{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Lecture23 - Jacobi Method x 1 new new x2 new x3 new x4 = b1...

Info iconThis preview shows pages 1–5. Sign up to view the full content.

View Full Document Right Arrow Icon
Jacobi Method - - - = - - - = - - - = - - - = 44 old 3 43 old 2 42 old 1 41 4 new 4 33 old 4 34 old 2 32 old 1 31 3 new 3 22 old 4 24 old 3 23 old 1 21 2 new 2 11 old 4 14 old 3 13 old 2 12 1 new 1 a x a x a x a b x a x a x a x a b x a x a x a x a b x a x a x a x a b x / ) ( / ) ( / ) ( / ) ( It is important to have diagonal dominance: 1, | | | | n ii ij j j i a a =
Background image of page 1

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

View Full Document Right Arrow Icon
- - - - - - - - = 9 3 2 3 3 12 6 1 5 2 10 1 3 2 1 8 A is strictly diagonally dominant because diagonal elements are greater than sum of absolute value of other elements in row is not diagonally dominant Diagonally Dominant Matrix - - - - - - - = 9 3 2 3 3 12 6 1 5 2 6 1 3 2 1 8 A 6<|-1|+2+5=8
Background image of page 2
Example Not diagonally dominant !! Order of the equation can be important Rearrange the equations to ensure convergence - - - = + - = - - = + - 0 8 6 1 1 4 12 0 5 45 x 8 x 6 2 x x x 4 80 x 12 x 5 2 1 3 2 1 3 1 - - - = + - = + - = - - 12 0 5 0 8 6 1 1 4 80 x 12 x 5 45 x 8 x 6 2 x x x 4 3 1 2 1 3 2 1
Background image of page 3

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

View Full Document Right Arrow Icon
* Achieving diagonal dominance through pivoting (before starting any iterative methods): Iterative Methods 1 2 3 6 2 1 11 2 2 5 1 2 1 7 5 x x x -     - =     -   1 2 3 6 2 1 11 1 1 2 5 5 x x x -     = -      
Background image of page 4
Image of page 5
This is the end of the preview. Sign up to access the rest of the document.
  • Spring '09
  • RAPHAELHAFTKA
  • 1 j, Gauss–Seidel method, Diagonally dominant matrix, 0.5000 6.0000 2.0000 2.6146 3.6641 3.0000 2.3550 3.8587 4.0000 2.3767 3.8425 5.0000 2.3749 3.8439 6.0000 2.3750 3.8437 7.0000 2.3750 3.8438 8.0000 2.3750 3.8437 Gauss, 1.1809 Gauss, 2.6146 Second

{[ snackBarMessage ]}