Question

Question 1 (10 marks) For a linear system Ax b with 1 0-1 A-1 2-1 2-13 and b4 18 compute by hand the first four iterations with the Jacobi method, usg0 Hint: for the ease of calculation, keep to rational fractions rather than decimals. (10 marks) Question 2 For the same linear svstem as in Question 1. compute by hand the first three iterations with the Gauss Seidel method, us0 Hint: for the ease of calculation, keep to rational fractions rather than decimals. Question 3 For the same linear system as in Question 1. compute by hand the first only iteration with the relaxation method, choosing the relaxation parameter w = 0.5 and using x()-0 Hint: for the answer, retain rational fractions rather than decimals (5 marks) Question 4 (5 marks) By analysing the matrix A used for Questions 1-3, explain whether it is possible to determine, prior to running iterations, if the iterative schemes will converge Question 5 (10 marks) Using any programming language, implement the algorithms for Jacobi, Gauss-Seidel and relaxation methods (do not submit the code) and use it for the following questions: a) With each method, solve the system used in Questions 1-3 to a relative precision 104 and find out how many iteration steps for supremum norm were required with each method b) With a restriction to one-digit (0.x) precision for w, figure out its optimal value in the range from 0.1 to 0.9 for the problem in Question 3

Answer 1

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