# invhilb

## Purpose

Inverse of the Hilbert matrix.

## Synopsis

    H = invhilb(n)

## Description

The exact inverse of the exact Hilbert matrix is a matrix whose elements are large integers. These integers can be represented as floatingpoint numbers without roundoff error as long as the order of the matrix, `n`, is less than 12 or 13. `invhilb(n)` generates this matrix. For larger `n`, `invhilb(n)` generates an approximation to the inverse Hilbert matrix.

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.

  ## Examples

  `invhilb(4)` is

           16    -120     240    -140
         -120    1200   -2700    1680
          240   -2700    6480   -4200
         -140    1680   -4200    2800

  ## See Also

      hilb

  ## References

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

  (c) Copyright 1994 by The MathWorks, Inc.