Question

Please do question 5 for me. Thanks

Question 1 (10 marks) For a linear system Ax- b with 1 0 -1 A-1 2-1 2 -1 3 b=14 18 and compute by hand the first four iterations with the Jacobi method, using x()0 Hint: for the ease of calculation, keep to rational fractions rather than decimals Question 2 For the same linear system as in Question 1, compute by hand the first three iterations (10 marks) with the Gauss Seidel method, using X(0)-0. 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)-0. Hint: for the answer, retain rational fractions rather than decimals (5 marks) 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 i lx'k+1)-X(k) 〈 10-4, and find out how many iteration steps x)x(k) x(k+D 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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