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

Iterative Jacobi solver with SIMD and OpenMP support. More...

#include <LinearSolver.hpp>

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

Static Public Member Functions
static Vector< K >	solve (const Matrix< K > &A, const Vector< K > &b, K tol=1e-10, int max_iter=2000)
	Solve the system using the Jacobi method.

Public Attributes
aligned_vector< K >	data

Detailed Description

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

Iterative Jacobi solver with SIMD and OpenMP support.

Iteratively solves \( Ax = b \) using the Jacobi method. Works best on diagonally dominant matrices.

Update rule:

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

Template Parameters

K	Scalar type (must be floating-point)

Member Function Documentation

solve()

template<typename K >

static Vector< K > tensorium::solver::Jacobi< K >::solve ( const Matrix< K > & A, const Vector< K > & b, K tol = 1e-10, int max_iter = 2000 )

inlinestatic

Solve the system using the Jacobi method.

Parameters

A	Matrix \( A \in \mathbb{R}^{n \times n} \)
b	Right-hand side vector
tol	Convergence tolerance (default = 1e-10)
max_iter	Maximum number of iterations (default = 2000)

Returns

Solution vector \( x \)

Exceptions

std::runtime_error

if diagonal is zero or near-zero

References MathsUtils::_abs(), tensorium::Matrix< K, RowMajor >::cols, tensorium::Matrix< K, RowMajor >::rows, sigma, and tensorium::Vector< K >::size().

Referenced by tensorium::jacobi_solve().

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Member Data Documentation

data

template<typename K >

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

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

• includes/Tensorium/Core/LinearSolver.hpp