Numerical Stability of Decent Methods for Solving Linear Equations.
Jo A.M. Bollen (1984)
Numerische Mathematik
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Jo A.M. Bollen (1984)
Numerische Mathematik
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H. Bauch (1984)
Banach Center Publications
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Guillaume Melquiond, Sylvain Pion (2007)
RAIRO - Theoretical Informatics and Applications
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Floating-point arithmetic provides a fast but inexact way of computing geometric predicates. In order for these predicates to be exact, it is important to rule out all the numerical situations where floating-point computations could lead to wrong results. Taking into account all the potential problems is a tedious work to do by hand. We study in this paper a floating-point implementation of a filter for the orientation-2 predicate, and how a formal and partially automatized verification...
Udovičić, Zlatko (2005)
Matematichki Vesnik
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Konstantinov, Mihail, Petkov, Petko (2011)
Union of Bulgarian Mathematicians
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Михаил М. Константинов, Петко Х. Петков - Разгледани са възможните катастрофални ефекти от неправилното използване на крайна машинна аритметика с плаваща точка. За съжаление, тази тема не винаги се разбира достатъчно добре от студентите по приложна и изчислителна математика, като положението в инженерните и икономическите специалности в никакъв случай не е по-добро. За преодоляване на този образователен пропуск тук сме разгледали главните виновници за загубата на точност при числените компютърни...
N. METROPOLIS, M. FRASER (1968)
Numerische Mathematik
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Ramon E. Moore (1968)
Aplikace matematiky
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D. Bini, G. Lotti (1980/81)
Numerische Mathematik
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Russell B. Richins, David C. Dobson (2012)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
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We use the work of Milton, Seppecher, and Bouchitté on variational principles for waves in lossy media to formulate a finite element method for solving the complex Helmholtz equation that is based entirely on minimization. In particular, this method results in a finite element matrix that is symmetric positive-definite and therefore simple iterative descent methods and preconditioning can be used to solve the resulting system of equations. We also derive an error bound for the method...