Geodesic
Variations on the Gram-Schmidt and the Huang algorithms for linear systems: A numerical study
Applications of Mathematics, Tome 38 (1993) no. 2, pp. 81-100

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

In this paper we compare the numerical performance on a set of ill conditioned problems of several algorithms for linear systems based upon the explicit QR factorization and the implicit LQ factorization associated with the Huang and the modified Huang algorithms in the ABS class. The results indicate that the modified Huang algorithm is generally more accurate than the Huang algorithm and competitive with commercial codes based upon the QR factorization with Householder of Givens reflections. The best version of the modified Huang algorithm performs similarly, as theoretically expected, to the doubly iterated Gram-Schmidt method of Daniel et al., applied on the rows to generate search vectors.
DOI : 10.21136/AM.1993.104537
Classification : 65F05, 65F10
Keywords: ABS methods; Huang algorithm; QR algorithm; Gram-Schmidt orthogonalization; ill-conditioned equations; numerical experiments 
@article{10_21136_AM_1993_104537,
     author = {Spedicato, Emilio and Vespucci, Maria Teresa},
     title = {Variations on the {Gram-Schmidt} and the {Huang} algorithms for linear systems: {A} numerical study},
     journal = {Applications of Mathematics},
     pages = {81--100},
     publisher = {mathdoc},
     volume = {38},
     number = {2},
     year = {1993},
     doi = {10.21136/AM.1993.104537},
     mrnumber = {1202746},
     zbl = {0783.65029},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/AM.1993.104537/}
}
TY  - JOUR
AU  - Spedicato, Emilio
AU  - Vespucci, Maria Teresa
TI  - Variations on the Gram-Schmidt and the Huang algorithms for linear systems: A numerical study
JO  - Applications of Mathematics
PY  - 1993
SP  - 81
EP  - 100
VL  - 38
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.21136/AM.1993.104537/
DO  - 10.21136/AM.1993.104537
LA  - en
ID  - 10_21136_AM_1993_104537
ER  - 
%0 Journal Article
%A Spedicato, Emilio
%A Vespucci, Maria Teresa
%T Variations on the Gram-Schmidt and the Huang algorithms for linear systems: A numerical study
%J Applications of Mathematics
%D 1993
%P 81-100
%V 38
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.21136/AM.1993.104537/
%R 10.21136/AM.1993.104537
%G en
%F 10_21136_AM_1993_104537
Spedicato, Emilio; Vespucci, Maria Teresa. Variations on the Gram-Schmidt and the Huang algorithms for linear systems: A numerical study. Applications of Mathematics, Tome 38 (1993) no. 2, pp. 81-100. doi: 10.21136/AM.1993.104537

Cité par Sources :