The Gauss Seidel method is an iterative process to solve a square system of (multiple) linear equations. It is also prominently known as ‘Liebmann’ method. In any iterative method in numerical analysis, every solution attempt is started with an approximate solution of an equation and iteration is performed until the desired accuracy is obtained. In Gauss-Seidel method, the most recent values are used in successive iterations. The Gauss-Seidel Method allows the user to control round-off error.
The Gauss Seidel method is very similar to Jacobi method and is called as the method of successive displacement. (Since recently obtained values are used in the subsquent equations). The Gauss Seidel convergence criteria depend upon the following two properties: (must be satisfied).
- The matrix is diagonally dominant.
- The matrix is symmetrical and positive.
- Step 1: Compute value for all the linear equations for Xi. (Initial array must be available)
- Step 2: Compute each Xi and repeat the above steps.
- Step 3: Make use of the absolute relative approximate error after every step to check if the error occurs within a pre-specified tolerance.
Code for Gauss Siedel method:
Enter the Total Number of Equations: 1 Enter Allowed Error: 0.5 Enter the Co-Efficients Matrix = 1 Matrix = 4 Y= 4.000000 Y= 4.000000 Solution Y: 4.000000
- Faster iteration process. (than other methods)
- Simple and easy to implement.
- Low on memory requirements.
- Slower rate of convergence. (than other methods)
- Requires a large number of iterations to reach the convergence point.
- Program for Picard's iterative method | Computational Mathematics
- Gauss's Forward Interpolation
- Mathematics | Probability
- Mathematics | Generalized PnC Set 1
- Mathematics | Generalized PnC Set 2
- Mathematics | Predicates and Quantifiers | Set 2
- Mathematics | Combinatorics Basics
- Mathematics | PnC and Binomial Coefficients
- Mathematics | Law of total probability
- Mathematics | Power Set and its Properties
- Mathematics | Covariance and Correlation
- Mathematics | Matrix Introduction
- Mathematics | Generating Functions - Set 2
- Mathematics | The Pigeonhole Principle
- Mathematics | Set Operations (Set theory)
If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to firstname.lastname@example.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.
Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.