we
can use the LU factorisation of
to
solve the linear system
in
a two-step triangular process.
University Maths Notes: Matrices and Linear Algebra – Solving Simultaneous Equations Using LU Decomposition
Given a system of linear equations in
the formwe
can use the LU factorisation ofto
solve the linear systemin
a two-step triangular process.
Let
so
that
The
solution is obtained by solving recursively the two systems
and
Example: Use LU decomposition to solve
x-2y+3z=4
2x-5y+12z=6
2y-10z=3
we can write the matrix form of the system
The matrix decomposes:
We solve
|From which
Now solve
We have
The original system of
equations is