04.09.1
Chapter 04.09
Adequacy of Solutions
After reading this chapter, you should be able to:
1. know the difference between ill-conditioned and well-conditioned systems of
equations,
2. define the norm of a matrix, and
3. relate the norm of a matrix and of its inverse to the ill or well conditioning of the
matrix, that is, how much trust can you having in the solution of the matrix.
What do you mean by ill-conditioned and well-conditioned system of equations?
A system
of equations is considered to be well-conditioned if a small change in the
coefficient matrix or a small change in the right hand side results in a small change in the
solution vector.
A system of equations is considered to be ill-conditioned if a small change in the
coefficient matrix or a small change in the right hand side results in a large change in the
solution vector.
Example 1
Is this syste
m of equations well-conditioned?
999.7
4
999.32
21
y
x
Solution
The solution to the above set of equations is
1
2
y
x
Make a small change in the right hand side vector of the equations
