Inverse of Hilbert matrix
H = invhilb(n)
H = invhilb(n) generates
the exact inverse of the exact Hilbert matrix for
than about 15. For larger
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.
the effects of two or three sets of roundoff errors:
The errors caused by representing
The errors in the matrix inversion process
The errors, if any, in representing
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.
Compute the fourth-order inverse Hilbert matrix.
ans = 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.