nbm_ind_sle_ppt_seidel

# nbm_ind_sle_ppt_seidel - http/numericalmethods.eng.usf.edu...

This preview shows pages 1–9. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 08/11/11 http://numericalmethods.eng.usf.edu 1 Gauss-Siedel Method Industrial Engineering Majors Authors: Autar Kaw http://numericalmethods.eng.usf.edu Transforming Numerical Methods Education for STEM Undergraduates Gauss-Seidel Method http://numericalmethods.eng.usf.edu http://numericalmethods.eng.usf.edu Gauss-Seidel Method An iterative method. Basic Procedure :-Algebraically solve each linear equation for x i - Assume an initial guess solution array-Solve for each x i and repeat- Use absolute relative approximate error after each iteration to check if error is within a pre-specified tolerance. http://numericalmethods.eng.usf.edu Gauss-Seidel Method Why? The Gauss-Seidel Method allows the user to control round-off error . Elimination methods such as Gaussian Elimination and LU Decomposition are prone to prone to round-off error. Also: If the physics of the problem are understood, a close initial guess can be made, decreasing the number of iterations needed. http://numericalmethods.eng.usf.edu Gauss-Seidel Method Algorithm A set of n equations and n unknowns: 1 1 3 13 2 12 1 11 ... b x a x a x a x a n n = + + + + 2 3 23 2 22 1 21 ... b x a x a x a x a n 2n = + + + + n n nn n n n b x a x a x a x a = + + + + ... 3 3 2 2 1 1 . . . . . . If: the diagonal elements are non-zero Rewrite each equation solving for the corresponding unknown ex: First equation, solve for x 1 Second equation, solve for x 2 http://numericalmethods.eng.usf.edu Gauss-Seidel Method Algorithm Rewriting each equation 11 1 3 13 2 12 1 1 a x a x a x a c x n n--- = nn n n n n n n n n n n n n n n n n n n n n n a x a x a x a c x a x a x a x a x a c x a x a x a x a c x 1 1 , 2 2 1 1 1 , 1 , 1 2 2 , 1 2 2 , 1 1 1 , 1 1 1 22 2 3 23 1 21 2 2---------------- =---- =--- = From Equation 1 From equation 2 From equation n-1 From equation n http://numericalmethods.eng.usf.edu Gauss-Seidel Method Algorithm General Form of each equation 11 1 1 1 1 1 a x a c x n j j j j ∑ ≠ =- = 22 2 1 2 2 2 a x a c x j n j j j ∑ ≠ =- = 1 , 1 1 1 , 1 1 1--- ≠ =--- ∑- = n n n n j j j j n n n a x a c x nn n n j j j nj n n a x a c x ∑ ≠ =- = 1 http://numericalmethods.eng.usf.edu Gauss-Seidel Method Algorithm General Form for any row ‘i’ . , , 2 , 1 , 1 n i a x a c x ii n i j j j ij i i =- = ∑ ≠ = How or where can this equation be used?...
View Full Document

## This note was uploaded on 08/11/2011 for the course MATH 663 taught by Professor Ron during the Spring '11 term at University of the Philippines Diliman.

### Page1 / 38

nbm_ind_sle_ppt_seidel - http/numericalmethods.eng.usf.edu...

This preview shows document pages 1 - 9. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online