MATLAB Function Reference |

**Syntax**

**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**

**See Also**

**References**

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

inv | ipermute |

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