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:
- 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,
- is the m ×p matrix B that is to be left multiplied
by the transposed m ×m matrix Q'.
- is an optional scalar specifying a singularity criterion.
The APPCORT subroutine returns the following values:
- is an n ×p matrix product
which is the minimum 2-norm solution of the (rank deficient)
least-squares problem | Ax- b|22.
Refer to Golub and Van Loan (1989,
pp. 241-242) for more details.
- 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.