Problem 2. The iteration matrix of the Successive Relaxation for an n x n matrix A...

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Problem 2. The iteration matrix of the Successive Relaxation for an n x n matrix A is shown in class as BSRw = (DA - WLA) - [(1 w)DA+WUA]. a) (3 points) Find how det(BSR), the product of two triangular determinants, depends on w. b) (3 points) Deduce from a) that w (0, 2) is a necessary condition for SR to converge. c) (1 points) For A = 2 -1] take p(BSR) as a function of w = (1, 2) and determine the approxi- mate value of w that gives the smallest p(BSR). (You can do it analytically or numerically.) Problem 2. The iteration matrix of the Successive Relaxation for an n x n matrix A is shown in class as BSRw = (DA - WLA) - [(1 w)DA+WUA]. a) (3 points) Find how det(BSR), the product of two triangular determinants, depends on w. b) (3 points) Deduce from a) that w (0, 2) is a necessary condition for SR to converge. c) (1 points) For A = 2 -1] take p(BSR) as a function of w = (1, 2) and determine the approxi- mate value of w that gives the smallest p(BSR). (You can do it analytically or numerically.)