Find a rearrangement of the following systemn that guarantees both te Jacobi iteration and the Gauss-Seidel iteration of this system will converge to the unique solution of the system for any x0): x(0). 21 — 2х2 + 3.хз — 10х4 40. | 10x1 – 2x2 + 3x3 + 4x4 10, x1 – 10x2 + 3x3 4х4 — 20, - - 1 + 212 — 10хз + 44 — 30. -

Find a rearrangement of the following systemn that guarantees both te Jacobi iteration and the Gauss-Seidel iteration of this system will converge to the unique solution of the system for any x0): x(0). 21 — 2х2 + 3.хз — 10х4 40. | 10x1 – 2x2 + 3x3 + 4x4 10, x1 – 10x2 + 3x3 4х4 — 20, - - 1 + 212 — 10хз + 44 — 30. -

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter7: Distance And Approximation

Section7.2: Norms And Distance Functions

Problem 49EQ

See similar textbooks

Similar questions

Assume we have the following system of linear equation x1 + 4x2 = 5 x2 + 2x3 = 2 4x1 + 3x3 = 0 Note that a strictly diagonally dominant system guarantee the convergence of the methods such as Jacobi or Gauss-Seidal Method. After transforming the above system into a strictly diagonally dominant system and if we apply two steps of the Gauss-Seidal Methods from an initial guess (x1(1) , x2(1) , x3(1) ) = (0, 0, 0), then we get (x1(3) , x2(3) , x3(3) ). Fill in the following blanks by rounding in four decimal place. x1(3) = x2(3) = x3(3) =
Solve the following system of liniar equation by gauss-Jordan method.
Find the sum of components (x₁⁽²⁾ +x₂⁽²⁾ +x₃⁽²⁾) of second iteration of the Jacobi method for the following linear system, using the initial iteraion x⁽⁰⁾ =0 x₁-x₂-6x₃=3, x₁-2x₂+4x₃=3, 3x₁-x₂-3x₃=4.
Solve the given system with Cholesky decomposition. Use two iterations.
Find the first three iterations of the Jacobi method for the following linear systems, using x (0) = 0.5: 4x_1+x_2-x_3=5,-x_1+3x_2+x_3=-4,2x_1+2x_2+5x_3=1.
Find the general solution of the linear system (1) when A is then x n diagonal matrix A = diag[Aj, A21... ,An]- What condition onthe eigenvalues Al, ... , An will guarantee that limt_,,. x(t) = 0 for allsolutions x(t) of (1)?
#: Perform the first three iterations of Jacobi and Gauss- Seidel method, to solve the following linear system. Use X(0)=0: