spaugment (MATLAB Functions)

Form least squares augmented system

Syntax

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

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)
```

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

See Also

spparms

sparse spconvert