Iterativos Methods

Iterativos Methods

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  SOLUTION OF EQUATIONSFOR ITERATIVOS METHODSJeannie Castaño 2053298
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  JACOBIA iterative methodis 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-Raphson
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  The Jacobi methodde 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
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  Leaving of x=1,y=2 applies two iterations of the Jacobi method to solve the system:
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  This Di itis used as unemployment approach in the iterations until Di it is smaller than certain given value.Being Di:
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  GAUSS-SEIDELGiven a squaresystem of n linear equations with unknown x:Where:
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  GAUSS-SEIDELThen A canbe decomposed into a lower triangular component L*, and a strictly upper triangular component U:The system of linear equations may be rewritten as:
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  GAUSS-SEIDELThe Gauss–Seidel methodis 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:
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  To solve thefollowing exercise for the method of Gauss-Seidel with an initial value of (0,0,0). Use three iterations1ra iteration
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  2da iteration3ra iteration
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  GAUSS-SEIDEL RELAXATIONTo solvethe previous exercise for the gauss method for relaxation. .Use two iterationsReplacing with the initial values (0,0,0)
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  1ra iteration
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  2da iteration
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  BIBLIOGRAFIAhttp://es.wikipedia.org/wiki/M%C3%A9todo_iterativohttp://search.conduit.com/Results.aspx?q=METODOS+ITERATIVOS&meta=all&hl=es&gl=co&SearchSourceOrigin=13&SelfSearch=1&ctid=CT2247187http://en.wikipedia.org/wiki/Gauss%E2%80%93Seidel_method