a) Use Gauss Seidel Method with X=[0 00 0]* to approximate the solution to the given linear system with an error tolerance of ɛ,-0.02 in the maximum magnitude norm (¥). Ensure convergence before starting to iterate. -x, - x, + 5x, + x, = 0 4x, +x2 - x3 + X4 =-2 x, +4x, - x, - x, =-1 X, - x, + x, +3x, =1 b) Solve the same set of equations with the same initial conditions and error tolerance using SOR Method with w-1.1.

a) Use Gauss Seidel Method with X=[0 00 0]* to approximate the solution to the given linear system with an error tolerance of ɛ,-0.02 in the maximum magnitude norm (¥). Ensure convergence before starting to iterate. -x, - x, + 5x, + x, = 0 4x, +x2 - x3 + X4 =-2 x, +4x, - x, - x, =-1 X, - x, + x, +3x, =1 b) Solve the same set of equations with the same initial conditions and error tolerance using SOR Method with w-1.1.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Similar questions

Consider the linear model Y; = B + B1X1¡ + B2X2i + u; where error term and where E (u;|X1i, X2;) = 0, observations (Yi, X1i, X2;) are independent and identically distributed, 0 < E (Y4) < ∞, 0 < E (X;) < o, 0 < E(X) < ∞ and where X2; OLS estimators ß, and B, of the coefficients B, and B, unbiased and is the X. Are the consistent? Explain.
The nonlinear system 13-x+4x, 11+X-x 22+. G(x,,X2, X3) = 35 25 20 G a) Show that has unique fixed point in %3D b) Apply functional to approximate 2-iteration of the solution. c) Find the error bound
Compute ten convergent iterations using Jacobi and Gauss-Seidel method for the following system of linear equation x + y + 5z + 2w = 12 7x – 3y + 2z +w = 12 x + 3y – 2z + 8w = 5 2x – 6y + z + 2w = 6 = 0 as your initial approximation Usex, = yo = Zg = Wo
Show steps with solution please!!
Solve the following system of linear equations by Jacobi method for 'K= (0,1,2,3) 5X₁ X₂ + 3x3 = -2 X₁ + 2X2 = 3 2 x₁ - x2 - 4 X 3 =6
[] Solve the following system of equations. 3x - 4y = 3 7x+6y=7 X J = 1 + Continue 4 ابن W= Integrating Evide....docx ( 3 X WRITING-CENTER_.
Suppose a, = (1 -1 1 1) 5. az = (1 0 1 0) %3D %3D az = (1 1 1 1)''a¸ = (3 2 3 0)" - Please find out whether a1,a2,a3,&4 are linear independent or not?
9. In each part, determine whether the given 3-tuple is a solution of the linear system (a) (3, 1, 1) 2x1 - 4x₂ - x3 = X3 X₁ - 3x₂ + 3х1 — 5x2 — 3х3 (b) (3,-1, 1) x3 = = = (c) (13, 5, 2)
3 Find the least squares cubic equation that best fits the points: (-2,-2), (-1, 1), (0, 1), (1, 2), (2, 2).
Find the least-squares solution * of the system 1 01 0 1i 0 0 5 2. || ||
Explain the Initial Value Problems in homogeneous linear system?
Consider the system below * + dx3 + kx = 0 Show that V(x) = (kx² + x²) is a Lyapunov function. Is the system Lyapunov stable, asymptotically stable?