翻訳と辞書 Words near each other ・ Quantity adjustment ・ Quantity calculus ・ Quantity Is Job 1 ・ Quantity of Books v. Kansas ・ Quantity surveyor ・ Quantity take-off ・ Quantity theory of money ・ Quantization ・ Quantization (image processing) ・ Quantization (linguistics) ・ Quantization (music) ・ Quantization (physics) ・ Quantization (signal processing) ・ Quantization commutes with reduction ・ Quantization of the electromagnetic field ・ Quantized state systems method ・ QuantLib ・ Quantm ・ Quanto ・ Quanto ao Tempo ・ Quanto è bello lu murire acciso ・ Quantock ・ Quantock Greenway ・ Quantock Hills ・ Quantock Lodge ・ Quantock Motor Services ・ Quantock, Saskatchewan ・ Quantone (company) ・ Quantopian ・ Quantos Possunt ad Satanitatem Trahunt Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Quantized state systems method ： ウィキペディア英語版 Quantized state systems method The quantized state systems (QSS) methods are a family of numerical integration solvers based on the idea of state quantization, dual to the traditional idea of time discretization. Unlike traditional numerical solution methods, which approach the problem by discretizing time and solving for the next (real-valued) state at each successive time step, QSS methods keep time as a continuous entity and instead quantize the system's state, instead solving for the ''time'' at which the state deviates from its quantized value by a ''quantum''. They can also have many advantages compared to classical algorithms. They inherently allow for modeling discontinuities in the system due to their discrete-event nature and asynchronous nature. They also allow for explicit root-finding and detection of zero-crossing using ''explicit'' algorithms, avoiding the need for iteration---a fact which is especially important in the case of stiff systems, where traditional time-stepping methods require a heavy computational penalty due to the requirement to implicitly solve for the next system state. Finally, QSS methods satisfy remarkable global stability and error bounds, described below, which are not satisfied by classical solution techniques. By their nature, QSS methods are therefore neatly modeled by the DEVS formalism, a discrete-event model of computation, in contrast with traditional methods, which form discrete-time models of the continuous-time system. They have therefore been implemented in (), a simulation engine for such discrete-event systems. ==Theoretical properties== In 2001, Ernesto Kofman proved a remarkable property of the quantized-state system simulation method: namely, that when the technique is used to solve a stable linear time-invariant (LTI) system, the global error is bounded by a constant that is proportional to the quantum, but (crucially) independent of the duration of the simulation. More specifically, for a stable multidimensional LTI system with the state-transition matrix $A$ and input matrix $B$, it was shown in () that the absolute error vector $\backslash vec(t)$ is bounded above by :$$ \left| \vec(t) \right| \leq \left| V \right|\ \left| \Re\left(\Lambda\right)^ \Lambda \right|\ \left| V^ \right|\ \Delta\vec + \left| V \right|\ \left| \Re\left(\Lambda\right)^ V^ B \right|\ \Delta\vec where $\backslash Delta\backslash vec$ is the vector of state quanta, $\backslash Delta\backslash vec$ is the vector with quanta adopted in the input signals, $V\; \backslash Lambda\; V^\; =\; A$ is the eigendecomposition or Jordan canonical form of $A$, and $\backslash left|\backslash ,\backslash cdot\backslash ,\backslash right|$ denotes the element-wise absolute value operator (not to be confused with the determinant or norm). It is worth noticing that this spectacular error bound comes at a price: the global error for a stable LTI system is also, in a sense, bounded ''below'' by a the quantum itself, at least for the first-order QSS1 method. This is because, unless the approximation happens to coincide ''exactly'' with the correct value (an event which will almost surely not happen), it will simply continue oscillating around the equilibrium, as the state is always (by definition) guaranteed to change by exactly one quantum outside of the equilibrium. Avoiding this condition would require finding a reliable technique for dynamically lowering the quantum in a manner analogous to adaptive stepsize methods in traditional simulation algorithms. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Quantized state systems method」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.