Problem 4. Find the first two iterations of the SOR method with w1.1, w 1.2 and 1.3 for the follo...
Problem 3. Find the first two iterations of both the Jacobi and the Gauss-Seidel methods for the following linear systems, using X 0. a. b. 1011-22-9
Problem 3. Find the first two iterations of both the Jacobi and the Gauss-Seidel methods for the following linear systems, using X 0. a. b. 1011-22-9
Test II. ITERATIVE SOLUTION OF SYSTEMS OF LINEAR EQUATIONS Solve the following linear system using Gauss-Seidel iterative method. Use x = x; = x; =0 as initial guesses. Perform two iterations of the method to find xị, xį and xſ and fill the following table. Show all the calculation steps. 10x, + 2x2 - X3 = 27 -3x, - 6x2 + 2xz = -61.5 X1 + x2 + 5x3 = -21.5
Question3 Find the first two iterations of the Gausses-Seidel iteration niethad, using the initial values (X ) = (0,0,0) and then calculate the maximum error. x2–2x2-*s=-4 Xz+2x = 0
2. 3x 25」LX2 (a) Perform three iterations for the following iterative methods using initial guess x0. Compute relative residual for each iteration. (You can use a calculator) · Jacobi method » Gauss-Seidel method · SOR method with ω 1.2 (b) For each iterative method, express its iteration procedure in the following matrix form: In other words, determine B and c for (2).
2. 3x 25」LX2 (a) Perform three iterations for the following iterative methods using initial guess x0. Compute relative...
Numerical method no programm needed
4. Use first three fixed point iterations to find the approximated so- lution of the following equation 2-e" +22 3 starting from Io = 1 and round the result to 4 significant digit. (Answer: r* 33 = 0.2459 ) =
Calculate two iterations of
Newton's Method to approximate a zero of the function using the
given initial guess. (Round your answers to three decimal
places.)
f(x) = x7 − 7, x1 =
1.2
Calculate two iterations of Newton's Method to approximate a zero of the function using the given initial guess. (Round your answers to three decimal places.) f(x) = x? - 7, x1 = 1.2 n X f(xn) f'(x) 1 2
4. Let A. Į2 2 01 carryonít 10 iterations of the power method with 4. Let A =-1 2-1 | . Carry out 10 iterations of the power method with normalization, starting with x( ) (1,1,1)T and using the linear functional p(x) = a1. What does the ratio Tk-(x(+)/x) approximate? Pxapproximate
4. Let A. Į2 2 01 carryonít 10 iterations of the power method with 4. Let A =-1 2-1 | . Carry out 10 iterations of the power method...
Question: 03 (9 Points) Solve the following equations using Newton Raphson method. Show first two iterations only (E3) f(x) = 4x1 + 2x1-6s。 五(x) =-3x1 + 2x2-x1x2 + 10-0
Question: 03 (9 Points) Solve the following equations using Newton Raphson method. Show first two iterations only (E3) f(x) = 4x1 + 2x1-6s。 五(x) =-3x1 + 2x2-x1x2 + 10-0
Use a calculator or program to compute the first 10 iterations of Newton's method for the given function and initial approximation. f(x) = 2 sinx-5x - 1, Xo = 1.3 Complete the table. (Do not round until the final answer. Then round to six decimal places as needed.) K хк k XK 1 6 2 7 3 8 4 9 5 10
(a) Draw the first two iterations of the Bisection method for finding the root of the nonlinear function in the figure below. Mark the first as I, and the second as 12. f(x) X a b (b) Compute the Taylor series approximation, up to and including third order terms of sin(I) about 10 = x/2.