tensorium::solver::GaussSeidel< K > Class Template Reference

Placeholder for Gauss–Seidel iterative solver. More...

#include <LinearSolver.hpp>

Collaboration diagram for tensorium::solver::GaussSeidel< K >:

Static Public Member Functions
static Vector< K >	solve (const Matrix< K > &A, const Vector< K > &b, K tol=1e-8, int max_iter=2000)
	Solve the system using Gauss–Seidel method.

Public Attributes
aligned_vector< K >	data

Detailed Description

template<typename K>
class tensorium::solver::GaussSeidel< K >

Placeholder for Gauss–Seidel iterative solver.

The Gauss–Seidel method improves on Jacobi by using updated values as soon as they are available.

Update rule:

\[ x_i^{(k+1)} = \frac{1}{A_{ii}} \left(b_i - \sum_{j < i} A_{ij} x_j^{(k+1)} - \sum_{j > i} A_{ij} x_j^{(k)} \right) \]

Template Parameters

K	Scalar type

Member Function Documentation

solve()

template<typename K >

static Vector< K > tensorium::solver::GaussSeidel< K >::solve ( const Matrix< K > & A, const Vector< K > & b, K tol = 1e-8, int max_iter = 2000 )

static

Solve the system using Gauss–Seidel method.

Parameters

A	Matrix \( A \in \mathbb{R}^{n \times n} \)
b	Right-hand side vector
tol	Convergence tolerance
max_iter	Max iterations allowed

Returns

Solution vector \( x \)

Member Data Documentation

data

template<typename K >

aligned_vector<K> tensorium::solver::GaussSeidel< K >::data

---

The documentation for this class was generated from the following file:

• includes/Tensorium/Core/LinearSolver.hpp