0
Upcoming SlideShare
×

Thanks for flagging this SlideShare!

Oops! An error has occurred.

×
Saving this for later? Get the SlideShare app to save on your phone or tablet. Read anywhere, anytime – even offline.
Standard text messaging rates apply

# Solution of equations for methods iterativos

987

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
987
On Slideshare
0
From Embeds
0
Number of Embeds
2
Actions
Shares
0
28
0
Likes
0
Embeds 0
No embeds

No notes for slide

### Transcript

• 1. SOLUTION OF EQUATIONS FOR ITERATIVOS METHODS
BY:DUBAN CASTRO FLOREZ
NUMERICS METHODS IN ENGINEERING
2010
• 2. JACOBI
A iterative method is 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
NUMERICS METHODS
• 3. NUMERICS METHODS
• 4. NUMERICS METHODS
The Jacobi method de 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
• 5. NUMERICS METHODS
Leaving of x=1, y=2 applies two iterations of the Jacobi method to solve the system:
• 6. NUMERICS METHODS
This Di it is used as unemployment approach in the iterations until Di it is smaller than certain given value.
Being Di:
• 7. NUMERICS METHODS
GAUSS-SEIDEL
Given a square system of n linear equations with unknown x:
Where:
• 8. NUMERICS METHODS
GAUSS-SEIDEL
Then A can be decomposed into a lower triangular component L*, and a strictly upper triangular component U:
The system of linear equations may be rewritten as:
• 9. NUMERICS METHODS
GAUSS-SEIDEL
The Gauss–Seidel method is 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:
• 10. To solve the following exercise for the method of Gauss-Seidel with an initial value of (0,0,0). Use three iterations
NUMERICS METHODS
• 1ra iteration
• 2da iteration
NUMERICS METHODS
• 3ra iteration
• NUMERICS METHODS
GAUSS-SEIDEL RELAXATION
To solve the previous exercise for the gauss method for relaxation. .Use two iterations
Replacing with the initial values (0,0,0)
• 11.
• 1ra iteration
NUMERICS METHODS
• 12.
• 2da iteration
NUMERICS METHODS
• 13. BIBLIOGRAFIA
• http://en.wikipedia.org/wiki/Gauss%E2%80%93Seidel_method
• 14. http://es.wikipedia.org/wiki/M%C3%A9todo_iterativo
• 15. http://search.conduit.com/Results.aspx?q=METODOS+ITERATIVOS&meta=all&hl=es&gl=co&SearchSourceOrigin=13&SelfSearch=1&ctid=CT2247187
NUMERICS METHODS