Temat: interval arithmetic

Skocz do pozycji: 1.

Tytuł:: A decomposition approach to type 2 interval arithmetic
Autorzy:: Piegat, Andrzej
Dobryakova, Larisa
Tematy:: multidimensional RDM interval arithmetic
type 2 interval arithmetic
RDM type 2 interval arithmetic
decomposition type 2 interval arithmetic
interval arithmetic; Pokaż więcej
Wydawca:: Uniwersytet Zielonogórski. Oficyna Wydawnicza
Powiązania:: https://bibliotekanauki.pl/articles/330100.pdf Link otwiera się w nowym oknie
Opis:: The classic interval has precise borders A = [a, ā] . Therefore, it can be called a type 1 interval. Because of great practical importance of such interval data, several versions of type 1 interval arithmetic have been created. However, sometimes precise borders a and ā of intervals cannot be determined in practice. If the borders are uncertain, then we have to do with type 2 intervals. A type 2 interval can be denoted as A_T2 = [a_L, a_R], [ā_L, ā_R]. The paper presents multidimensional decomposition RDM type 2 interval arithmetic (D-RDM-T2-I arithmetic), where RDM means relative-distance measure. The decomposition approach considerably simplifies calculations and is transparent for users. Apart from this arithmetic, examples of its applications are also presented. To the authors’ best knowledge, no papers on this arithmetic exist. D-RDM-T2-I arithmetic is necessary to create type 2 fuzzy arithmetic based on horizontal µ-cuts, which the authors aim to do.
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 2.

Tytuł:: Is an interval the right result of arithmetic operations on intervals?
Autorzy:: Piegat, A.
Landowski, M.
Tematy:: interval arithmetic
one dimensional interval arithmetic
multidimensional interval arithmetic
RDM interval arithmetic
arytmetyka interwałowa
arytmetyka interwałowa jednowymiarowa
arytmetyka interwałowa wielowymiarowa; Pokaż więcej
Wydawca:: Uniwersytet Zielonogórski. Oficyna Wydawnicza
Powiązania:: https://bibliotekanauki.pl/articles/330098.pdf Link otwiera się w nowym oknie
Opis:: For many scientists interval arithmetic (IA, I arithmetic) seems to be easy and simple. However, this is not true. Interval arithmetic is complicated. This is confirmed by the fact that, for years, new, alternative versions of this arithmetic have been created and published. These new versions tried to remove shortcomings and weaknesses of previously proposed options of the arithmetic, which decreased the prestige not only of interval arithmetic itself, but also of fuzzy arithmetic, which, to a great extent, is based on it. In our opinion, the main reason for the observed shortcomings of the present IA is the assumption that the direct result of arithmetic operations on intervals is also an interval. However, the interval is not a direct result but only a simplified representative (indicator) of the result. This hypothesis seems surprising, but investigations prove that it is true. The paper shows what conditions should be satisfied by the result of interval arithmetic operations to call it a “result”, how great its dimensionality is, how to perform arithmetic operations and solve equations. Examples illustrate the proposed method of interval computations.
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 3.

Tytuł:: New Approach to the Uncertainty Assessment of Acoustic Effects in the Environment
Autorzy:: Batko, W.
Pawlik, P.
Tematy:: interval arithmetic
uncertainty
railway noise; Pokaż więcej
Wydawca:: Polska Akademia Nauk. Czytelnia Czasopism PAN
Powiązania:: https://bibliotekanauki.pl/articles/177204.pdf Link otwiera się w nowym oknie
Opis:: The acoustic climate assessment needed for the selection of solutions (technical, legal and organisa- tional), which will help to minimise the acoustic hazards in the analysed areas, is realised on the basis of acoustic maps. The reference computational algorithms, assigned to them, require very thorough prepa- ration of input data for the considered noise source model representing – in the best possible way – the acoustic climate. These input data are burdened with certain uncertainties in this class of computational tasks. The uncertainties are related to the problem of selecting proper argument values (from the inter- val of their possible variability) for the modelled processes. This situation has a direct influence on the uncertainty of acoustic maps. The idea of applying the interval arithmetic for the assessment of acoustic models uncertainty is formulated in this paper. The computational formalism assigned to the interval arithmetic was discussed. The rules of interval estimations for the model solutions determining the sound level distribution around the analysed noise source – caused by possible errors in the input data – were presented. The application of this formalism was illustrated in uncertainty assessments of modelling acoustic influences of the railway noise linear source on the environment.
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 4.

Tytuł:: A realistic tolerant solution of a system of interval linear equations with the use of multidimensional interval arithmetic
Autorzy:: Piegat, Andrzej
Pluciński, Marcin
Tematy:: interval arithmetic
interval linear equation
tolerable solution
multidimensional interval arithmetic
arytmetyka interwałowa
równanie liniowe przedziałowe
arytmetyka interwałowa wielowymiarowa; Pokaż więcej
Wydawca:: Uniwersytet Zielonogórski. Oficyna Wydawnicza
Powiązania:: https://bibliotekanauki.pl/articles/11542697.pdf Link otwiera się w nowym oknie
Opis:: The paper presents a method of determining the robustness of solutions of systems of interval linear equations (ILEs). The method can be applied also for the ILE systems for which it has been impossible to find solutions so far or for which solutions in the form of improper intervals have been obtained (which cannot be implemented in practice). The research conducted by the authors has shown that for many problems it is impossible to arrive at ideal solutions that would be fully robust to data uncertainty. However, partially robust solutions can be obtained, and those with the highest robustness can be selected and put into practice. The paper shows that the degree of robustness to the uncertainty of the entire system can be calculated on the basis of the degrees of robustness of individual equations, which greatly simplifies calculations. The presented method is illustrated with a series of examples (also benchmark ones) that facilitate its understanding. It is an extension of the authors’ previously published method for first-order ILEs.
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 5.

Tytuł:: Central configurations in planar n-body problem with equal masses for n=5,6,7
Autorzy:: Moczurad, Małgorzata
Zgliczyński, Piotr
Opis:: We give a computer-assisted proof of the full listing of central configuration for n-body problem for Newtonian potential on the plane for n=5,6,7 with equal masses. We show all these central configurations have a reflective symmetry with respect to some line. For n=8,9,10, we establish the existence of central configurations without any reflectional symmetry.
Dostawca treści:: Repozytorium Uniwersytetu Jagiellońskiego

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Skocz do pozycji: 6.

Tytuł:: Interval boundary element method for transient diffusion problem in two-layered domain
Przedziałowa metoda elementów brzegowych dla zadań dyfuzji w obszarach dwuwarstwowych
Autorzy:: Piasecka-Belkhayat, A.
Tematy:: directed interval arithmetic
interval boundary element method
heat transfer; Pokaż więcej
Wydawca:: Polskie Towarzystwo Mechaniki Teoretycznej i Stosowanej
Powiązania:: https://bibliotekanauki.pl/articles/280879.pdf Link otwiera się w nowym oknie
Opis:: In the paper, the description of an unsteady heat transfer for one- dimensional problem proceeding in a two-layered domain is presented. It is assumed that all thermophysical parameters appearing in the mathematical description of the problem analysed are given as directed interval values. The problem discussed has been solved using the 1st scheme of the interval boundary element method. The interval Gauss elimination method has been applied to solve the obtained interval system of equations. In the final part of the paper, results of numerical computations are shown.
W pracy przedstawiono opis nieustalonego przepływu ciepła dla zadań jednowymiarowych w obszarach dwuwarstwowych. Założono, że wszystkie parametry termofizyczne pojawiające się w opisie matematycznym analizowanego zadania są wartościami przedziałowymi skierowanymi. Omawiane zagadnienie zostało rozwiązane za pomocą pierwszego schematu przedziałowej metody elementów brzegowych. Do rozwiązania otrzymanego interwałowego układu równań zastosowano przedziałową metodę eliminacji Gaussa. W końcowej części pracy pokazano wyniki obliczeń numerycznych.
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 7.

Tytuł:: Central configurations in the spatial $n$-body problem for $n$=5,6 with equal masses
Autorzy:: Moczurad, Małgorzata
Zgliczyński, Piotr
Opis:: We present a computer assisted proof of the full listing of central configurations for spatial n-body problem for n=5 and 6, with equal masses. For each central configuration, we give a full list of its Euclidean symmetries. For all masses sufficiently close to the equal masses case, we give an exact count of configurations in the planar case for n=4,5,6,7 and in the spatial case for n=4,5,6.
Dostawca treści:: Repozytorium Uniwersytetu Jagiellońskiego

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Skocz do pozycji: 8.

Tytuł:: An interval difference method for solving the wave equation
Autorzy:: Szyszka, B.
Tematy:: wave equation
difference interval method
interval method
floating point interval arithmetic; Pokaż więcej
Wydawca:: Politechnika Poznańska. Wydawnictwo Politechniki Poznańskiej
Powiązania:: https://bibliotekanauki.pl/articles/378277.pdf Link otwiera się w nowym oknie
Opis:: In the paper a difference interval method for solving the wave equation together the initial-boundary value problems is presented. Using an interval method together floating-point interval arithmetic guarantee, that obtained interval solutions contain all numerical errors. Additionally, each exact solution is included into interval solution. In numerical experiments it is guarantee contain all numerical errors in obtained interval solutions. Taken into consideration is the central discretization method with regard to space and time. An initial condition is approximated by the third-order Taylor polynomial with local truncation error of order 0(h4). In the paper new formula, which described discretization of the initial condition, is proposed. Therefore more exact solutions are obtained then in the previous considerations.
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 9.

Tytuł:: On an application of an interval backward ﬁnite diﬀerence method for solving the one-dimensional heat conduction problem
Autorzy:: Jankowska, M.
Marciniak, A.
Hoﬀmann, T.
Tematy:: interval methods
interval arithmetic
ﬁnite diﬀerence methods
heat conduction problem; Pokaż więcej
Wydawca:: Polska Akademia Nauk. Instytut Badań Systemowych PAN
Powiązania:: https://bibliotekanauki.pl/articles/205521.pdf Link otwiera się w nowym oknie
Opis:: The paper concerns the interval method for solving the one-dimensional heat conduction problem. It is based on the conventional backward ﬁnite diﬀerence scheme with the appropriate local truncation error terms that are also taken into account. For the theoretical formulation of the interval approach we can show that the exact solution is included in the interval one. In practice, there are problems, for which we cannot determine the endpoints of the error term intervals exactly. Nevertheless, if we use the appropriate approximation, related to the endpoints considered, then the numerical experiments conﬁrm that the interval solution includes the exact one.
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 10.

Tytuł:: Set arithmetic and the enclosing problem in dynamics
Autorzy:: Mrozek, Marian
Zgliczyński, Piotr
Tematy:: dynamical systems
interval arithmetic
rigorous numerical analysis
enclosing problem; Pokaż więcej
Wydawca:: Polska Akademia Nauk. Instytut Matematyczny PAN
Powiązania:: https://bibliotekanauki.pl/articles/1207977.pdf Link otwiera się w nowym oknie
Opis:: We study the enclosing problem for discrete and continuous dynamical systems in the context of computer assisted proofs. We review and compare the existing methods and emphasize the importance of developing a suitable set arithmetic for efficient algorithms solving the enclosing problem.
Dostawca treści:: Biblioteka Nauki

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