We expose the orthogonal decomposition called Generalized QR Factorization (GQR) and RQ factorization applied to equality constrained least squares problem (LSE).

The solution of the LSE problem is given through four analytics methods:

1. Generalized QR Factorization.
2. Lagrange Multipliers.
3. Direct Elimination.
4. Nullspace method.

Also, is given a solution of the model of quaternion equality constrained least squares problem through the transformations from quaternions to real value matrices, and viceversa.

Ther code developed in RStudio, requires package MASS and pracma. https://cran.r-project.org/web/packages/LSE/index.html

For more details: https://revistas.unitru.edu.pe/index.php/SSMM/article/view/3889

References about Constrained Least Squares Lawson, C. L., & Hanson, R. J. (1995). Solving least squares problems. Society for Industrial and Applied Mathematics. Rao, C. R., & Toutenburg, H. (1995). Linear models. In Linear models (pp. 3-18). Springer, New York, NY.

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

References about Null Space method, Direct Elimination and Lagrange Multipliers Lawson, C. L., & Hanson, R. J. (1995). Solving least squares problems. Society for Industrial and Applied Mathematics. Van Benthem, M., Keenan, M. and Haaland, M. (2002). Application of equality constraints on variables during alternating least squares procedures, 16, 613-622.

References about quaternions Jiang, T., & Wei, M. (2003). Equality constrained least squares problem over quaternion field. Applied mathematics letters, 16(6), 883-888. Jiang, T., Zhao, J., & Wei, M. (2008). A new technique of quaternion equality constrained least squares problem. Journal of computational and applied mathematics, 216(2), 509-513.

For more information please, contact us: Sergio Andrés Cabrera Miranda email Juan Gabriel Triana Laverde email