# invhilb

Inverse of Hilbert matrix

## Syntax

``H = invhilb(n)``
``H = invhilb(n,classname)``

## Description

example

````H = invhilb(n)` generates the exact inverse of the exact Hilbert matrix for `n` less than about 15. For larger `n`, the `invhilb` function generates an approximation to the inverse Hilbert matrix. ```
````H = invhilb(n,classname)` returns a matrix of class `classname`, which can be either `'single'` or `'double'`.```

## Examples

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Compute the fourth-order inverse Hilbert matrix.

`invhilb(4)`
```ans = 4×4 16 -120 240 -140 -120 1200 -2700 1680 240 -2700 6480 -4200 -140 1680 -4200 2800 ```

## Input Arguments

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Matrix order, specified as a scalar, nonnegative integer.

Example: `invhilb(10)`

Data Types: `single` | `double` | `int8` | `int16` | `int32` | `int64` | `uint8` | `uint16` | `uint32` | `uint64` | `logical`

Matrix class, specified as either `'double'` or `'single'`.

Example: `invhilb(10,'single')`

Data Types: `char`

## Limitations

The exact inverse of the exact Hilbert matrix is a matrix whose elements are large integers. As long as the order of the matrix `n` is less than 15, these integers can be represented as floating-point numbers without roundoff error.

Comparing `invhilb(n)` with `inv(hilb(n))` involves the effects of two or three sets of roundoff errors:

• Errors caused by representing `hilb(n)`

• Errors in the matrix inversion process

• Errors, if any, in representing `invhilb(n)`

The first of these roundoff errors involves representing fractions like 1/3 and 1/5 in floating-point representation and is the most significant.

 Forsythe, G. E. and C. B. Moler. Computer Solution of Linear Algebraic Systems. Englewood Cliffs, NJ: Prentice-Hall, 1967.