Practical aspects of interval computation
Ramon E. Moore (1968)
Aplikace matematiky
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Ramon E. Moore (1968)
Aplikace matematiky
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Jorba, Àngel, Zou, Maorong (2005)
Experimental Mathematics
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Tamás Ladics, István Faragó (2013)
Open Mathematics
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The properties of iterative splitting with two bounded linear operators have been analyzed by Faragó et al. For more than two operators, iterative splitting can be defined in many different ways. A large class of the possible extensions to this case is presented in this paper and the order of accuracy of these methods are examined. A separate section is devoted to the discussion of two of these methods to illustrate how this class of possible methods can be classified with respect to...
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...
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...
K. Surla, D. Herceg (1977)
Matematički Vesnik
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J. A. M. Bollen (1984)
Banach Center Publications
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D. Tošić, Lj. Protić (1983)
Matematički Vesnik
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Bohlender, Gerd, Kulisch, Ulrich (2010)
Serdica Journal of Computing
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Basic concepts for an interval arithmetic standard are discussed in the paper. Interval arithmetic deals with closed and connected sets of real numbers. Unlike floating-point arithmetic it is free of exceptions. A complete set of formulas to approximate real interval arithmetic on the computer is displayed in section 3 of the paper. The essential comparison relations and lattice operations are discussed in section 6. Evaluation of functions for interval arguments is studied in section...
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...