metodos interactivos
TRANSCRIPT
INTERACTIVE METHODS
Method of Jacobi and Gauss-Seidel
CONCEPT OF SYSTEM OF LINEAR EQUATIONS.System of m equations with n unknowns. It is a set of algebraic expressions of the form
Two numerical methods, which allows us to find solutions to systems with the same number of equations as unknowns.
In both methods the following process is done with a little variation on Gauss-Seidel
We have these equations:
1. Solve each of the unknowns in terms of the others.
2. Give initial values to the unknowns
By Jacobi:Replace in each equation the initial values, this will give new values to be used in the next iteration
For Gauss-SeidelReplace the values in each equation but found next.
It performs many iterations you want, using as initial values the new values found. You can stop the execution of the algorithm to calculate the error of calculation, which we can find with this formula: sqr ((x1-x0) ^ 2 + (y1-y0) ^ 2 + (z1-z0) ^ 2)
With jacobi
With Gauss-Seidel
The main difference is that the method of gauss_seidel uses the values found immediately, then makes the whole process faster, and consequently makes this a more effective method.
The formulas used in the excel sheet for the method of Jacobi is
Corresponding to the variable X, Y, Z and failure respectively.And to the Gauss-Seidel: