Relevant bibliographies by topics / Backward error

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Academic literature on the topic 'Backward error'

Author: Grafiati
Published: 4 June 2021
Last updated: 7 July 2024

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Journal articles on the topic "Backward error"

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Reich, Sebastian. "Backward Error Analysis for Numerical Integrators." SIAM Journal on Numerical Analysis 36, no. 5 (January 1999): 1549–70. http://dx.doi.org/10.1137/s0036142997329797.

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Debussche, Arnaud, and Erwan Faou. "Weak Backward Error Analysis for SDEs." SIAM Journal on Numerical Analysis 50, no. 3 (January 2012): 1735–52. http://dx.doi.org/10.1137/110831544.

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Jiránek, Pavel, and David Titley-Peloquin. "Estimating the Backward Error in LSQR." SIAM Journal on Matrix Analysis and Applications 31, no. 4 (January 2010): 2055–74. http://dx.doi.org/10.1137/090770655.

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Alonso, P., M. Gasca, and J. M. Peña. "Backward error analysis of Neville elimination." Applied Numerical Mathematics 23, no. 2 (March 1997): 193–204. http://dx.doi.org/10.1016/s0168-9274(96)00051-7.

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Varah, J. M. "Backward Error Estimates for Toeplitz Systems." SIAM Journal on Matrix Analysis and Applications 15, no. 2 (April 1994): 408–17. http://dx.doi.org/10.1137/s0895479891219976.

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Hairer, Ernst. "Backward error analysis for multistep methods." Numerische Mathematik 84, no. 2 (December 1, 1999): 199–232. http://dx.doi.org/10.1007/s002110050469.

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刘, 玉玲. "Backward Error of Complex Linear System." Pure Mathematics 13, no. 06 (2023): 1677–88. http://dx.doi.org/10.12677/pm.2023.136171.

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Tang, L., and S. Yu. "Error concealment with error level tracking and backward frame update." Electronics Letters 40, no. 17 (2004): 1049. http://dx.doi.org/10.1049/el:20045313.

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Romanovsky, A., and L. Strigini. "Backward error recovery via conversations in Ada." Software Engineering Journal 10, no. 6 (1995): 219. http://dx.doi.org/10.1049/sej.1995.0027.

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Nagasaka, Kosaku. "Backward error analysis of approximate Gröbner basis." ACM Communications in Computer Algebra 46, no. 3/4 (January 15, 2013): 116–17. http://dx.doi.org/10.1145/2429135.2429161.

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Dissertations / Theses on the topic "Backward error"

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Cottrell, David 1979. "Symplectic integration of simple collisions : a backward error analysis." Thesis, McGill University, 2004. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=81322.

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Molecular Dynamics simulations often involve the numerical integration of pair-wise particle interactions with a constant, step size method. Of primary concern in these simulations is the introduction of error in velocity statistics. We consider the simple example of the symplectic Euler method applied to two-particle collisions in one dimension governed by linear restoring force and use backward error analysis to predict, these errors. For nearly all choices of system and method parameters, the post-collision energy is not conserved and depends upon the initial conditions of the particles and the step size of the method. The analysis of individual collisions is extended to predict energy growth in systems of particles in one dimension.
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Zivcovich, Franco. "Backward error accurate methods for computing the matrix exponential and its action." Doctoral thesis, Università degli studi di Trento, 2020. http://hdl.handle.net/11572/250078.

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The theory of partial differential equations constitutes today one of the most important topics of scientific understanding. A standard approach for solving a time-dependent partial differential equation consists in discretizing the spatial variables by finite differences or finite elements. This results in a huge system of (stiff) ordinary differential equations that has to be integrated in time. Exponential integrators constitute an interesting class of numerical methods for the time integration of stiff systems of differential equations. Their efficient implementation heavily relies on the fast computation of the action of certain matrix functions; among those, the matrix exponential is the most prominent one. In this manuscript, we go through the steps that led to the development of backward error accurate routines for computing the action of the matrix exponential.
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Zivcovich, Franco. "Backward error accurate methods for computing the matrix exponential and its action." Doctoral thesis, Università degli studi di Trento, 2020. http://hdl.handle.net/11572/250078.

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The theory of partial differential equations constitutes today one of the most important topics of scientific understanding. A standard approach for solving a time-dependent partial differential equation consists in discretizing the spatial variables by finite differences or finite elements. This results in a huge system of (stiff) ordinary differential equations that has to be integrated in time. Exponential integrators constitute an interesting class of numerical methods for the time integration of stiff systems of differential equations. Their efficient implementation heavily relies on the fast computation of the action of certain matrix functions; among those, the matrix exponential is the most prominent one. In this manuscript, we go through the steps that led to the development of backward error accurate routines for computing the action of the matrix exponential.
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Moan, Per Christian. "On backward error analysis and Nekhoroshev stability in the numerical analysis of conservative systems of ODEs." Thesis, University of Cambridge, 2002. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.620431.

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Tantardini, F. "QUASI-OPTIMALITY IN THE BACKWARD EULER-GALERKIN METHOD FOR LINEAR PARABOLIC PROBLEMS." Doctoral thesis, Università degli Studi di Milano, 2014. http://hdl.handle.net/2434/229462.

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We analyse the backward Euler-Galerkin method for linear parabolic problems, looking for quasi-optimality results in the sense of Céa's Lemma. We cast the problem into the framework given by the inf-sup theory, and we analyse the spatial discretization, the discretization in time and the topic of varying the spatial discretization separately. Concerning the spatial discretization, we prove the the H1-stability of the L2-projection is also a necessary condition for quasi-optimality, both in the H1(H-1)∩L2(H1)-norm and in the L2(H1)-norm. Concerning the discretization in time, we prove that the error in a norm that mimics the H1(H-1)∩L2(H1)-norm is equivalent to the sum of the best errors with piecewise constants for the exact solution and its time derivative, if the partition is locally quasi-uniform. Turning to the topic of varying the spatial dicretization, we provide a bound for the error that includes the best error and an additional term, which vanishes if there are not modifications of the spatial dicretization and which is consistent with the example of non convergence in Dupont '82. We combine these elements in an analysis of the backward Euler-Galerkin method and derive error estimates in case the spatial discretization is based on finite elements.
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Volz, Claudius. "Concealment of Video Transmission Packet Losses Based on Advanced Motion Prediction." Thesis, Linköping University, Department of Electrical Engineering, 2003. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-1771.

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Recent algorithms for video coding achieve a high-quality transmission at moderate bit rates. On the other hand, those coders are very sensitive to transmission errors. Many research projects focus on methods to conceal such errors in the decoded video sequence.

Motion compensated prediction is commonly used in video coding to achieve a high compression ratio. This thesis proposes an algorithm which uses the motion compensated prediction of a given video coder to predict a sequence of several complete frames, based on the last correctly decoded images, during a transmission interruption. The proposed algorithm is evaluated on a video coder which uses a dense motion field for motion compensation.

A drawback of predicting lost fields is the perceived discontinuity when the decoder switches back from the prediction to a normal mode of operation. Various approaches to reduce this discontinuity are investigated.

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Beuzeville, Theo. "Analyse inverse des erreurs des réseaux de neurones artificiels avec applications aux calculs en virgule flottante et aux attaques adverses." Electronic Thesis or Diss., Université de Toulouse (2023-....), 2024. http://www.theses.fr/2024TLSEP054.

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L'utilisation d'intelligences artificielles, dont les implémentations reposent souvent sur des réseaux de neurones artificiels, se démocratise maintenant dans une grande variété de tâches. En effet, ces modèles d'apprentissage profond produisent des résultats bien meilleurs que de nombreux algorithmes spécialisés précédemment utilisés et sont donc amenés à être déployés à grande échelle.C'est dans ce contexte de développement très rapide que des problématiques liées au stockage de ces modèles émergent, car ils sont parfois très profonds et comprennent donc jusqu'à des milliards de paramètres, ainsi que des problématiques liées à leurs performances en termes de calcul tant d'un point de vue de précision que de coût en temps et en énergie. Pour toutes ces raisons, l'utilisation de précision réduite est de plus en plus indispensable.D'autre part, il a été noté que les réseaux de neurones souffrent d'un manque d'interprétabilité, étant donné qu'ils sont souvent des modèles très profonds, entraînés sur de vastes quantités de données. Par conséquent, ils sont très sensibles aux perturbations qui peuvent toucher les données qu'ils traitent. Les attaques adverses en sont un exemple ; ces perturbations, souvent imperceptibles à l'œil humain, sont conçues pour tromper un réseau de neurones, le faisant échouer dans le traitement de ce qu'on appelle un exemple adverse. Le but de cette thèse est donc de fournir des outils pour mieux comprendre, expliquer et prédire la sensibilité des réseaux de neurones artificiels à divers types de perturbations. À cette fin, nous avons d'abord étendu à des réseaux de neurones artificiels certains concepts bien connus de l'algèbre linéaire numérique, tels que le conditionnement et l'erreur inverse. Nous avons donc établi des formules explicites permettant de calculer ces quantités et trouvé des moyens de les calculer lorsque nous ne pouvions pas obtenir de formule. Ces quantités permettent de mieux comprendre l'impact des perturbations sur une fonction mathématique ou un système, selon les variables qui sont perturbées ou non.Nous avons ensuite utilisé cette analyse d'erreur inverse pour démontrer comment étendre le principe des attaques adverses au cas où, non seulement les données traitées par les réseaux sont perturbées, mais également leurs propres paramètres. Cela offre une nouvelle perspective sur la robustesse des réseaux neuronaux et permet, par exemple, de mieux contrôler la quantification des paramètres pour ensuite réduire la précision arithmétique utilisée et donc faciliter leur stockage. Nous avons ensuite amélioré cette approche, obtenue par l'analyse d'erreur inverse, pour développer des attaques sur les données des réseaux comparables à l'état de l'art. Enfin, nous avons étendu les approches d'analyse d'erreurs d'arrondi, qui jusqu'à présent avaient été abordées d'un point de vue pratique ou vérifiées par des logiciels, dans les réseaux de neurones en fournissant une analyse théorique basée sur des travaux existants en algèbre linéaire numérique. Cette analyse permet d'obtenir des bornes sur les erreurs directes et inverses lors de l'utilisation d'arithmétiques flottantes. Ces bornes permettent à la fois d'assurer le bon fonctionnement des réseaux de neurones une fois entraînés, mais également de formuler des recommandations concernant les architectures et les méthodes d'entraînement afin d'améliorer la robustesse des réseaux de neurones
The use of artificial intelligence, whose implementations are often based on artificial neural networks, is now becoming widespread across a wide variety of tasks. These deep learning models indeed yield much better results than many specialized algorithms previously used and are therefore being deployed on a large scale.It is in this context of very rapid development that issues related to the storage of these models emerge, since they are sometimes very deep and therefore comprise up to billions of parameters, as well as issues related to their computational performance, both in terms of accuracy and time- and energy-related costs. For all these reasons, the use of reduced precision is increasingly being considered.On the other hand, it has been noted that neural networks suffer from a lack of interpretability, given that they are often very deep models trained on vast amounts of data. Consequently, they are highly sensitive to small perturbations in the data they process. Adversarial attacks are an example of this; since these are perturbations often imperceptible to the human eye, constructed to deceive a neural network, causing it to fail in processing the so-called adversarial example.The aim of this thesis is therefore to provide tools to better understand, explain, and predict the sensitivity of artificial neural networks to various types of perturbations.To this end, we first extended to artificial neural networks some well-known concepts from numerical linear algebra, such as condition number and backward error. These quantities allow to better understand the impact of perturbations on a mathematical function or system, depending on which variables are perturbed or not.We then use this backward error analysis to demonstrate how to extend the principle of adversarial attacks to the case where not only the data processed by the networks is perturbed but also their own parameters. This provides a new perspective on neural networks' robustness and allows, for example, to better control quantization to reduce the precision of their storage. We then improved this approach, obtained through backward error analysis, to develop attacks on network input comparable to state-of-the-art methods.Finally, we extended approaches of round-off error analysis, which until now had been approached from a practical standpoint or verified by software, in neural networks by providing a theoretical analysis based on existing work in numerical linear algebra.This analysis allows for obtaining bounds on forward and backward errors when using floating-point arithmetic. These bounds both ensure the proper functioning of neural networks once trained, and provide recommendations on architectures and training methods to enhance the robustness of neural networks
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Relton, Samuel. "Algorithms for matrix functions and their Fréchet derivatives and condition numbers." Thesis, University of Manchester, 2015. https://www.research.manchester.ac.uk/portal/en/theses/algorithms-for-matrix-functions-and-their-frechet-derivatives-and-condition-numbers(f20e8144-1aa0-45fb-9411-ddc0dc7c2c31).html.

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Al-Mohy, Awad. "Algorithms for the matrix exponential and its Fréchet derivative." Thesis, University of Manchester, 2011. https://www.research.manchester.ac.uk/portal/en/theses/algorithms-for-the-matrix-exponential-and-its-frechet-derivative(4de9bdbd-6d79-4e43-814a-197668694b8e).html.

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New algorithms for the matrix exponential and its Fréchet derivative are presented. First, we derive a new scaling and squaring algorithm (denoted expm[new]) for computing eA, where A is any square matrix, that mitigates the overscaling problem. The algorithm is built on the algorithm of Higham [SIAM J.Matrix Anal. Appl., 26(4): 1179-1193, 2005] but improves on it by two key features. The first, specific to triangular matrices, is to compute the diagonal elements in the squaring phase as exponentials instead of powering them. The second is to base the backward error analysis that underlies the algorithm on members of the sequence {||Ak||1/k} instead of ||A||. The terms ||Ak||1/k are estimated without computing powers of A by using a matrix 1-norm estimator. Second, a new algorithm is developed for computing the action of the matrix exponential on a matrix, etAB, where A is an n x n matrix and B is n x n₀ with n₀ << n. The algorithm works for any A, its computational cost is dominated by the formation of products of A with n x n₀ matrices, and the only input parameter is a backward error tolerance. The algorithm can return a single matrix etAB or a sequence etkAB on an equally spaced grid of points tk. It uses the scaling part of the scaling and squaring method together with a truncated Taylor series approximation to the exponential. It determines the amount of scaling and the Taylor degree using the strategy of expm[new].Preprocessing steps are used to reduce the cost of the algorithm. An important application of the algorithm is to exponential integrators for ordinary differential equations. It is shown that the sums of the form $\sum_{k=0}^p\varphi_k(A)u_k$ that arise in exponential integrators, where the $\varphi_k$ are related to the exponential function, can be expressed in terms of a single exponential of a matrix of dimension $n+p$ built by augmenting $A$ with additional rows and columns. Third, a general framework for simultaneously computing a matrix function, $f(A)$, and its Fréchet derivative in the direction $E$, $L_f(A,E)$, is established for a wide range of matrix functions. In particular, we extend the algorithm of Higham and $\mathrm{expm_{new}}$ to two algorithms that intertwine the evaluation of both $e^A$ and $L(A,E)$ at a cost about three times that for computing $e^A$ alone. These two extended algorithms are then adapted to algorithms that simultaneously calculate $e^A$ together with an estimate of its condition number. Finally, we show that $L_f(A,E)$, where $f$ is a real-valued matrix function and $A$ and $E$ are real matrices, can be approximated by $\Im f(A+ihE)/h$ for some suitably small $h$. This approximation generalizes the complex step approximation known in the scalar case, and is proved to be of second order in $h$ for analytic functions $f$ and also for the matrix sign function. It is shown that it does not suffer the inherent cancellation that limits the accuracy of finite difference approximations in floating point arithmetic. However, cancellation does nevertheless vitiate the approximation when the underlying method for evaluating $f$ employs complex arithmetic. The complex step approximation is attractive when specialized methods for evaluating the Fréchet derivative are not available.
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Kuo, Hui-Ying. "Comparison of temporal processing and motion perception in emmetropes and myopes." Thesis, Queensland University of Technology, 2009. https://eprints.qut.edu.au/31905/1/Hui-Ying_Kuo_Thesis.pdf.

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While spatial determinants of emmetropization have been examined extensively in animal models and spatial processing of human myopes has also been studied, there have been few studies investigating temporal aspects of emmetropization and temporal processing in human myopia. The influence of temporal light modulation on eye growth and refractive compensation has been observed in animal models and there is evidence of temporal visual processing deficits in individuals with high myopia or other pathologies. Given this, the aims of this work were to examine the relationships between myopia (i.e. degree of myopia and progression status) and temporal visual performance and to consider any temporal processing deficits in terms of the parallel retinocortical pathways. Three psychophysical studies investigating temporal processing performance were conducted in young adult myopes and non-myopes: (1) backward visual masking, (2) dot motion perception and (3) phantom contour. For each experiment there were approximately 30 young emmetropes, 30 low myopes (myopia less than 5 D) and 30 high myopes (5 to 12 D). In the backward visual masking experiment, myopes were also classified according to their progression status (30 stable myopes and 30 progressing myopes). The first study was based on the observation that the visibility of a target is reduced by a second target, termed the mask, presented quickly after the first target. Myopes were more affected by the mask when the task was biased towards the magnocellular pathway; myopes had a 25% mean reduction in performance compared with emmetropes. However, there was no difference in the effect of the mask when the task was biased towards the parvocellular system. For all test conditions, there was no significant correlation between backward visual masking task performance and either the degree of myopia or myopia progression status. The dot motion perception study measured detection thresholds for the minimum displacement of moving dots, the maximum displacement of moving dots and degree of motion coherence required to correctly determine the direction of motion. The visual processing of these tasks is dominated by the magnocellular pathway. Compared with emmetropes, high myopes had reduced ability to detect the minimum displacement of moving dots for stimuli presented at the fovea (20% higher mean threshold) and possibly at the inferior nasal retina. The minimum displacement threshold was significantly and positively correlated to myopia magnitude and axial length, and significantly and negatively correlated with retinal thickness for the inferior nasal retina. The performance of emmetropes and myopes for all the other dot motion perception tasks were similar. In the phantom contour study, the highest temporal frequency of the flickering phantom pattern at which the contour was visible was determined. Myopes had significantly lower flicker detection limits (21.8 ± 7.1 Hz) than emmetropes (25.6 ± 8.8 Hz) for tasks biased towards the magnocellular pathway for both high (99%) and low (5%) contrast stimuli. There was no difference in flicker limits for a phantom contour task biased towards the parvocellular pathway. For all phantom contour tasks, there was no significant correlation between flicker detection thresholds and magnitude of myopia. Of the psychophysical temporal tasks studied here those primarily involving processing by the magnocellular pathway revealed differences in performance of the refractive error groups. While there are a number of interpretations for this data, this suggests that there may be a temporal processing deficit in some myopes that is selective for the magnocellular system. The minimum displacement dot motion perception task appears the most sensitive test, of those studied, for investigating changes in visual temporal processing in myopia. Data from the visual masking and phantom contour tasks suggest that the alterations to temporal processing occur at an early stage of myopia development. In addition, the link between increased minimum displacement threshold and decreasing retinal thickness suggests that there is a retinal component to the observed modifications in temporal processing.
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Books on the topic "Backward error"

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Skeel, Robert D. Global error estimation and the backward differentiation formulas. Urbana, IL (1304 W. Springfield Ave., Urbana 61801): Dept. of Computer Science, University of Illinois at Urbana-Champaign, 1986.

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Arioli, M. Solving sparse linear systems with sparse backward error. New York: Courant Institute of Mathematical Sciences, New York University, 1988.

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Graduate Introduction to Numerical Methods: From the Viewpoint of Backward Error Analysis. Springer New York, 2013.

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Corless, Robert M., and Nicolas Fillion. A Graduate Introduction to Numerical Methods: From the Viewpoint of Backward Error Analysis. Springer, 2013.

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Corless, Robert M., and Nicolas Fillion. A Graduate Introduction to Numerical Methods: From the Viewpoint of Backward Error Analysis. Springer, 2016.

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Doyle, Christine A. Health Information Technology Use for Quality Assurance and Improvement. Oxford University Press, 2016. http://dx.doi.org/10.1093/med/9780199366149.003.0015.

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Health information technology (HIT) has become an important part of patient care, and can provide useful solutions for a quality assurance and improvement (QA&I) program by illustrating current quality and demonstrating gaps in quality that can be targeted for improvement. Like any other information technology project, however, HIT solutions can give misleading results if the wrong information is selected for review or if there are systematic errors in data handling. Although many health information systems are sometimes maligned as a glorified statistical tool or billing document, well-designed and implemented anesthesia information management systems (AIMS), perioperative electronic health records (EHR), and other software solutions can provide an excellent vehicle for use in quality programs. When planning the implementation of a major HIT project, it is usually best to start at the “end”—the desired workflow and goals of the project—and then work backward.
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Book chapters on the topic "Backward error"

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Kettner, Lutz, Kurt Mehlhorn, Sylvain Pion, Stefan Schirra, and Chee Yap. "Reply to “Backward Error Analysis ...”." In Computational Science and Its Applications - ICCSA 2006, 60. Berlin, Heidelberg: Springer Berlin Heidelberg, 2006. http://dx.doi.org/10.1007/11751540_7.

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Corless, Robert M., and Nicolas Fillion. "Backward Error Analysis for Perturbation Methods." In Algorithms and Complexity in Mathematics, Epistemology, and Science, 35–79. New York, NY: Springer New York, 2019. http://dx.doi.org/10.1007/978-1-4939-9051-1_3.

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Hairer, Ernst, Gerhard Wanner, and Christian Lubich. "Backward Error Analysis and Structure Preservation." In Springer Series in Computational Mathematics, 287–326. Berlin, Heidelberg: Springer Berlin Heidelberg, 2002. http://dx.doi.org/10.1007/978-3-662-05018-7_9.

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Jiang, Di, and Neil F. Stewart. "Backward Error Analysis in Computational Geometry." In Computational Science and Its Applications - ICCSA 2006, 50–59. Berlin, Heidelberg: Springer Berlin Heidelberg, 2006. http://dx.doi.org/10.1007/11751540_6.

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Shrivastava, S. K. "Concurrent Pascal with Backward Error Recovery: Implementation." In Reliable Computer Systems, 344–57. Berlin, Heidelberg: Springer Berlin Heidelberg, 1985. http://dx.doi.org/10.1007/978-3-642-82470-8_25.

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Islas, A. L., and C. M. Schober. "Backward Error Analysis for a Multi-Symplectic Integrator." In Mathematical and Numerical Aspects of Wave Propagation WAVES 2003, 799–804. Berlin, Heidelberg: Springer Berlin Heidelberg, 2003. http://dx.doi.org/10.1007/978-3-642-55856-6_130.

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Higham, N. J. "Perturbation Theory and Backward Error for AX - XB = C." In Linear Algebra for Large Scale and Real-Time Applications, 391. Dordrecht: Springer Netherlands, 1993. http://dx.doi.org/10.1007/978-94-015-8196-7_39.

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Ghaffari, Fakhreddine, Olivier Romain, and Bertrand Granado. "Mitigation Transient Faults by Backward Error Recovery in SRAM-FPGA." In Radiation Effects on Integrated Circuits and Systems for Space Applications, 249–76. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-04660-6_10.

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Shrivastava, S. K. "Concurrent Pascal with Backward Error Recovery: Language Features and Examples." In Reliable Computer Systems, 322–43. Berlin, Heidelberg: Springer Berlin Heidelberg, 1985. http://dx.doi.org/10.1007/978-3-642-82470-8_24.

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Mortenson, Torrey, and Ronald L. Boring. "Forward and Backward Error Recovery Factors in Digital Human-System Interface Design." In Advances in Intelligent Systems and Computing, 267–73. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-50946-0_36.

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Conference papers on the topic "Backward error"

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Fan, Xiaopeng, Oscar C. Au, and Jiantao Zhou. "Backward error concealment of redundantly coded video." In 2010 IEEE International Conference on Acoustics, Speech and Signal Processing. IEEE, 2010. http://dx.doi.org/10.1109/icassp.2010.5495985.

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Fu, Zhoulai, Zhaojun Bai, and Zhendong Su. "Automated backward error analysis for numerical code." In SPLASH '15: Conference on Systems, Programming, Languages, and Applications: Software for Humanity. New York, NY, USA: ACM, 2015. http://dx.doi.org/10.1145/2814270.2814317.

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Kalal, Zdenek, Krystian Mikolajczyk, and Jiri Matas. "Forward-Backward Error: Automatic Detection of Tracking Failures." In 2010 20th International Conference on Pattern Recognition (ICPR). IEEE, 2010. http://dx.doi.org/10.1109/icpr.2010.675.

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Skeel, R. D. "Global error estimation and the backward differentiation formulas." In the conference. New York, New York, USA: ACM Press, 1989. http://dx.doi.org/10.1145/101007.101030.

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Wang, Ping-Chin, and Chow-Sing Lin. "Enhanced Backward Error Concealment for H.264/AVC Videos on Error-Prone Networks." In 2013 International Symposium on Biometrics and Security Technologies (ISBAST). IEEE, 2013. http://dx.doi.org/10.1109/isbast.2013.12.

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Quintela-Pumares, Manuel, Bruno Cabral, Daniel Fernandez-Lanvin, and Alberto-Manuel Fernandez-Alvarez. "Integrating automatic backward error recovery in asynchronous rich clients." In ICSE '16: 38th International Conference on Software Engineering. New York, NY, USA: ACM, 2016. http://dx.doi.org/10.1145/2889160.2889241.

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Fan, Xiaopeng, Oscar C. Au, Debin Zhao, and Wen Gao. "Joint forward backward error concealment of redundantly coded video." In 2010 18th International Packet Video Workshop (PV). IEEE, 2010. http://dx.doi.org/10.1109/pv.2010.5706816.

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Petrisor, Gregory C., Adam A. Goldstein, Edward J. Herbulock, B. Keith Jenkins, and Armand R. Tanguay. "Convergence of Backward Error Propagation Learning in Photorefractive Crystals." In Optical Computing. Washington, D.C.: Optica Publishing Group, 1995. http://dx.doi.org/10.1364/optcomp.1995.otue1.

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Although backward error propagation learning in photorefractive crystals has been previously investigated by simulation and experiment, theoretical results governing convergence have been lacking. In this paper we prove analytically that such learning in multilayer neural networks implemented using photorefractive crystals can have similar convergence properties to those of an ideal backward error propagation network. Further, we derive relationships between two learning parameters that will ensure these convergence properties are satisfied under the assumption of small weight-update sizes, and we relate these parameters to spatial light modulator gain and holographic grating update exposure energy.
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Hewage, Chaminda T. E. R., and Maria G. Martini. "Joint Error Concealment Method for Backward Compatible 3D Video Transmission." In 2011 IEEE Vehicular Technology Conference (VTC 2011-Spring). IEEE, 2011. http://dx.doi.org/10.1109/vetecs.2011.5956767.

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Fouad, Sahraoui, Fakhreddine Ghaffari, Mohamed El Amine Benkhelifa, and Bertrand Granado. "Reliability assessment of backward error recovery for SRAM-based FPGAs." In 2014 9th International Design & Test Symposium (IDT). IEEE, 2014. http://dx.doi.org/10.1109/idt.2014.7038622.

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Reports on the topic "Backward error"

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Gallegos, José-Elías. Inflation persistence, noisy information and the Phillips curve. Madrid: Banco de España, February 2023. http://dx.doi.org/10.53479/29569.

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A vast literature has documented how US inflation persistence has fallen in recent decades, but this finding is difficult to explain in monetary models. Using survey data on inflation expectations, I document a positive co-movement between ex-ante average forecast errors and forecast revisions (suggesting forecast sluggishness) from 1968 to 1984, but no co-movement thereafter. I extend the New Keynesian setting to include noisy and dispersed information about the aggregate state, and show that inflation is more persistent in periods of greater forecast sluggishness. My results suggest that changes in firm forecasting behavior explain around 90% of the fall in inflation persistence since the mid-1980s. I also find that the changes in the dynamics of the Phillips curve can be explained by the change in information frictions. After controlling for changes in information frictions, I estimate only a modest decline in the slope. I find that a more significant factor in the dynamics of the Phillips curve is the shift towards greater forward-lookingness and less backward-lookingness. Finally, I find evidence of forecast underrevision in the post-COVID period, which explains the increase in the persistence of current inflation.
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