Matlab

This problem, suggested by R.V. Andree, demonstrates ill conditioning where small changes in the coefficients cause large changes in the solu- tion). Use the left division operator to show that the solution of the systenm I .5x + 7.50 l y = 25.503 is x-2, v 3. Compute the residual Now change the term on the right-hand side of the second equation to 25.501, a change of about one part in 12000, and find the new solution and the residual. The solution is completely different. Also try changing this term to 25.502, 25.504, etc. If the coefficients are subject to experi- mental errors, the solution is clearly meaningless. Use rcond to find the condition estimator and det to compute the determinant. Do these values confirm ill conditioning? Another way to anticipate ill conditioning is to perform a sensitivity analysis on the coefficients: change them all in turn by the same small percentage, and observe what effect this has on the solution This problem, suggested by R.V. Andree, demonstrates ill conditioning where small changes in the coefficients cause large changes in the solu- tion). Use the left division operator to show that the solution of the systenm I .5x + 7.50 l y = 25.503 is x-2, v 3. Compute the residual Now change the term on the right-hand side of the second equation to 25.501, a change of about one part in 12000, and find the new solution and the residual. The solution is completely different. Also try changing this term to 25.502, 25.504, etc. If the coefficients are subject to experi- mental errors, the solution is clearly meaningless. Use rcond to find the condition estimator and det to compute the determinant. Do these values confirm ill conditioning? Another way to anticipate ill conditioning is to perform a sensitivity analysis on the coefficients: change them all in turn by the same small percentage, and observe what effect this has on the solution