# Documentation

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# spaugment

Form least squares augmented system

## Syntax

```S = spaugment(A,c) S = spaugment(A) ```

## Description

`S = spaugment(A,c)` creates the sparse, square, symmetric indefinite matrix ```S = [c*I A; A' 0]```. The matrix `S` is related to the least squares problem

````min` `norm`(b - A*x) ```

by

```r = b - A*x S * [r/c; x] = [b; 0] ```

The optimum value of the residual scaling factor `c`, involves `min(svd(A))` and `norm(r)`, which are usually too expensive to compute.

`S = spaugment(A)` without a specified value of `c`, uses `max(max(abs(A)))/1000`.

### Note

In previous versions of MATLAB® product, the augmented matrix was used by sparse linear equation solvers, \ and /, for nonsquare problems. Now, MATLAB software performs a least squares solve using the `qr` factorization of `A` instead.

## See Also

#### Introduced before R2006a

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