Condition Numbers

In the previous section there appears to be a problem involved in accurately computing the inverse of R (Hilbert matrix). This was attributed to the so-called ill conditioning of R. We begin here with some simpler lower-order examples that illustrate how the solution to a linear system Ax = y can depend sensitively on A and y. This will lead us to develop a theory of condition numbers that warn us that the solution x might be inaccurately computed due to this sensitivity.