MATLAB Function Reference  invhilb

Inverse of the Hilbert matrix

Syntax

• ```H = invhilb(n)
```

Description

```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.

Limitations

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.

Examples

`invhilb(4)` is

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

See Also

`hilb`

References

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

© 1994-2005 The MathWorks, Inc.