Gauss-Seidel Method with Relaxation

[ErickOF]

Select the programming language

Python, Octave

Select the method type

Systems of Equations

Describe the algorithm steps

Must follow Gauss-Seidel steps, but after compute $x_{i+1}$ value, must apply relaxation following $x_{i+1}^{relaxed} = \lambda x_{i+1} + (1 - \lambda) x_{i}$. Then apply a new Gauss-Seidel step using the new $x_{i+1}^{relaxed}$.

Input values

Same as Gauss-Seidel Method, but with the new param $\lambda$.

Expected behavior

Must return the solution for each steps and the error.

Tests

Test 1: 03 Numerical Methods CH12 Gauss Seidel with Relaxation
Test 2: Numerics 6e: Gauss-Seidel and Relaxation Method (Fall 2023)
Test 3: Iterative Methods for Linear Systems, Jacobi, Gauss Seidel, and Relaxation (Matlab Implementation)