# GQR: Generalized QR Factorization In LSE: Constrained Least Squares and Generalized QR Factorization

## Description

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

## Usage

 `1` ```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 sergio05acm@gmail.com

## 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

 ```1 2 3``` ```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)) ```

LSE documentation built on Feb. 2, 2022, 5:07 p.m.