Consider 4 1 2 A = 24 -1 , x= (x1, x2, x3), b = =...

  

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Consider 4 1 2 A = 24 -1 , x= (x1, x2, x3), b = = (9, -5,-9). 1 1 -3 (a) (3 points) Write the Jacobi'e iteration formula for computing the approximations xk of the exact solution (b) (7 points) Let the initial approximation be x = (3). (i) Compute x1, x2, and x by using the formula from part(a). (ii) Compute the error err = ||3x|| (You can consider the solution obtained in question 6 as the exact solution). (c) (3 points) Write the Gauss-Seidel iteration formula for computing the approximations xk of the exact solution x*. (d) (7 points) Let the initial approximation be x0 = (1,,3). (i) Compute x1, x, and x by using the formula from part(c). (ii) Compute the error err = ||3x|| (this error should, theoretically, be smaller than the error on part (b)). Consider 4 1 2 A = 24 -1 , x= (x1, x2, x3), b = = (9, -5,-9). 1 1 -3 (a) (3 points) Write the Jacobi'e iteration formula for computing the approximations xk of the exact solution (b) (7 points) Let the initial approximation be x = (3). (i) Compute x1, x2, and x by using the formula from part(a). (ii) Compute the error err = ||3x|| (You can consider the solution obtained in question 6 as the exact solution). (c) (3 points) Write the Gauss-Seidel iteration formula for computing the approximations xk of the exact solution x*. (d) (7 points) Let the initial approximation be x0 = (1,,3). (i) Compute x1, x, and x by using the formula from part(c). (ii) Compute the error err = ||3x|| (this error should, theoretically, be smaller than the error on part (b)).