This document discusses iterative methods for solving systems of equations. It describes the Jacobi method, which solves systems by iteratively updating solutions. It also describes Gauss-Seidel method, which improves on Jacobi by using previous updated solutions in the current iteration. Both methods are used to progressively calculate better approximations to the solution until reaching an acceptable level of accuracy.

1. SOLUTION OF EQUATIONS FOR ITERATIVOS METHODSBY:DUBAN CASTRO FLOREZ NUMERICS METHODS IN ENGINEERING2010

2. JACOBIA iterative method is a method that progressively it calculates approaches to the solution of a problem. To difference of the direct methods, in which the process should be finished to have the answer, in the iterative methods you can suspend the process to the i finish of an iteration and an approach is obtained to the solution.For example the method of Newton-RaphsonNUMERICS METHODS

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4. NUMERICS METHODSThe Jacobi method de is the iterative method to solve system of equations simple ma and it is applied alone to square systems, that is to say to systems with as many equations as incognito.The following steps should be continued: First the equation de recurrence is determined. Of the equation i and the incognito iclears. In notation matricial is written: where x is the vector of incognito It takes an approach for the solutions and to this it is designated for 3. You itera in the cycle that changes the approach

5. NUMERICS METHODSLeaving of x=1, y=2 applies two iterations of the Jacobi method to solve the system:

6. NUMERICS METHODSThis Di it is used as unemployment approach in the iterations until Di it is smaller than certain given value.Being Di:

7. NUMERICS METHODSGAUSS-SEIDELGiven a square system of n linear equations with unknown x:Where:

8. NUMERICS METHODSGAUSS-SEIDELThen A can be decomposed into a lower triangular component L*, and a strictly upper triangular component U:The system of linear equations may be rewritten as:

9. NUMERICS METHODSGAUSS-SEIDELThe Gauss–Seidel method is an iterative technique that solves the left hand side of this expression for x, using previous value for x on the right hand side. Analytically, this may be written as:However, by taking advantage of the triangular form of L*, the elements of x(k+1) can be computed sequentially using forward substitution:

10. BIBLIOGRAFIAhttp://en.wikipedia.org/wiki/Gauss%E2%80%93Seidel_method

11. http://es.wikipedia.org/wiki/M%C3%A9todo_iterativo

12. http://search.conduit.com/Results.aspx?q=METODOS+ITERATIVOS&meta=all&hl=es&gl=co&SearchSourceOrigin=13&SelfSearch=1&ctid=CT2247187NUMERICS METHODS