12x, +3x, – 5x, = 1 {3x, + 7x, +13.x, = 76 xq +5x, +3x, = 28 Using (a) Jacobi Iterative Method and (b) Gauss-Seidel Method, obtain the solution to the system with = [1,0, 1].Do four iterations only for each and compute for the relative error on the fourth iteration.
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- Apply the Gauss-Seidel Method to solve the linear system below with precision ε = 0.001. Consider as stopping criterion max1 ≤ i ≤ 3 |xki −x(k−1)i|<0.001 and, as initial approximation, x01=−5.6,x02=−2.5 ,x03=1.3 . Fill in the table below with the approximations obtained at each iteration of the method, until obtaining the established precision or until calculating 5 iterations. Leave the remaining rows with a value of 0 in all columns. Note that iteration 0 is already populated. Perform calculations with 4 decimal places and rounding. Use comma as separator for fractional values (Ex: 3.145 instead of 3.145).Find an example of a nonlinear equation, which is not solvable using any of the methods: separable, linear, solvable by a standard substitution (Bernoulli, homogeneous or linear combination) and which hasy=x2as one of its solutions.Find the solution to following system of equations by Gauss-Seidel Method, accurate to five (5) decimal digits. Start with x1 = x2 = x3 = x4 = x5 = x6 = 0. Show transformed equations.
- #: Perform the first three iterations of Jacobi and Gauss- Seidel method, to solve the following linear system. Use X(0)=0:Obtain the solution set of the linear equation system given below by using the Jacobi method.Take the initial values 0.NOTE: Proceed only 7 iterations.Solve the given system with Cholesky decomposition. Use two iterations.
- Consider finding an approximate solution to the nonlinear system of equations2x1 − x22 = 0,x1 + 0.77x2 = 1,where x(0) = 0.(a) Apply one iteration of the Newton method to obtain x(1)(b) Redo the previous part but by applying one iteration of the steepest descentmethod.Consider the following SEL. Calculate the solution for the system using the Gauss-Jacob iterative method (Consider k=3 and initial values equal to zero)Given the system of equationsx − 5y − z = −84x + y − z = 132x − y − 6z = −2Start with P0 = (0, 0, 0) and use Gauss-Seidel iteration to fi nd Pk for k = 1, 2, 3.Will Gauss-Seidel iteration converge to the solution