1. Forward elimination of unknowns
2. Back substitution.
2. Back substitution.
The first part aims to reduce the original system of nxn matrix, n unknowns and n equations to upper triangular form.
Now you begin to eliminate the first unknown of the second equation to the last equation, in this case the pivot is the first variable in the first equation.
To do so first multiply the first equation by ( a_21)/a_11 so that a pivot is one, then subtracted from the second equation to make this the first unknown zero, the other unknowns in their coefficients change due to the abduction.
To do so first multiply the first equation by ( a_21)/a_11 so that a pivot is one, then subtracted from the second equation to make this the first unknown zero, the other unknowns in their coefficients change due to the abduction.
In general the factor will a_n1/a_11 where n indicates the equation that we are. After removal of the unknowns in the first column, we move the second equation but in this case the pivot is the second unknown and repeats the steps above to make this one of the original matrix upper triangular form.
Already in the upper triangular form we move to the next part of the method is the back substitution.
In the equation n unknown we would only equal to the answer’s vector, so using the following formula Xn= b_n/a_nn get the latest variable, and I know this can go back in the matrix and calculate all the variables.
In the equation n unknown we would only equal to the answer’s vector, so using the following formula Xn= b_n/a_nn get the latest variable, and I know this can go back in the matrix and calculate all the variables.
Digrama de flujo
From:Metodos numericos Grupo O1, Sudgrupo 2, UIS
A video demostration
Bibliografy
- Steven Chapra, Metodos numericos quinta edicion.
- http://www.slideshare.net/nestorbalcazar/mtodos-numricos-05
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