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: