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# Iterative methods for the solution of systems of linear equations

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### Iterative methods for the solution of systems of linear equations

1. 1. ITERATIVE METHODS FOR THE SOLUTION OF SYSTEMS OF LINEAR EQUATIONS NORAIMA ZARATE GARCIA COD. 2073173 ING. DE PETROLEOS
2. 2. 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
3. 3. 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 :
4. 4. 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.
5. 5. METHOD OF GAUSS - SEIDEL RELAXATION WITH  Relaxation methods have the following scheme.  i 1      n w   aij x j   aij x (jk 1)  bi   (k )  xi( k )   j 1 j i 1   1  wx ( k 1) i aii  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.    a 1  wx   i 1 n a x  w a x (k ) ii i (k ) ij j ii ( k 1) i  w  aij x (jk 1)  wbi j 1 j i 1
6. 6. BIBLIOGRAPY  Es. Wikipedia.org.com
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