Page 13 - NUMERICAL METHOD

LU DECOMPOSITION : 8

DOOLITTLE METHOD

With Doolittle method, the solution of the system of linear equations still
uses the matrix form of = . But this time, coefficient matrix A is
decomposed into the product of a lower triangular matrix L and
an upper triangular matrix U. That is, = . The solution is
derived by solving the equation = by forward substitution
for y, and then solving the equations = by backward
substitution for x. Let’s work on an example to understand the whole
process.

EXAMPLE 1

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Using LU Doolittle Method, write the value of , and .

3 + 2 − = 10

7 − + 6 = 8

3 + 2 = 5

Solution :

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STEP 1 :

Rearrange the equation and write in the form of × = .

× =

3 2 −1 10
7 −1 6 × = 8
3 0 2 5