NORAIMA ZARATE GARCIA

COD. 2073173

ING. DE PETROLEOS

ITERATIVE METHODS FOR

THE SOLUTION OF SYSTEMS

OF LINEAR EQUATIONS

JACOBI METHOD

Solve systems of linear equations simpler and applies only to square systems, ie systems with as many

unknowns as equations

First, we determine the recurrence equation. For this order the equations and the Equations incógnitas. De

incógnitai is cleared. In matrix notation is written as matrix notation is written as

where x is the vector of unknowns.

It takes an approach to the solutions and this is designated by x

Is iterated in the cycle that changes the approach

METHOD OF GAUSS - SEIDEL

Lets find a solution to a system of 'n' equations in 'n' unknowns.

In each iteration we obtain a possible solution to the system with a particular error, as we

apply the method again, the solution may be more accurate, then the system is said to

converge, but if you repeatedly apply the solution method has an error growing states

that the system does not converge and can not solve the system of equations by this

method.

A general form:

Then solve for X :

METHOD OF GAUSS - SEIDEL There are zeros to the value of X and replaced in the equations to replace and so obtain

the unknowns

Repeating the procedure on two occasions we can go to find the error rate if it is minimal

or no podavia not about to suggest we should repeat the procedure until fingertips.

METHOD OF GAUSS - SEIDEL

RELAXATION WITH

Relaxation methods have the following scheme.

If 0 < w < 1 subrelajación called and is used when the Gauss-Seidel method does not

converge

1 < w Overrelaxation called and serves to accelerate the convergence.

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BIBLIOGRAPY

Es. Wikipedia.org.com