## APPCORT Call

**applies complete orthogonal decomposition by Householder
transformations on the right-hand-side matrix, ****B** for
the solution of rank-deficient linear least-squares systems
**CALL APPCORT(** *prqb, lindep, **a*, *b*<, sing>**);**

The inputs to the APPCORT subroutine are:
*a*
- is an
*m* ×*n* matrix **A**, with , which
is to be decomposed into the product of the *m* ×*m*
orthogonal matrix **Q**, the *n* ×*n* upper triangular
matrix **R**, and the *n* ×*n* orthogonal matrix **P**,

*b*
- is the
*m* ×*p* matrix **B** that is to be left multiplied
by the transposed *m* ×*m* matrix **Q**'.

*sing*
- is an optional scalar specifying a singularity criterion.

The APPCORT subroutine returns the following values:
*prqb*
- is an
*n* ×*p* matrix product

which is the minimum 2-norm solution of the (rank deficient)
least-squares problem | **A****x**- **b**|^{2}_{2}.
Refer to Golub and Van Loan (1989,
pp. 241-242) for more details.

*lindep*
- is the number of linearly dependent columns in the matrix
**A** detected by applying the *r* Householder transformations.
That is, *lindep*=*n*-*r*, where *r* = rank(**A**).

See "COMPORT Call" for
information on complete orthogonal decomposition.

Copyright © 1999 by SAS Institute Inc., Cary, NC, USA. All rights reserved.