# A numerical experiment with huang algorithm

It is believed that the Huang method is the best one to solve a system of linear equations in the class of ABS methods. Having presented 10 versions of the Huang method and compared them numerically, we will compare the best version of the Huang method with LU along with partial pivoting and QR through Householder transformations methods. Numerical results show that all three methods yield approximately similar output in well-conditioned problems while the Huang method works more effectively in ill-conditioned problems.

Tipo de documento: Artículo - Article

Palabras clave: ABS Methods, Huang Algorithm, Ill-Conditioned Systems.

Source: http://www.bdigital.unal.edu.co

## Teaser

Boletı́n de Matemáticas Nueva Serie, Volumen XIV No.
1 (2007), pp.
1–13 A NUMERICAL EXPERIMENT WITH HUANG ALGORITHM HAMID ESMAEILI (*) Abstract.
It is believed that the Huang method is the best one to solve a system of linear equations in the class of ABS methods.
Having presented 10 versions of the Huang method and compared them numerically, we will compare the best version of the Huang method with LU (along with partial pivoting) and QR (through Householder transformations) methods. Numerical results show that all three methods yield approximately similar output in well-conditioned problems while the Huang method works more effectively in ill-conditioned problems. Key words and phrases.
ABS Methods, Huang Algorithm, Ill-Conditioned Systems. Resumen.
Se cree que el método Huang es el mejor de los métodos ABS para resolver un sistema de ecuaciones lineales.
Habiendo presentado 10 versiones del método Huang y evaluándolas numéricamente, compararemos la mejor versión del método Huang con los métodos LU (a través de pivotaje parcial) y QR (por medio de transformaciones de Householder). Las pruebas numéricas muestran que los tres métodos producen resultados similares en problemas bien condicionados, mientras que el método Huang trabaja más efectivamente en problemas mal condicionados. Palabras claves.
Métodos ABS, Algoritmo Huang , sistemas mal condicionados. 2000 Mathematics Subject Classification: 65F05, 65F20, 65F30. (*) H.
Esmaeili.
Department of Mathematics, Bu-Ali Sina University, Hamedan, Iran. E-mail: esmaeili@basu.ac.ir. 1 2 H.
ESMAEILI 1.
Introduction In many numerical methods for mathematical programming problems, it is often required to solve a system of linear equations which is usually consistent and, therefore, solvable.
However, the exact nature of the system is not known a priori.
The system may be determined and admits a unique solution or it may be underdetermined and admits infinite solutions.
In either case, ...