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.
