codac2::CtcGaussSeidel Class Reference

Contractor for a linear system of interval equations, using a fixed-point approach based on the Gauss Seidel method. More...

#include <codac2_linear_ctc.h>

Public Member Functions
	CtcGaussSeidel ()
	Creates a contractor based on the Gauss Seidel method.
void	contract (IntervalMatrix &A, IntervalVector &x, IntervalVector &b) const
	Creates the domains according to the linear system: \(\mathbf{A}\cdot\mathbf{x}=\mathbf{b}\).

Detailed Description

Contractor for a linear system of interval equations, using a fixed-point approach based on the Gauss Seidel method.

No preconditioning is done (see CtcLinearPrecond for preconditioning).

The associated constraint is under the form \(\mathbf{A}\cdot\mathbf{x}=\mathbf{b}\), where \(\mathbf{A}\) is a squared matrix in \(\mathbb{R}^{n\times n}\) and \(\mathbf{x}\), \(\mathbf{b}\) vectors in \(\mathbb{R}^{n}\), provided that \(\textrm{diag}(\mathbf{A})\) is invertible (i.e., \(\mathbf{A}\) has no zero entry on its diagonal),

Note that it is efficient when the interval matrix \([\mathbf{A}]\) is close to the identity matrix. See the CtcLinearPrecond for this purpose.

Note also that this contractor is not idempotent, better improvements can be obtained with successive calls.

Reference: Applied Interval Analysis Luc Jaulin, Michel Kieffer, Olivier Didrit, Éric Walter 2001, Springer London doi: https://doi.org/10.1007/978-1-4471-0249-6 Sec 4.2.3, Page 73

Member Function Documentation

contract()

void codac2::CtcGaussSeidel::contract	(	IntervalMatrix &	A,
		IntervalVector &	x,
		IntervalVector &	b ) const

Creates the domains according to the linear system: \(\mathbf{A}\cdot\mathbf{x}=\mathbf{b}\).

Parameters

A	the domain \([\mathbf{A}]\)
x	the domain \([\mathbf{x}]\)
b	the domain \([\mathbf{b}]\)

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

• /home/simon/codac-simon/src/core/contractors/codac2_linear_ctc.h