GQR {LSE}

Generalized QR Factorization

Description

This code provides a simultaneous orthogonal factorization for two matrices A and B. This code requires pracma library.

Usage

GQR(x,y)

Arguments

x

Numerical matrix with m rows and n columns.

y

Numerical matrix with p rows and n columns.

Details

Given two matrices, with the same number of rows, this algorithm provides a single factorization, such that A=QR and (Q^T)B=WS.

Value

Q

Orthogonal matrix for A

R

Trapezoidal matrix for A

W

Orthogonal matrix for (Q^T)B

S

Trapezoidal matrix for (Q^T)B

Author(s)

Sergio Andrés Cabrera Miranda Statician [e-mail]

References

Cabrera Miranda, S. A., & Triana Laverde, J. G. (2021). El problema de los mínimos cuadrados con restricciones de igualdad mediante la factorización QR generalizada. Selecciones Matemáticas, 8(02), 437-443. (English Article).

Anderson, E., Bai, Z., & Dongarra, J. (1992). Generalized QR factorization and its applications. Linear Algebra and its Applications, 162, 243-271.

Examples

A = matrix(c(1,1,1,1,3,1,1,-1,1,1,1,1),4,3,byrow=TRUE)
C = matrix(c(1,1,1,1,1,-1),2,3,byrow=TRUE)
GQR(t(A),t(C))