Accounting for Round-Off Errors When Using Gradient Minimization Methods

Autor:	Dmitry Lukyanenko, Valentin Shinkarev, Anatoly Yagola
Jazyk:	angličtina
Rok vydání:	2022
Předmět:	gradient method conjugate gradient method round-off error rounding error stopping criteria Industrial engineering. Management engineering T55.4-60.8 Electronic computers. Computer science QA75.5-76.95
Zdroj:	Algorithms, Vol 15, Iss 9, p 324 (2022)
Druh dokumentu:	article
ISSN:	1999-4893
DOI:	10.3390/a15090324
Popis:	This paper discusses a method for taking into account rounding errors when constructing a stopping criterion for the iterative process in gradient minimization methods. The main aim of this work was to develop methods for improving the quality of the solutions for real applied minimization problems, which require significant amounts of calculations and, as a result, can be sensitive to the accumulation of rounding errors. However, this paper demonstrates that the developed approach can also be useful in solving computationally small problems. The main ideas of this work are demonstrated using one of the possible implementations of the conjugate gradient method for solving an overdetermined system of linear algebraic equations with a dense matrix.
Databáze:	Directory of Open Access Journals
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