## What is Gauss-Seidel method with example?

# What is Gauss-Seidel method with example?

Table of Contents

## What is Gauss-Seidel method with example?

The coefficient matrix of the given system is not diagonally dominant. Hence, we re-arrange the equations as follows, such that the elements in the coefficient matrix are diagonally dominant….(New) All problem can be solved using search box.

Algebra | Matrix & Vector | Numerical Methods |
---|---|---|

Calculus | Geometry | Pre-Algebra |

## What is the condition for convergence of Gauss-Seidel method?

The Gauss-Seidel method converges if the number of roots inside the unit circle is equal to the order of the iteration matrix.

**Which of the following is applicable to the Gauss-Seidel method?**

Explanation: Gauss-Seidel method is applicable to strictly diagonally dominant or symmetric positive definite matrices because only in this case convergence is possible.

**What is the advantage of Gauss-Seidel method over Gauss Jacobi method?**

The results show that Gauss-Seidel method is more efficient than Jacobi method by considering maximum number of iteration required to converge and accuracy.

### Does Gauss-Seidel always converge?

Gauss-Seidel method is an iterative technique whose solution may or may not converge. Convergence is only ensured is the coefficient matrix, @ADnxn,is diagonally dominant, otherwise the method may or may not converge.

### What is disadvantages of Gauss-Seidel method?

Right Answer is: This method is not applicable to large power system. The convergence is affected by the choice of slack bus. It requires more number of iteration to obtain the solution. The rate of convergence is slow.

**Is the Gauss-Seidel method guaranteed to converge?**

The 2 x 2 Jacobi and Gauss-Seidel iteration matrices always have two distinct eigenvectors, so each method is guaranteed to converge if all of the eigenvalues of B corresponding to that method are of magnitude < 1. This includes cases in which B has complex eigenvalues.

**Why Gauss-Seidel is better than Gauss-Jordan?**

Answer. Gaussian Elimination helps to put a matrix in row echelon form, while Gauss-Jordan Elimination puts a matrix in reduced row echelon form. For small systems (or by hand), it is usually more convenient to use Gauss-Jordan elimination and explicitly solve for each variable represented in the matrix system.