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 n, 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.

Comparing invhilb(n) with 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.


invhilb(4) is

See Also



[1] Forsythe, G. E. and C. B. Moler, Computer Solution of Linear Algebraic Systems, Prentice-Hall, 1967, Chapter 19.

  inv invoke (COM)