03: The Gauss-Seidel is considered to approximate the solution for the linear systemAx =b. Given0.5-0.250.5T0.125-0.250.5|0 -0.0625 0.125 -0.25exact solution is i =[l 1 -1 l], with initial guess ) = 0 , and the secondapproximations is r =[1.375 0.375 -0.46875 0.734375]. In l norm, find3. the relative error in approximating ž using .

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03: The Gauss-Seidel is considered to approximate the solution for the linear system Ax =b. Given 0.5 -0.25 0.5 0.125 -0.25 0.5 0 -0.0625 0.125 -0.25 exact solution is i =[l 1 -1 lJ, with initial guess ) = 0 , and the second approximations is r =[1.375 0.375 -0.46875 0.734375]. In l norm, find 3. the relative error in approximating i using i.

03: The Gauss-Seidel is considered to approximate the solution for the linear system Ax =b. Given 0.5 -0.25 0.5 0.125 -0.25 0.5 0 -0.0625 0.125 -0.25 exact solution is i =[l 1 -1 lJ, with initial guess ) = 0 , and the second approximations is r =[1.375 0.375 -0.46875 0.734375]. In l norm, find 3. the relative error in approximating i using i.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Differential Equations

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Question

03: The Gauss-Seidel is considered to approximate the solution for the linear system
Ax =b. Given
0.5
-0.25
0.5
T
0.125
-0.25
0.5
|0 -0.0625 0.125 -0.25
exact solution is i =[l 1 -1 l], with initial guess ) = 0 , and the second
approximations is r =[1.375 0.375 -0.46875 0.734375]. In l norm, find
3. the relative error in approximating ž using .

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03: The Gauss-Seidel is considered to approximate the solution for the linear system Ax =b. Given 0.5 -0.25 0.5 0.125 -0.25 0.5 0 -0.0625 0.125 -0.25 exact solution is i =[1 1 -1 1], with initial guess =0, and the second approximations is r = [1.375 0.375 -0.46875 0.734375]. In l norm, find 4. an error bound for approximating ï using .
Use the Jacobi method to find approximate solutions to 3x110x24x3 = 9 20x1 + 2x2 + 3x3 = 25 2x1x2 + 5x3 = 6 starting the initial values 1 = 1,2 = 1,and x3 = 1.2 and iterating until error is less than 2%. Round-off intermediate computed values to 7 decimal places and the answer to 5 decimal places. Reminder: Arrange the system to be Diagonally Dominant before iteration. O x1 =0.99789, x2 -1.00353, x3 =1.00476 X1 -0.99893, X2=1.00254, x3 =1.00155 O x1 =1.00092, x2 -0.99867, x3 =0.99761 O x₁ =1.00022, x2 -0.99960, x3 =0.99956 O none of the choices
Need to be solved correclty
When Newton's method with x0 = (1, 1)' is used to compute x2) for the system of equations given by 4 x1? – x3 4 x1x - x1 the value of x is equal to: (Choose the closest answer) = 0, = 1, Select one: O a. O.465116279069767 O b. 0.60000000000000 c. 0.449191878350617 d. 0.898160940910907 e. 0.890310077519380
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Q. 3 Find the solution of the following system of linear equations using Jacobi's method, starting with the initial approximation of XU = [0, 0, 01' . Perform only two iterations. %3D x+3y-5z = 4 x+4y-8z = 7 - 3x-7y+9z = -6
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Q3: The Gauss-Seidel is considered to approximate the solution for the linear system Ax =b. Given 0.5 -0.25 0.5 T = 0.125 -0.25 0.5 0 -0.0625 0.125 -0.25 exact solution is i=[1 1 -1 l], with initial guess =0 , and the second approximations is ) =[1.375 0.375 -0.46875 0.734375]. In l_ norm, find 3. the relative error in approximating i using .
5. Find the general solution of the given system. X' = [; x. Х.
Solve the following system of linear differential equations: y = 6y, - y2 y, = 2y, + 3y, а. 1 1 5r = k,e 2 4r + kge be 2 y 1 5r = k,e + kze² = k,e -4r + ke -5r Od. 1 -41 + ke -5r = kje
proof