Upcoming SlideShare
×

# Gauss

661 views

Published on

0 Likes
Statistics
Notes
• Full Name
Comment goes here.

Are you sure you want to Yes No
• Be the first to comment

• Be the first to like this

Views
Total views
661
On SlideShare
0
From Embeds
0
Number of Embeds
13
Actions
Shares
0
23
0
Likes
0
Embeds 0
No embeds

No notes for slide

### Gauss

1. 1.
2. 2. Gaussian Elimination<br />This method, which is a variation of Gauss elimination method, can solve up to 15 or 20 simultaneous equations, with 8 or 10 significant digits in the arithmetic of the computer.<br />This procedure differs from the Gaussian method in which when you delete an unknown, is removed from all remaining equations, ie, the preceding equation as well as pivot to follow.<br />Also all the rows are normalized when taken as pivot equation. The end result of such disposal creates an identity matrix instead of a triangular Gauss as it does, so do not use the back substitution.<br />
3. 3. EXAMPLE<br />Resoverthe following system of equations.<br /> 3X1 -0.1X2 - 0.2 X 3 = 7.85<br /> 0.1X1 +7X2 - 0.3 X 3 = -19.5<br /> 0.3X1 -0.2X2 +10 X 3 = 7.85<br /> First we express the coefficients and the vector of independent terms as an augmented matrix.<br />
4. 4. The first line is normalized by dividing by 3 for<br /> The term X1 can be removed from the second row by subtracting 0.1 times the first in the second row. In a similar way, subtracting 0.3 times the first in the third line delete the term with the third row X1F2-0.1F1F3-0.3F1<br />
5. 5. Then, the second line is normalized by dividing by 7.00333:<br /> Reducing X2 terms in the first and third equation is obtained:F1+ 0.033 F2F3+0.0190 F2 <br />
6. 6. The third line is normalized dividing by 10 010:<br /> Finally, the terms with X3 be reduced in the first and second equation to get:F1+ 0.068 F3F3+0.0425 F2 <br />X1=3<br />X2=-2.499<br />X3=7.001<br />
7. 7. ADVANTAGES OF THE METHOD OF GAUSS-JORDAN<br /> Note that back substitution is required for the solution.Although the methods of Gauss-Jordan and Gauss elimination can look almost identical, the former requires approximately 50% fewer operations.One of the main reasons for including the Gauss-Jordan, is to provide a direct method for obtaining the inverse matrix.<br />
8. 8. BIBLIOGRAPHY<br /><ul><li>http://personal.redestb.es/ztt/tem/t6_matrices.htm
9. 9. http://es.wikipedia.org/wiki/Matriz_(matem%C3%A1tica)
10. 10. http://www.gaussjordan.edu.mx/metodogj.html
11. 11. http://docencia.udea.edu.co/GeometriaVectorial/uni2/seccion21.html
12. 12. http://thales.cica.es/rd/Recursos/rd99/ed99-0289-02/inv02.html</li>