Consider the linear system, 2x1+ 2 = 1, 21 +2x2 = -1, with solution r1 =...

 

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Consider the linear system, 2x1+ 2 = 1, 21 +2x2 = -1, with solution r1 = 1, x2 = -1. %3D a) Write Jacobi's method in component form and take three steps starting from initial guess To (0,0)". Present the results in a table with the following format. column 1: k (iteration step) column 2: z (1st component of computed solution vector) column 3: (2nd component of computed solution vector) column 4: |leall (error norm) column 5: |lell/llek-1|| (ratio of successive error norms) Find the iteration matrix BJ and compute ||B||, p(B). Does the method converge? %3D (k) (k) b) Repeat for Gauss-Seidel. c) Repeat for optimal SOR. Which method converges fastest? Explain. Consider the linear system, 2x1+ 2 = 1, 21 +2x2 = -1, with solution r1 = 1, x2 = -1. %3D a) Write Jacobi's method in component form and take three steps starting from initial guess To (0,0)". Present the results in a table with the following format. column 1: k (iteration step) column 2: z (1st component of computed solution vector) column 3: (2nd component of computed solution vector) column 4: |leall (error norm) column 5: |lell/llek-1|| (ratio of successive error norms) Find the iteration matrix BJ and compute ||B||, p(B). Does the method converge? %3D (k) (k) b) Repeat for Gauss-Seidel. c) Repeat for optimal SOR. Which method converges fastest? Explain.

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Given Solution given system is 2221 X 2121 diagmatly olomunant we X2 ... View the full answer