Consider the linear system Ax = b, where, 3 ^-(). b-(3). A = b= ). Q1....

 

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Consider the linear system Ax = b, where, 3 ^-(²). b-(3). A = b= §). Q1. Show that p(A) < || A||... Q2. Find the LU decomposition of the matrix A using Cholesky method and then find the eigenvalues of the matrix U. Q3. Use necessary and sufficient condition of convergence to show that SOR method converges faster than Jacobi and Gauss-Seidel methods. Q4. Find error bound ||x-x(5) using SOR method when x(0) = [0.5, 0.5] for the solution of the linear system. Q5. How many iterations needed to get an accuracy within 10-4 using SOR method for solving the linear system. Q6. Find error bound for the relative error for the solution of linear system using approximate solution x() [1.001, 1.001]. Q7. If x)= [1.2, 1.2] is the approximate solution of linear system, then use the residual correction method (one iteration only) to improve the approximate solution. Consider the linear system Ax = b, where, 3 ^-(²). b-(3). A = b= §). Q1. Show that p(A) < || A||... Q2. Find the LU decomposition of the matrix A using Cholesky method and then find the eigenvalues of the matrix U. Q3. Use necessary and sufficient condition of convergence to show that SOR method converges faster than Jacobi and Gauss-Seidel methods. Q4. Find error bound ||x-x(5) using SOR method when x(0) = [0.5, 0.5] for the solution of the linear system. Q5. How many iterations needed to get an accuracy within 10-4 using SOR method for solving the linear system. Q6. Find error bound for the relative error for the solution of linear system using approximate solution x() [1.001, 1.001]. Q7. If x)= [1.2, 1.2] is the approximate solution of linear system, then use the residual correction method (one iteration only) to improve the approximate solution.

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