APPCORT Call

Language Reference

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 $m \geq n$ , 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,

$A= Q[ R\ 0 ] {{\Pi}}^' P^' {{\Pi}}$

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

$P{{\Pi}}[ (L^')^{-1} & 0 \ 0 & 0 ] Q^' B$

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.

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.

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