Abstract
The use of modifications of certain well-known methods of the conjugate direction type for solving systems of linear algebraic equations with rectangular matrices is examined. The modified methods are shown to be superior to the original versions with respect to the round-off accumulation; the advantage is especially large for ill-conditioned matrices. Examples are given of the efficient use of the modified methods for solving certain fairly large ill-conditioned problems.
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References
D. K. Faddeev and V. N. Faddeeva, Computational Methods in Linear Algebra (Lan’, St. Petersburg, 2002) [in Russian].
L. F. Yukhno, “A Modification of Conjugate Direction Methods,” Zh. Vychisl. Mat. Mat. Fiz. 46, 7–11 (2006) [Comput. Math. Math. Phys. 46, 5–9 (2006)].
L. F. Yukhno, “On Modification of Certain Methods of the Conjugate Direction Type for Solving Systems of Linear Algebraic Equations,” Zh. Vychisl. Mat. Mat. Fiz. 47, 1811–1818 (2007) [Comput. Math. Math. Phys. 47, 1737–1744 (2007)].
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Original Russian Text © L.F. Yukhno, 2007, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2007, Vol. 47, No. 12, pp. 1979–1987.
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Yukhno, L.F. On modification of certain methods of the conjugate direction type for solving rectangular systems of linear algebraic equations. Comput. Math. and Math. Phys. 47, 1893–1901 (2007). https://doi.org/10.1134/S0965542507120020
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DOI: https://doi.org/10.1134/S0965542507120020