Dissertations / Theses on the topic 'Backward error'
Create a spot-on reference in APA, MLA, Chicago, Harvard, and other styles
Consult the top 20 dissertations / theses for your research on the topic 'Backward error.'
Next to every source in the list of references, there is an 'Add to bibliography' button. Press on it, and we will generate automatically the bibliographic reference to the chosen work in the citation style you need: APA, MLA, Harvard, Chicago, Vancouver, etc.
You can also download the full text of the academic publication as pdf and read online its abstract whenever available in the metadata.
Browse dissertations / theses on a wide variety of disciplines and organise your bibliography correctly.
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.
Full textZivcovich, 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.
Full textZivcovich, 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.
Full textMoan, 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.
Full textTantardini, 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.
Full textVolz, 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.
Full textRecent 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.
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.
Full textThe 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
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.
Full textAl-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.
Full textKuo, 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.
Full textAydin, Ayhan. "Geometric Integrators For Coupled Nonlinear Schrodinger Equation." Phd thesis, METU, 2005. http://etd.lib.metu.edu.tr/upload/12605773/index.pdf.
Full textdinger equations (CNLSE). Energy, momentum and additional conserved quantities are preserved by the multisymplectic integrators, which are shown using modified equations. The multisymplectic schemes are backward stable and non-dissipative. A semi-explicit method which is symplectic in the space variable and based on linear-nonlinear, even-odd splitting in time is derived. These methods are applied to the CNLSE with plane wave and soliton solutions for various combinations of the parameters of the equation. The numerical results confirm the excellent long time behavior of the conserved quantities and preservation of the shape of the soliton solutions in space and time.
Worrall, S. T. "Backwards compatible adaptive error resilience techniques for MPEG-4 over mobile networks." Thesis, University of Surrey, 2001. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.365149.
Full textFreeman, Michael. "Hardware support of recovery blocks." Thesis, University of York, 1999. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.341599.
Full textSegura, ugalde Esteban. "Computation of invariant pairs and matrix solvents." Thesis, Limoges, 2015. http://www.theses.fr/2015LIMO0045/document.
Full textIn this thesis, we study some symbolic-numeric aspects of the invariant pair problem for matrix polynomials. Invariant pairs extend the notion of eigenvalue-eigenvector pairs, providing a counterpart of invariant subspaces for the nonlinear case. They have applications in the numeric computation of several eigenvalues of a matrix polynomial; they also present an interest in the context of differential systems. Here, a contour integral formulation is applied to compute condition numbers and backward errors for invariant pairs. We then adapt the Sakurai-Sugiura moment method to the computation of invariant pairs, including some classes of problems that have multiple eigenvalues, and we analyze the behavior of the scalar and block versions of the method in presence of different multiplicity patterns. Results obtained via direct approaches may need to be refined numerically using an iterative method: here we study and compare two variants of Newton’s method applied to the invariant pair problem. The matrix solvent problem is closely related to invariant pairs. Therefore, we specialize our results on invariant pairs to the case of matrix solvents, thus obtaining formulations for the condition number and backward errors, and a moment-based computational approach. Furthermore, we investigate the relation between the matrix solvent problem and the triangularization of matrix polynomials
Argyridou, Eleni. "Estimating errors in quantities of interest in the case of hyperelastic membrane deformation." Thesis, Brunel University, 2018. http://bura.brunel.ac.uk/handle/2438/16205.
Full textHorsin, Romain. "Comportement en temps long d'équations de type Vlasov : études mathématiques et numériques." Thesis, Rennes 1, 2017. http://www.theses.fr/2017REN1S062/document.
Full textThis thesis concerns the long time behavior of certain Vlasov equations, mainly the Vlasov- HMF model. We are in particular interested in the celebrated phenomenon of Landau damp- ing, proved mathematically in various frameworks, foar several Vlasov equations, such as the Vlasov-Poisson equation or the Vlasov-HMF model, and exhibiting certain analogies with the inviscid damping phenomenon for the 2D Euler equation. The results described in the document are the following.The first one is a Landau damping theorem for numerical solutions of the Vlasov-HMF model, constructed by means of time-discretizations by splitting methods. We prove more- over the convergence of the schemes. The second result is a Landau damping theorem for solutions of the Vlasov-HMF model linearized around inhomogeneous stationary states. We provide moreover a quite large amount of numerical simulations, which are designed to study numerically the nonlinear case, and which seem to show new phenomenons. The last result is the convergence of a scheme that discretizes in time the 2D Euler equation by means of a symplectic Crouch-Grossmann integrator
Kopec, Marie. "Quelques contributions à l'analyse numérique d'équations stochastiques." Electronic Thesis or Diss., Rennes, École normale supérieure, 2014. http://www.theses.fr/2014ENSR0002.
Full textThis work presents some results about behavior in long time and in finite time of numerical methods for stochastic equations.In a first part, we are considered with overdamped Langevin Stochastic Differential Equations (SDE) and Langevin SDE. We show a weak backward error analysis result for its numerical approximations defined by implicit methods. In particular, we prove that the generator associated with the numerical solution coincides with the solution of a modified Kolmogorov equation up to high order terms with respect to the stepsize. This implies that every measure of the numerical scheme is close to a modified invariant measure obtained by asymptotic expansion. Moreover, we prove that, up to negligible terms, the dynamic associated with the implicit scheme considered is exponentially mixing.In a second part, we study the long-time behavior of fully discretized semilinear SPDEs with additive space-time white noise, which admit a unique invariant probability measure μ. We focus on the discretization in time thanks to a scheme of Euler type, and on a Finite Element discretization in space and we show that the average of regular enough test functions with respect to the (possibly non unique) invariant laws of the approximations are close to the corresponding quantity for μ.More precisely, we analyze the rate of the convergence with respect to the different discretization parameters. Finally, we are concerned with semilinear SPDEs with additive space-time white noise, which the nonlinear term is a polynomial function. We analyze the rate of the weak convergence for discretization in time with an implicit splitting method
Vestin, Albin, and Gustav Strandberg. "Evaluation of Target Tracking Using Multiple Sensors and Non-Causal Algorithms." Thesis, Linköpings universitet, Reglerteknik, 2019. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-160020.
Full textWang, Ping-chin, and 王昞清. "Enhanced Backward Error Concealment for H.264/AVC Videos on Error-Prone Networks." Thesis, 2012. http://ndltd.ncl.edu.tw/handle/05006064494876470532.
Full text國立臺南大學
資訊工程學系碩士班
100
Transmitting compressed video data is quite common over the wireless network or wired network. In error-prone networks, packet loss could lead to decode incorrectly. With the new generation standard, H.264/AVC, such issue incurs error propagation and makes quality of decoded video degrade drastically. To solve such issue, error concealment is applied in decoder. However, traditional error concealment cannot give satisfactory result in some cases, such as whole frame loss. Such issue is addressd by backword error concealment that concealing corrupted frame by utilizing succeeding frame which is correctly received. Nevertheless, backward error concealment efficiently conceal most of the corrupted pixels except the unreferenced pixels. In this thesis, we propose an enhanced backward error concealment method.Based on moving objects continuity, the porposed method provide estimated motion vectors to conceal the unreferenced pixels. Experimental results showed that the proposed method achieve better performance in measuring of distortion.
Tsai, Ming-Kuang, and 蔡茗光. "Synchronous Backward Error Tracking Algorithm in H.264 Video Coding." Thesis, 2004. http://ndltd.ncl.edu.tw/handle/16606590106382645211.
Full text國立中央大學
通訊工程研究所
92
The most recent H.264 video coding utilizes complex predictions in both the temporal and spatial domains to get better performance than other standards. Certainly, such predictions may cause serious error propagation effects when suffering from transmission errors. Therefore, the objective of this paper is to develop a robust error resilient algorithm, named as the Synchronous Backward Error Tracking (SBET) algorithm, to completely terminate the error propagation. If the state of the encoder can synchronize to that of the decoder, the error propagation effects can be entirely terminated. Therefore, we assume that a feedback channel is available and the encoder can be aware of the decoder’s error concealment by external means. The pixel-based Precise Backward Error Tracking (PBET) is utilized to track the error locations and propagate the concealment error of erroneous frame to the corresponding areas to reconstruct the state of the decoder in the encoder. Comparing with the full re-encoding method, the proposed method only involves memory access, simple addition and multiplication operations for the error-contaminated pixels. By observing the simulation results, the rate-distortion performance of the proposed algorithm is always better than that of the conventional algorithms. SBET outperforms PBET up to 1.21 dB under 3% slice error rate for the QCIF Foreman sequence. In addition, without using forced INTRA refreshing, the phenomenon of burst bit rate can be avoided. In the future, if a better error concealment technique is utilized, a better performance of SBET is also expected.