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Inexact subspace iteration to accelerate the solution of linear systems with multiple right-hand sides

Balsa, Carlos
Fonte: University of Porto Publicador: University of Porto
Tipo: Conferência ou Objeto de Conferência
Português
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We analyze the convergence and propose some strategy to monitor an inexact subspace iteration type of algorithm called BlockCGSI. This algorithm is purely iterative and combines the block Conjugate Gradient (blockCG) algorithm with the Subspace Iteration. We proceed to an inner-outer convergence analyze and exploit the possibility of reducing the total amount of computational work by controlling the accuracy during the solution of linear systems at each inverse iteration. The proposed method can be adequate for large scale problems where we need to solve consecutively several linear systems with the same coefficient matrix (or with very close spectral properties) but with changing right-hand sides. The BlockCGSI algorithm can be used to compute some spectral information, which is then used to remove the effect of the smallest eigenvalues in two different ways: either by building a Spectral Low Rank Update (SLRU) preconditioner that basically adds the value 1 to these eigenvalues, or by performing a deflation of the initial residual in order to remove part of the solution corresponding to the smallest eigenvalues. Both techniques can reduce substantially the total number of iterations and computational work in each subsequent runs of the Conjugate Gradient algorithm.

The Policy Iteration Algorithm for Average Continuous Control of Piecewise Deterministic Markov Processes

Costa, Oswaldo Luiz do Valle; DUFOUR, F.
Fonte: SPRINGER Publicador: SPRINGER
Tipo: Artigo de Revista Científica
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The main goal of this paper is to apply the so-called policy iteration algorithm (PIA) for the long run average continuous control problem of piecewise deterministic Markov processes (PDMP`s) taking values in a general Borel space and with compact action space depending on the state variable. In order to do that we first derive some important properties for a pseudo-Poisson equation associated to the problem. In the sequence it is shown that the convergence of the PIA to a solution satisfying the optimality equation holds under some classical hypotheses and that this optimal solution yields to an optimal control strategy for the average control problem for the continuous-time PDMP in a feedback form.; CNPq (Brazilian National Research Council)[301067/09-0]; French National Agency of Research (ANR)[ANR-09-SEGI-004]

On the iteration of smooth maps

Correia, Maria de Fátima; Ramos, Carlos; Vinagre, Sandra
Fonte: Discrete Dynamics and Difference Equations - Proceedings of the Twelfth International Conference on Difference Equations and Applications, World Scientific Publishing Publicador: Discrete Dynamics and Difference Equations - Proceedings of the Twelfth International Conference on Difference Equations and Applications, World Scientific Publishing
Tipo: Artigo de Revista Científica
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Iteration of smooth maps appears naturally in the study of continuous difference equations and boundary value problems. Moreover, it is a subject that may be studied by its own interest, generalizing the iteration theory for interval maps. Our study is motivated by the works of A. N. Sharkovsky et al. [1,3], E. Yu. Romanenko et al. [2], S. Vinagre et al. [4] and R. Severino et al. [5]. We study families of discrete dynamical systems of the type (Ω,f), where Ω is some class of smooth functions, e.g., a sub-class of C^r(J,R), where J is an interval, and f is a smooth map f:R→R. The action is given by ϕ→foϕ. We analyze in particular the case when f is a family of quadratic maps. For this family we analyze the topological behaviour of the system and the parameter dependence on the spectral decomposition of the iterates.

Spectral properties of the preconditioned AHSS iteration method for generalized saddle point problems

Huang,Zhuo-Hong; Huang,Ting-Zhu
Fonte: Sociedade Brasileira de Matemática Aplicada e Computacional Publicador: Sociedade Brasileira de Matemática Aplicada e Computacional
Tipo: Artigo de Revista Científica Formato: text/html
Publicado em 01/06/2010 Português
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In this paper, we study the distribution on the eigenvalues of the preconditioned matrices that arise in solving two-by-two block non-Hermitian positive semidefinite linear systems by use of the accelerated Hermitian and skew-Hermitian splitting iteration methods. According to theoretical analysis, we prove that all eigenvalues of the preconditioned matrices are very clustered with any positive iteration parameters α and β; especially, when the iteration parameters α and β approximate to 1, all eigenvalues approach 1. We also prove that the real parts of all eigenvalues of the preconditioned matrices are positive, i.e., the preconditioned matrix is positive stable. Numerical experiments show the correctness and feasibility of the theoretical analysis. Mathematical subject classification: 65F10, 65N22, 65F50.

A modified parametric iteration method for solving nonlinear second order BVPs

Ghorbani,Asghar; Gachpazan,Morteza; Saberi-Nadjafi,Jafar
Fonte: Sociedade Brasileira de Matemática Aplicada e Computacional Publicador: Sociedade Brasileira de Matemática Aplicada e Computacional
Tipo: Artigo de Revista Científica Formato: text/html
Publicado em 01/01/2011 Português
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The original parametric iteration method (PIM) provides the solution of a nonlinear second order boundary value problem (BVP) as a sequence of iterations. Since the successive iterations of the PIM may be very complex so that the resulting integrals in its iterative relation may not be performed analytically. Also, the implementation of the PIM generally leads to calculation of unneeded terms, which more time is consumed in repeated calculations for series solutions. In order to overcome these difficulties, in this paper, a useful improvement of the PIM is proposed. The implementation of the modified method is demonstrated by solving several nonlinear second order BVPs. The results reveal that the new developed method is a promising analytical tool to solve the nonlinear second order BVPs and more promising because it can further be applied easily to solve nonlinear higher order BVPs with highly accurate. Mathematical subject classification: Primary: 34B15; Secondary: 41A10.

Application of iteration perturbation method and Hamiltonian approach for nonlinear vibration of Euler-Bernoulli beams

Ahmadi,Morteza; Hashemi,Gholamreza; Asghari,Ali
Fonte: Associação Brasileira de Ciências Mecânicas Publicador: Associação Brasileira de Ciências Mecânicas
Tipo: Artigo de Revista Científica Formato: text/html
Publicado em 01/11/2014 Português
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This paper is devoted to the new classes of analytical techniques called the Iteration Perturbation Method (IPM)and Hamiltonian Approach(HA) for solving the equation of motion governing the nonlinear vibration of Euler-Bernoulli beams subjected to the axial loads. It has been found that theIPMand HAare very prolific, rapid, functional and do not demand small perturbation and are also sufficiently accurate to both linear and nonlinear problems in engineering. Comparison of the results of these methods with together and with the results of numerical solution reveals that the IPM and HA are very effective and convenient, and can be easily extended to other nonlinear systems so that can be found widely applicable in engineering and other sciences.

Application of Iteration Perturbation Method in studying dynamic pull-in instability of micro-beams

Sedighi,Hamid M.; Daneshmand,Farhang; Yaghootian,Amin
Fonte: Associação Brasileira de Ciências Mecânicas Publicador: Associação Brasileira de Ciências Mecânicas
Tipo: Artigo de Revista Científica Formato: text/html
Publicado em 01/12/2014 Português
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In the present study, dynamic pull-in instability of electrostatically-actuated micro-beams is investigated through proposing the nonlinear frequency amplitude relationship. An approximate analytical expression of the fundamental natural frequency is presented by modern asymptotic approach namely Iteration Perturbation Method (IPM). Influences of vibrational amplitude as well as different parameters on dynamic pull-in voltage are investigated. It is demonstrated that two terms in series expansions is sufficient to produce an acceptable solution of the mentioned microstructure. The simulations from numerical methods verify the validity of the analytical procedure.

Sources of iteration and a risk mitigation methodology in semiconductor new product development projects

Murphy, Evan
Fonte: University of Limerick Publicador: University of Limerick
Tipo: info:eu-repo/semantics/doctoralThesis; all_ul_research; ul_published_reviewed; ul_theses_dissertations
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peer-reviewed; Iteration is the major source of risk in semiconductor New Product Development (NPD) projects, occurring in approximately 90% of projects and causing on average approximately 30% schedule slippage. As such, iteration risk in semiconductor NPD projects is a very important issue that needs to be addressed. NPD projects bring specific challenges for a company due to the innate uncertainty involved in producing a new product. One major consequence of the inherent uncertainty involved in NPD projects is the resultant uncertainty and risk of iteration in project schedules. A challenge when trying to generate a product development schedule is to accurately account for the uncertainty caused by iteration and potential schedule slippage. The occurrence of iteration in NPD projects can directly lead to budget over-runs, schedule delays and missed product release. With time to market often being an important determinant of NPD success any factor that can potentially cause project delay must be fully understood. This research aims to further examine iteration risk in a semiconductor NPD project context, and explore how a more accurate iteration risk mitigation methodology can be established. Providing management within a firm with a process specific risk analysis regarding iteration can enable a proactive approach to NPD scheduling and contingency planning. The goal of the research is to provide an iteration risk analysis methodology where the risks of delay due to iteration in NPD projects can be identified...

Accelerated landweber iteration with convex penalty for linear inverse problems in Banach spaces

Hegland, Markus; Jin, Qinian; Wang, Wei
Fonte: Taylor & Francis Publicador: Taylor & Francis
Tipo: Artigo de Revista Científica Formato: 24 pages
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In recent years, Landweber iteration has been extended to solve linear inverse problems in Banach spaces by incorporating non-smooth convex penalty functionals to capture features of solutions. This method is known to be slowly convergent. However, because it is simple to implement, it still receives a lot of attention. By making use of the subspace optimization technique, we propose an accelerated version of Landweber iteration with non-smooth convex penalty which significantly speeds up the method. Numerical simulations are given to test the efficiency.; M Hegland is partially supported under Australian Research Council’s Discovery Projects funding scheme (DP130101738) and the Technische Universität München Institute for Advanced Study, funded by the German Excellence Initiative. Q Jin is partially supported by the grant DE120101707 of Australian Research Council. W Wang is partially supported by Zhejiang Provincial Natural Science Foundation of China (No. LQ14A010013).

Neural-network based online policy iteration for continuous-time infinite-horizon optimal control of nonlinear systems

Tang, D.; Chen, L.; Tian, Z.F.
Fonte: Institute of Electrical and Electronics Engineers (IEEE) Publicador: Institute of Electrical and Electronics Engineers (IEEE)
Tipo: Conference paper
Publicado em //2015 Português
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A new policy-iteration algorithm based on neural networks (NNs) is proposed in this paper to synthesize optimal control laws online for continuous-time nonlinear systems. Latest advances in this field have enabled synchronous policy iteration but require an additional tuning loop or a logic switch mechanism to maintain system stability. A new algorithm is thus derived in this paper to address this limitation. The optimal control law is found by solving the Hamilton-Jacobi- Bellman (HJB) equation for the associated value function via synchronous policy iteration in a critic-actor configuration. As a major contribution, a new form of NN approximation for the value function is proposed, offering the closed-loop system asymptotic stability without additional tuning scheme or logic switch mechanism. As a second contribution, an extended Kalman filter is introduced to estimate the critic NN parameters for fast convergence. The efficacy of the new algorithm is verified by simulations.; Difan Tang, Lei Chen, and Zhao Feng Tian; IEEE Catalog Number: CFP15SIP-USB

Analysis and implementation of an implicitly restarted Arnoldi iteration

Lehoucq, Richard Bruno
Fonte: Universidade Rice Publicador: Universidade Rice
Tipo: Thesis; Text Formato: 193 p.; application/pdf
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The Arnoldi algorithm, or iteration, is a computationally attractive technique for computing a few eigenvalues and associated invariant subspace of large, often sparse, matrices. The method is a generalization of the Lanczos process and reduces to that when the underlying matrix is symmetric. This thesis presents an analysis of Sorensen's Implicitly Re-started Arnoldi iteration, (scIRA-iteration), by exploiting its relationship with the scQR algorithm. The goal of this thesis is to present numerical techniques that attempt to make the scIRA-iteration as robust as the implicitly shifted scQR algorithm. The benefit is that the Arnoldi iteration only requires the computation of matrix vector products w = Av at each step. It does to rely on the dense matrix similarity transformations required by the EISPACK and LAPACK software packages. Five topics form the contribution of this dissertation. The first topic analyzes re-starting the Arnoldi iteration in an implicit or explicit manner. The second topic is the numerical stability of an scIRA-iteration. The forward instability of the scQR algorithm and the various schemes used to re-order the Schur form of a matrix are fundamental to this analysis. A sensitivity analysis of the Hessenberg decomposition is presented. The practical issues associated with maintaining numerical orthogonality among the Arnoldi/Lanczos basis vectors is the third topic. The fourth topic is deflation techniques for an scIRA-iteration. The deflation strategies introduced make it possible to compute multiple or clustered eigenvalues with a single vector re-start method. The block Arnoldi/Lanczos methods commonly used are not required. The final topic is the convergence typical of an scIRA-iteration. Both formal theory and heuristics are provided for making choices that will lead to improved convergence of an scIRA-iteration.

Iteration as a strategy for teaching architectural technologies in an architecture studio

Shannon, S.; Radford, A.
Fonte: University of Sydney Publicador: University of Sydney
Tipo: Artigo de Revista Científica
Publicado em //2010 Português
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The linking of architectural technologies and design is problematic in the education of architects. While students can understand how environment, building performance, structure, construction and building services interact and work in a particular building, they often find devising strategies and technologies for designs of their own to be difficult. In this article, we describe the learning outcomes and student responses to an experimental integrated building design studio that explored whether planned iteration would promote learning of these issues and technologies. By planned iteration we mean the programming of the explicit cycles in which the same issues and technologies are revisited several times in a way that recognizes and develops a student's increasing understanding. This positions design (in a broad sense) as a cyclical process of reflective practice, where the design situation and potential are only fully understood through the process of postulating and reflecting on design proposals. The design knowledge needed is only fully apparent once the process is underway. Results indicate that 'low-risk attempt followed by feedback' is an effective mode of learning. Such an approach has dangers of requiring unrealistic staff time in providing feedback; in this experimental studio most feedback was offered to groups rather than individuals.; Susan Shannon and Antony Radford

A few ants are enough: ACO with iteration-best update

Neumann, F.; Sudholt, D.; Witt, C.
Fonte: ACM Press; New York Publicador: ACM Press; New York
Tipo: Conference paper
Publicado em //2010 Português
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Ant colony optimization (ACO) has found many applications in different problem domains. We carry out a first rigorous runtime analysis of ACO with iteration-best update, where the best solution in the each iteration is reinforced. This is similar to comma selection in evolutionary algorithms. We compare ACO to evolutionary algorithms for which it is well known that an offspring size of (log n), n the problem dimension, is necessary to optimize even simple functions like OneMax. In sharp contrast, ACO is efficient on OneMax even for the smallest possible number of two ants. Remarkably, this only holds if the pheromone evaporation rate is small enough; the collective memory of many ants stored in the pheromones makes up for the small number of ants. We further prove an exponential lower bound for ACO with iteration-best update that depends on a trade-off between the number of ants and the evaporation rate.; Frank Neumann, Dirk Sudholt and Carsten Witt

A Picard-S hybrid type iteration method for solving a differential equation with retarded argument

Gürsoy, Faik; Karakaya, Vatan
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
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We introduce a new iteration method called Picard-S iteration. We show that the Picard-S iteration method can be used to approximate fixed point of contraction mappings. Also, we show that our new iteration method is equivalent and converges faster than CR iteration method for the aforementioned class of mappings. Furthermore, by providing an example, it is shown that the Picard-S iteration method converges faster than all Picard, Mann, Ishikawa, Noor, SP, CR, S and some other iteration methods in the existing literature when applied to contraction mappings. A data dependence result is proven for fixed point of contraction mappings with help of the new iteration method. Finally, we show that the Picard-S iteration method can be used to solve differential equations with retarded argument.

Axiomatizing Flat Iteration

van Glabbeek, R. J.
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 07/10/1998 Português
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Flat iteration is a variation on the original binary version of the Kleene star operation P*Q, obtained by restricting the first argument to be a sum of atomic actions. It generalizes prefix iteration, in which the first argument is a single action. Complete finite equational axiomatizations are given for five notions of bisimulation congruence over basic CCS with flat iteration, viz. strong congruence, branching congruence, eta-congruence, delay congruence and weak congruence. Such axiomatizations were already known for prefix iteration and are known not to exist for general iteration. The use of flat iteration has two main advantages over prefix iteration: 1.The current axiomatizations generalize to full CCS, whereas the prefix iteration approach does not allow an elimination theorem for an asynchronous parallel composition operator. 2.The greater expressiveness of flat iteration allows for much shorter completeness proofs. In the setting of prefix iteration, the most convenient way to obtain the completeness theorems for eta-, delay, and weak congruence was by reduction to the completeness theorem for branching congruence. In the case of weak congruence this turned out to be much simpler than the only direct proof found. In the setting of flat iteration on the other hand...

Investigating the Impact of Changes in Iteration-likelihoods on Design Process Performance

Shapiro, Daniel; Hamraz, Bahram; Sommer, Anita F.; Clarkson, P. John
Fonte: SAGE Publicador: SAGE
Tipo: Article; accepted version
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This is the author accepted manuscript. The final version is available from SAGE via http://dx.doi.org/10.1177/1063293X15588202; Research on changes in design has mainly focused on the product domain, which is the manifestation of the design process. This article investigates changes in the process domain, which describes the execution of coordinated and concurrent design activities through interdisciplinary teams. More specifically this article focusses on changes in the iterative behavior of activities as one of the key levers determining the performance of complex concurrent design processes. In activity network-based models of design processes the occurrence of such behavior is often expressed probabilistically through iteration-likelihoods. First, the impact of changes in iteration-likelihoods on the effort and duration of both individual activities and the overall design process is examined through stochastic analysis. Consequently a method for the investigation of changes in iteration-likelihoods is developed, which grounds on an experimental approach using Monte Carlo simulation of activity network-based process models. The method is applied to the design process of a high-speed machining device for the manufacturing of planetary-ball-bearing housings. This analysis results in a two-dimensional...

Modelling iteration in engineering design

Wynn, David C.; Eckert, Claudia M.; Clarkson, P. John
Fonte: Universidade de Cambridge Publicador: Universidade de Cambridge
Tipo: Conferência ou Objeto de Conferência
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INTERNATIONAL CONFERENCE ON ENGINEERING DESIGN, ICED?07 28 - 31 AUGUST 2007, CITE DES SCIENCES ET DE L'INDUSTRIE, PARIS, FRANCE; This paper examines design iteration and its modelling in the simulation of New Product Development (NPD) processes. A framework comprising six perspectives of iteration is proposed and it is argued that the importance of each perspective depends upon domain-specific factors. Key challenges of modelling iteration in process simulation frameworks such as the Design Structure Matrix are discussed, and we argue that no single model or framework can fully capture the iterative dynamics of an NPD process. To conclude, we propose that consideration of iteration and its representation could help identify the most appropriate modelling framework for a given process and modelling objective, thereby improving the fidelity of design process simulation models and increasing their utility.

Feature Matching and Pose Estimation Using Newton Iteration

Li, Hongdong; Hartley, Richard
Fonte: Springer Publicador: Springer
Tipo: Conference paper
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Feature matching and pose estimation are two crucial tasks in computer vision. The widely adopted scheme is first find the correct matches then estimate the transformation parameters. Unfortunately, such simple scheme does not work well sometimes, because these two tasks of matching and estimation are mutually interlocked. This paper proposes a new method that is able to estimate the transformation and find the correct matches simultaneously. The above interlock is disentangled by an alternating Newton iteration method. We formulate the problem as a nearest-matrix problem, and provide a different numerical technique. Experiments on both synthetic and real images gave good results. Fast global convergence was obtained without the need of good initial guess.

A fractal valued random iteration algorithm and fractal hierachy

Barnsley, Michael; Hutchinson, John; Stenflo, Orjan
Fonte: World Scientific Publishing Company Publicador: World Scientific Publishing Company
Tipo: Artigo de Revista Científica
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We describe new families of random fractals, referred to as "V-variable", which are intermediate between the notions of deterministic and of standard random fractals. The parameter V describes the degree of "variability": at each magnification level any V-variable fractals has at most V key "forms" or "shapes". V-variable random fractals have the surprising property that they can be computed using a forward process. More precisely, a version of the usual Random Iteration Algorithm, operating on sets (or measures) rather than points, can be used to sample each family. To present this theory, we review relevant results on fractals (and fractal measures), both deterministic and random. Then our new results are obtained by constructing an iterated function system (a super IPS) from a collection of standard IFSs together with a corresponding set of probabilities. The attractor of the super IFS is called a superfractal; it is a collection of V-variable random fractals (sets or measures) together with an associated probability distribution on this collection. When the underlying space is for example ℝ2, and the transformations are computationally straightforward (such as affine transformations), the superfractal can be sampled by means of the algorithm...

A Grassmann-Rayleigh Quotient Iteration for Computing Invariant Subspaces

Absil, P-A; Mahony, Robert; Sepulchre, R; Van Dooren, P
Fonte: SIAM Publications Publicador: SIAM Publications
Tipo: Artigo de Revista Científica
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The classical Rayleigh quotient iteration (RQI) allows one to compute a one-dimensional invariant subspace of a symmetric matrix A. Here we propose a generalization of the RQI which computes a p-dimensional invariant subspace of A. Cubic convergence is preserved and the cost per iteration is low compared to other methods proposed in the literature.