each search method. For the first search direction, present calculations in two first steps of numerical procedure used to find the value of a; for subsequent steps it will be sufficient to provide the a value. 2. Prepare 3D plot of the function (to check the shape of the functions and to be able to discuss the results) and contour plots. The iterations should be illustrated using these contour plots. 3. Use existing software (e.g. Matlab or Wolfram Alpha)to find the solution and check it against the plot obtained in the previous point. 4. Write simple programs that find the solution using both methods that have been assigned to the section. 5. Check the results obtained in subsequent iterations (repeat this point for various initial points). 6. Explain the differences that are apparent when various methods are applied to find a solution to the same problem. For the given problem: xe [-1.1] and ye [-1.1] = 0.001 And given algorithms: f(x, y)=sin(x-0.7) + sin (y-0.7) Powell's method: Steepest descent gradient method 1. Calculate first two iterations of one assigned algorithm on paper. Please note that in the R space a single iteration consists of two steps - one for each search method. For the first search direction, present calculations in two first steps of numerical procedure used to find the value of a; for subsequent steps it will be sufficient to provide the a value. 2. Prepare 3D plot of the function (to check the shape of the functions and to be able to discuss the results) and contour plots. The iterations should be illustrated using these contour plots. 3. Use existing software (e.g. Matlab or Wolfram Alpha)to find the solution and check it against the plot obtained in the previous point. 4. Write simple programs that find the solution using both methods that have been assigned to the section. 5. Check the results obtained in subsequent iterations (repeat this point for various initial points). 6. Explain the differences that are apparent when various methods are applied to find a solution to the same problem.