Example: Determinant of a Hilbert Matrix

Consider the problem of computing the determinant of a 10 by 10 Hilbert matrix. The (i,j)-th entry of a Hilbert matrix is given by 1/(i+j+1). First do the computation using rational numbers to obtain the exact result.

This version of determinant uses Gaussian elimination.

Now use hardware floats.

The result given by hardware floats is correct to only four significant digits of precision. In the jargon of numerical analysis, the Hilbert matrix is said to be "ill-conditioned".

Now repeat the computation at a higher precision using Float

Reset digits to its default value.