The Gauss-Seidel Method is an iterative technique used to solve systems of linear equations, particularly useful for large, sparse systems where direct methods are computationally expensive. It improves upon the Jacobi Method by using the latest available values for the variables as soon as they are computed, potentially leading to faster convergence under certain conditions.

Gauss-Seidel Method

iterative technique

Systems of linear equations consist of two or more linear equations involving the same set of variables, and their solutions represent the points where these equations intersect in n-dimensional space. Solving these systems can be achieved through methods such as graphing, substitution, elimination, or using matrix operations like Gaussian elimination or Cramer's Rule.

systems of linear equations

Large sparse systems

direct methods

computationally expensive

The Jacobi Method is an iterative algorithm used to solve systems of linear equations, particularly useful for diagonally dominant or symmetric positive definite matrices. It operates by decomposing the matrix into its diagonal and off-diagonal components, iteratively refining the solution until convergence is achieved based on a specified tolerance level.

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