Engineering Computation

Question

How to write a C program to read a linear system of equations, then how to evaluate it by using LU-Decomposition method and show the result. By using this program, how to solve the system of equation

4x1 2x2-x3=12

x1 x2 x3=6

2x1-x2-x3=3

Answer 1

Let's see. You want the readers to teach you C programming, write a program and help you understand LU? Why not do it yourself? Here are some hints to help you understand the math:

Put your equations above in the form A x = b, where

x-transpose = [ x1 x2 x3] and

b-transpose = [12 6 3]

The LU method decomposes A into LU where L is a lower triangular

matrix and U is an upper triangular matrix.

Let y = U x.

Then A x = b can be written as L U x = b, or L y = b.

Solve L y = b by forward substitution. Then using Ux = y, solve for x by a backward substitution.

Lookup a book called Numerical Recipes in C.