Displaying similar documents to “Loss of Accuracy in Numerical Computations Загуба на точност в числените пресмятания”

Numerical Issues in Using MATLAB Числени аспекти при използване на MATLAB

Konstantinov, Mihail, Pasheva, Vesela, Petkov, Petko (2012)

Union of Bulgarian Mathematicians

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Михаил Константинов, Весела Пашева, Петко Петков - Разгледани са някои числени проблеми при използването на компютърната система MATLAB в учебната дейност: пресмятане на тригонометрични функции, повдигане на матрица на степен, спектрален анализ на целочислени матрици от нисък ред и пресмятане на корените на алгебрични уравнения. Причините за възникналите числени трудности могат да се обяснят с особеностите на използваната двоичната аритметика с плаваща точка. In this tutorial...

Verified numerical computations for large-scale linear systems

Katsuhisa Ozaki, Takeshi Terao, Takeshi Ogita, Takahiro Katagiri (2021)

Applications of Mathematics

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This paper concerns accuracy-guaranteed numerical computations for linear systems. Due to the rapid progress of supercomputers, the treatable problem size is getting larger. The larger the problem size, the more rounding errors in floating-point arithmetic can accumulate in general, and the more inaccurate numerical solutions are obtained. Therefore, it is important to verify the accuracy of numerical solutions. Verified numerical computations are used to produce error bounds on numerical...

Formally certified floating-point filters for homogeneous geometric predicates

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...