|MATLAB Function Reference|
Inverse of the Hilbert matrix
H = invhilb(n)
generates the exact inverse of the exact Hilbert matrix for
n less than about 15. For larger
invhilb(n) generates an approximation to the inverse Hilbert matrix.
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.
inv(hilb(n)) involves the effects of two or three sets of roundoff errors:
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.
 Forsythe, G. E. and C. B. Moler, Computer Solution of Linear Algebraic Systems, Prentice-Hall, 1967, Chapter 19.