In this problem, we want to figure out how the rate of convergence to the successive over-relaxation (SOR) solution of a linear system of equations depends on the relaxation parameter for w = 0.1, 0.2, … , 1.9. You can download the 100 × 100 matrix A and the 100 × 1 forcing function b as a zip file and put them in the memory by using the load command in MATLAB. Write a MATLAB program that determines the number of iterations to reach and error smaller than 10−4, where we will define the error at the end of step k as ||Ax(k) − b||. Use the initial condition x(0)i = 0 for all i. Your program should automatically make a plot of the number of iterations for convergence versus the value of w. Include a brief explanation of what you are seeing.
A deputy sheriff has been using a variety of problem solving approaches to address problems at a shopping mall where juveniles have been loitering, engaging in acts of vandalism, dumping trash, and generally causing traffic problems after hours in the parking lot.
February 18, 2021
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