Download presentation

Presentation is loading. Please wait.

Published byAllan Batty Modified over 3 years ago

1
Method If an nxn matrix A has an LU-factorization, then the solution of AX = b can be determined by a Forward substitution followed by a Back substitution [A] = [L][U] where [L] = lower triangular matrix all of whose diagonal entries are different from zero. [U] = upper triangular matrix all of whose diagonal entries are different from zero. LU Decomposition

2
How can this be used? Given [A][X] = [b] 1.Decompose [A] into [L] and [U] (LU)X = b L(UX) = b ; Let UX = z then LZ = b 1.Use Forward substitution to Solve [L][Z] = [b] for [Z] 2.Use Back substitution to Solve [U][X] = [Z] for [X]

3
Exercise 2.5 ; Page # 136; Qn # 1 3

4
Ax = b (LU)X = b L(UX) = b LZ = b; Let UX = Z 4

5
[L][Z] = [b] Solve for [Z] using Forward Substitution :

6
Complete the forward substitution to solve for [Z]

7
[U][X] = [Z] Solve for [X] using Back Substitution :

8
The Solution is :

9
Method: [A] Decompose to [L] and [U] Storage of Multipliers Scheme :

10
Exercise 2.5; Page #136; Qn # 5 Finding the [U] matrix Step 1:

11
Finding the [U] Matrix Step 2: Matrix after Step 1:

12
Finding the [L] matrix http://numericalmethods.eng.usf.edu

13
Finding the [L] Matrix

14
[L][Z] = [b] Solve for [Z] using Forward Substitution :

15
Complete the forward substitution to solve for [Z]

16
[U][X] = [Z] Solve for [X] using Back Substitution :

17
The Solution is :

18
Limitations to use this Procedure : Interchanging of any two rows not allowed. Only elementary row operation permitted is the one that subtract a multiple of one row to another. In matrix A, if then this procedure fails. In matrix if, or in if then this procedure fails.

19
Test for you? Exercise 2.5 ; Page # 136; Qn # 7 19

Similar presentations

OK

Mujahed AlDhaifallah (Term 342) Read Chapter 9 of the textbook

Mujahed AlDhaifallah (Term 342) Read Chapter 9 of the textbook

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on aircraft landing gear systems Ppt on natural disasters in india Ppt on keeping it from harold free download Ppt on total internal reflection experiment Ppt on market friendly state Ppt online shopping project Ppt on bharatiya janata party Converter pub to ppt online shopping Ppt on interesting facts about dreams Ppt on cloud computing in ieee format