DSECL-ZC416 - Mathematical Foundations for Data Science - Science & Maths Assignment Help

Assignment Task

Answer all the questions

Q1) Write a code to perform Gauss elimination with and without pivoting for a 2 x 2 system, taking the number of significant digits (d) to be considered as user input. Using the code, solve the 2 x 2 system with random coefficients for d = 3, 4, 5 and 6. Display the results in a tabular form.

Q2) Write a code to perform

a) Gauss Jacobi method

b) Gauss Seidel method

for a 3 x 3 system by checking the convergence criteria using a suitable norm. Test the method on a random 3 x 3 system, which is diagonally dominant and check your results. A comparison between the two methods should be presented in tabular form. The stopping criteria could be taken as the lowest iteration number when the relative percentage error is less than 1%. Generate a random matrix of size 3 x 3 which cannot be made diagonally dominant and check if the iterates converge. The random entries generated should be of the form n.dddd

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