Inverse of Hilbert matrix
H = invhilb(n)
The exact inverse of the exact Hilbert matrix is a matrix whose elements are large integers. These integers may be represented as floating-point numbers without roundoff error as long as the order of the matrix, n, is less than 15.
Comparing invhilb(n) with inv(hilb(n)) involves the effects of two or three sets of roundoff errors:
The errors caused by representing hilb(n)
The errors in the matrix inversion process
The errors, if any, in representing invhilb(n)
It turns out that the first of these, which involves representing fractions like 1/3 and 1/5 in floating-point, is the most significant.
16 -120 240 -140 -120 1200 -2700 1680 240 -2700 6480 -4200 -140 1680 -4200 2800
 Forsythe, G. E. and C. B. Moler, Computer Solution of Linear Algebraic Systems, Prentice-Hall, 1967, Chapter 19.