Lecture+22-LU+methods

Lecture+22-LU+methods - LU Decomposition Decomposition...

Info iconThis preview shows pages 1–7. Sign up to view the full content.

View Full Document Right Arrow Icon

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

View Full DocumentRight Arrow Icon

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

View Full DocumentRight Arrow Icon

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

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: LU Decomposition Decomposition Methods (more than ONE!) * Doolittle decomposition lii = 1 * Crout decomposition uii = 1 (omitted) * Cholesky decomposition (for symmetric matrices) uii = lii Doolittle LU Decomposition Doolittle Algorithm Get 1s on diagonal of [ L ] ( lii =1) Operate on rows and columns sequentially, narrowing down to single element Identical to LU decomposition based on Gauss elimination, but different approach Doolittle LU Decomposition [ ] = = 44 34 33 24 23 22 14 13 12 11 43 42 41 32 31 21 44 43 42 41 34 33 32 31 24 23 22 21 14 13 12 11 u u u u u u u u u u 1 l l l 1 l l 1 l 1 a a a a a a a a a a a a a a a a A st 21 21 11 31 31 11 41 41 11 1 column: / ; / ; / l a u l a u l a u = = = 14 14 13 13 12 12 11 11 st a u ; a u ; a u ; a u : row 1 = = = = [ ] u u l u l u l u l u l u l u l u l u l u u l u l u u l u l u l u l u l u u l u u l u u l u l u u u u A 44 34 43 24 42 14 41 33 43 23 42 13 41 22 42 12 41 11 41 34 24 32 14 31 33 23 32 13 31 22 32 12 31 11 31 24 14 21 23 13 21 22 12 21 11 21 14 13 12 11 + + + + + + + + + + + + + + = Doolittle LU Decomposition nd 31 12 32 22 32 41 12 42 22 42 32 32 31 12 22 42 42 41 12 22 2 column: ; ( ) / ( ) / l u l u a l u l u a l a l u u l a l u u + = + = =- =- nd 21 12 22 22 21 13 23 2 22 23 3 21 14 24 24 22 21 12 23 21 13 24 4 4 2 21 1 2 : ; ; row l u u a l u u a l u u a a l u a u u u l u a l u + = + = + = =- =- =- [ ] 11 12 13 14 21 11 21 12 21 13 21 14 31 11 31 12 32 22 31 13 32 23 33 31 14 32 24 34 41 11 41 12 42 22 41 13 42 23 43 33 41 14 42 24 43 34 4 22 23 4 24 u u u u l u l u l u l u A l u l u l u l u l u u l u l u u l u l u l u l u l u l u l u l u u l u u u u + + + = + + + + + + + + + + + 11 12 13 14 21 22 23 24 31 32 33 34 41 42 43 44 a a a a a a a a a a a a a a a a Doolittle LU Decomposition rd 43 43 41 13 42 23 3 column: ( ) l a l u l u =-- 31 13 32 23 33 33 31 14 32 24 34 34 33 33 31 13 32 23 34 34 31 14 32 24 3 : ; rd row l u l u u a l u l u u a u a l u l u u a l u l u + + = + + = =-- =-- th 44 44 41 14 42 24 43 34 4 row: u a l u l u l u =--- [ ] u u l u l u l u l u l u l u l u l u l u u l u l u u l u l u l u l u l u u l u u l u u l u l u u u u A 44 34 43 24 42 14 41 33 43 23 42 13 41 22 42 12 41 11 41 34 24 32 14 31 33 23 32 13 31 22 32 12 31 11 31 24 14 21 23 13 21 22 12 21 11 21 14 13 12 11 + + + + + + + + + + + + + + = 11 12 13 14 21 22 23 24 31 32 33 34 41 42 43 44 a a a a a a a a a a a a a a a a Forward Substitution Very efficient for large matrices !...
View Full Document

This note was uploaded on 11/07/2011 for the course EGM 3344 taught by Professor Raphaelhaftka during the Spring '09 term at University of Florida.

Page1 / 35

Lecture+22-LU+methods - LU Decomposition Decomposition...

This preview shows document pages 1 - 7. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online