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# Topic: Iterative methods

###### In the News (Tue 16 Jul 19)

 Citations: Asynchronous iterative methods for multiprocessors - Baudet (ResearchIndex) Citations: Asynchronous iterative methods for multiprocessors - Baudet (ResearchIndex) Baudet, Asynchronous Iterative Methods for Multiprocessors, J. of the ACM 25, pp. Baudet (1978) Asynchronous Iterative Methods for Multiprocessors, J. of the ACM 25, pp. citeseer.ist.psu.edu /context/40276/0   (2558 words)

 Iterative methods -- CFD-Wiki, the free CFD reference Iterative methods, unlike direct methods, generate a sequence of approximate solutions to the system that (hopefully) converges to the exact solution. The convergence of such iterative methods can be investigated using the Fixed point theorem. When during the iterations B and c changes during the iterations, the method is called Nonstationary Iterative Method. www.cfd-online.com /Wiki/Iterative_methods   (173 words)

 Iterative Methods and Complex Dynamics The attraction basins of the Newton and Halley methods. The quasi-Halley method is a method of order 2.41, which uses the same information as Newton's method (except for an additional point z- and derivative f'(z-) at the initial iteration), see Ref. The global behavior of the Newton method is chaotic: the (common) boundary of the different basins is a Julia set of intricate shape, see Fig. rutcor.rutgers.edu /~bisrael/Halley.html   (591 words)

 The Dispatch - Serving the Lexington, NC - News   (Site not responding. Last check: ) Iterative methods are useful for problems involving a large number of variables (sometimes of the order of millions), where direct methods would be prohibitively expensive and in some cases impossible even with the best available computing power. Stationary iterative methods solve a linear system with an operator approximating the original one; and based on a measurement of the error (the residual), form a correction equation for which this process is repeated. The approximating operator that appears in stationary iterative methods can also be incorporated in Krylov subspace methods such as GMRES (alternatively, preconditioned Krylov methods can be considered as accelerations of stationary iterative methods), where they become transformations of the original operator to a presumably better conditioned one. www.the-dispatch.com /apps/pbcs.dll/section?category=NEWS&template=wiki&text=Iterative_methods   (587 words)

 First Steps in Numerical Analysis Recall that an iterative method starts with an approximate solution, and uses it by means of a recurrence formula to provide another approximate solution; by repeatedly applying the formula, a sequence of solutions is obtained which (under suitable conditions) converges to the exact solution. Iterative methods have the advantages of simplicity of operation and ease of implementation on computers, and they are relatively insensitive to propagation of errors; they would be used in preference to direct methods for solving linear systems involving several hundred variables, particularly, if many of the coefficients were zero. As in the above example, the Gauss-Seidel method may quickly lead to a solution very close to the exact one; on the other hand, it may converge too slowly to be of practical use, or it may produce a sequence which diverges from the exact solution. mpec.sc.mahidol.ac.th /numer/STEP13.HTM   (724 words)

 Iterative Image Restoration In comparison with non-iterative methods iterative procedures offer the advantage that no matrix inverses need to be implemented, and that additional deterministic constraints can be incorporated into the solution algorithms. Additional advantages of using iterative optimization algorithms are that they allow for more flexible, possible more complex but certainly improved formulation of the solution to the identification and restoration problem. As opposite to non-iterative methods, such as the recursive or frequency domain filters, iterative schemes can also handle problems, which do not have an explicit analytical solution, but have been formulated as the optimization of a nonlinear and/or spatially variant objective function. www.cs.technion.ac.il /Labs/Isl/Project/Projects_done/VisionClasses/DIP/Iterative_Restoration   (2456 words)

 Computational Methods In order to apply fictitious domain methods to the problem of simulating the flow of a fluid with free particles (i.e., obstacles with unprescribed motion), the hydrodynamic forces and torques exerted by the fluid on the particles must be accurately evaluated. The efficient handling of multiple right-hand sides proves to be a challenge to most iterative methods because one of their main advantages is that not much information needs to be stored and therefore very little information is saved from the solution of one system which can be reused for the solution of subsequent systems. Consider using the Lanczos method for solving the linear systems since it is well known that the conjugate gradient method is mathematically equivalent to the Lanczos method. www.aem.umn.edu /Solid-Liquid_Flows/methods.html   (3005 words)

 Software Development: Iterative & Evolutionary > Iterative Development   (Site not responding. Last check: ) Iterative and evolutionary development is a foundation not only of modern software methods, but—as the history section of the "Evidence" chapter shows—of methods used as far back as the 1960s. Agile methods are a subset of iterative and evolutionary methods. Iterative development is an approach to building software (or anything) in which the overall lifecycle is composed of several iterations in sequence. www.informit.com /articles/article.asp?p=102256&seqNum=1   (507 words)

 CiteULike: Iterative Methods by Space Decomposition and Subspace Correction   (Site not responding. Last check: ) The main purpose of this paper is to give a systematic introduction to a number of iterative methods for symmetric positive definite problems. Based on results and ideas from various existing works on iterative methods, a unified theory for a diverse group of iterative algorithms, such as Jacobi and Gauss-Seidel iterations, diagonal preconditioning, domain decomposition methods, multigrid methods, multilevel nodal basis preconditioners and hierarchical basis methods, is presented. For example, subspaces arising from the domain decomposition method are associated with subdomains whereas with the multigrid method subspaces are provided by multiple "coarser" grids. www.citeulike.org /user/rblake/article/1269165   (444 words)

 A Survey of Preconditioned Iterative Methods A Survey of Preconditioned Iterative Methods presents an up to date overview of iterative methods for numerical solution of such systems. Typically, the methods considered are well suited for the kind of systems arising from the discretization of partial differential equations. In addition to an introduction to the basic principles of such methods, a large number of specific algorithms for symmetric and nonsymmetric problems are discussed. www.ramex.com /title.asp?id=4717   (449 words)

 MathDL | Iterative Methods for Solving Ax = b This module comprises two tutorials with associated exercises and a Java applet to do the necessary computations and display the results graphically.  We explore three different iterative methods, that is, methods that are intended to generate successive approximations to the exact solution of a linear system of equations. Iterative methods are important in solving many of today’s real world problems, so it is important that your first exposure to these methods be as positive and simple, as well as informative and educational, as possible. Still, these methods are very straightforward, which makes them relatively easy to understand, and that is why they are your first taste of iterative methods for solving linear systems. mathdl.maa.org /mathDL/?pa=content&sa=viewDocument&nodeId=607   (600 words)

 Survey of iterative methods   (Site not responding. Last check: ) CGS is an iterative method based on the Bi-Lanczos algorithm [27]. An iterative method, which computes an approximation with a minimal residual [22]. For iterative methods it is necessary to specify a stopping criterion. ta.twi.tudelft.nl /isnas/isnas_mathmanual/node58.html   (238 words)

 Iterative Methods The term ``iterative method'' refers to a wide range of techniques that use successive approximations to obtain more accurate solutions to a linear system at each step. Stationary methods are older, simpler to understand and implement, but usually not as effective. Nonstationary methods are a relatively recent development; their analysis is usually harder to understand, but they can be highly effective. www.netlib.org /linalg/html_templates/node9.html   (292 words)

 UCES Methods and Analysis Chap. 3.3: Numerical Soln. of Boundary Value Problems   (Site not responding. Last check: ) General Information: Although iterative methods are not practical (use the tridiagonal algorithm) for tridiagonal problems, they are very useful for more complicated problems that arise from 2D and 3D physical problems. Alternatives to the full version of Gaussian elimination, which requires large storage and number of operations, are the iterative methods. Another iterative method called preconditioned conjugate gradient (PCG) is particularly useful, but it is beyond the scope of these notes. www.krellinst.org /UCES/archive/classes/CNA/dir3.3/uces3.3.html   (1372 words)

 On Convergence and Performance of Iterative Methods for Solving Variable Coefficient Convection-Diffusion Equation with ... Abstract: We conduct convergence analysis on some classical stationary iterative methods for solving the two dimensional variable coefficient convection-diffusion equation discretized by a fourth-order compact difference scheme. We further investigate the effect of different orderings of the grid points on the performance of some stationary iterative methods, multigrid method, and preconditioned... 3 Analysis of stationary iterative methods for discrete convec.. citeseer.ist.psu.edu /408631.html   (631 words)

 SIAM: Author Index Numerical Methods for Unconstrained Optimization and Nonlinear Equations Kelley, C. Iterative Methods for Linear and Nonlinear Equations Linz, P. Analytical and Numerical Methods for Volterra Equations www.siam.org /catalog/alpha.php   (4224 words)

 Iterative Methods for Sparse Linear Systems - Cambridge University Press Tremendous progress has been made in the scientific and engineering disciplines regarding the use of iterative methods for linear systems. The size and complexity of linear and nonlinear systems arising in typical applications has grown, meaning that using direct solvers for the three-dimensional models of these problems is no longer effective. Iterative methods are easier than direct solvers to implement on parallel computers but require approaches and solution algorithms that are different from classical methods. www.cambridge.org /us/catalogue/catalogue.asp?isbn=0898715342   (170 words)

 Mozilla's New Array Methods - WebReference.com - methods that can be separated into two categories, item location methods and iterative methods. methods, which is the index at which to begin searching the array. From that position, the method continues to search forward and the next instance of "green" is in position 5. www.webreference.com /programming/javascript/ncz/column4   (740 words)

 Jacobi-type iterative methods   (Site not responding. Last check: ) The method works by repeated application of orthogonal Jacobi rotations, which, depending on the order of them, bring the matrix more or less quickly to diagonal form. The original method used by Jacobi in 1846 applied the rotations to zero the largest non-zero off-diagonal element, but on a computer a re-designed pattern is easier. A one-sided method is likely to be better for this reason. www.dl.ac.uk /TCSC/Subjects/Parallel_Algorithms/diagreport/node16.html   (298 words)

 CiteULike: Iterative Methods for Sparse Linear Systems, Second Edition   (Site not responding. Last check: ) Since the first edition of this book was published in 1996, tremendous progress has been made in the scientific and engineering disciplines regarding the use of iterative methods for linear systems. Iterative methods are easier than direct solvers to implement on parallel computers but require approaches and solution algorithms that are different from classical methods. The methods described are iterative, i.e., they provide sequences of approximations that will converge to the solution. www.citeulike.org /user/bastibarry1/article/658062   (692 words)

 MATH5315 - Iterative Methods   (Site not responding. Last check: ) Iterative methods for solving the linear system A x = b, where A is an n by n nonsingular matrix, maintain a vector (or an array if there are multiple right-hand-side vectors b) x The best iterative methods for a particular computing platform is a trade-off between choosing an M to improve the rate of convergence and the computational cost of solving the linear system M x Ways in which this structure can be exploited to produce more efficient solution methods are considered in the page on symmetric positive definite linear systems. web.maths.unsw.edu.au /~rsw/MATH5315/iter.shtml   (800 words)

 Prentice Hall PTR - 0131111558 - Agile and Iterative Development: A Manager's Guide This is the definitive guide for managers and students to agile and iterative development methods: what they are, how they work, how to implement them—and why you should. To my knowledge it's the first book that summarizes all the basics of what it means to to iterative development and all the basics of agile methods. The rest of the chapters are summaries of other methods which are ok, but I'd recommend to read the original work on each of these methods instead. safari.phptr.com /0131111558   (683 words)

 java.net: Agile Legacies: Using Iterative Methods to Import Legacy Data Nevertheless, despite the benefits of an iterative development cycle, this approach is often not applied to the process of importing legacy data. In iterative development, software is designed, built, and tested incrementally, in a series of "iterations." Each iteration aims to implement a working version of the application with a subset of the requirements. Iterative development has an important place in use-case-driven, architecture-centric approaches such as the Rational Unified Process (RUP), and in the more lightweight methodologies of the Agile family such as XP (Extreme Programming), Feature-Driven Development, SCRUM, DDSM, and others. today.java.net /pub/a/today/2006/03/02/agile-legacy-data-import.html   (1803 words)

 methods - eigenfactor.org - ranking and mapping scientific journals By this approach, journals are considered to be influential if they are cited often by other influential journals. Iterative ranking schemes of this type, known as eigenvector centrality methods [3], are notoriously sensitive to “dangling nodes” and “dangling clusters”: nodes or groups of nodes which link seldom if at all to other parts of the network. The modified eigenvector centrality algorithm used to rank journals at Eigenfactor.org expands upon a thirty-year tradition of using iterative methods to quantify the influence of scholarly publications. www.eigenfactor.org /methods.htm   (883 words)

 Amazon.ca: Iterative Methods for Queuing and Manufacturing Systems: Books: Wai K. Ching   (Site not responding. Last check: ) Iterative Methods for Queuing and Manufacturing Systems introduces the recent advances and developments in iterative methods for solving Markovian queuing and manufacturing problems. With numerous exercises and fully-worked examples, this book will be essential reading for anyone interested in the formulation and computation of queuing and manufacturing systems but it will be of particular interest to students, practitioners and researchers in Applied Mathematics, Scientific Computing and Operational Research. Introduces recent advances and developments in iterative methods for solving Markovian queing and manufacturing problems, presenting future directions for research as well. www.amazon.ca /Iterative-Methods-Queuing-Manufacturing-Systems/dp/1852334169   (390 words)

 Amazon.co.jp： Iterative Methods in Scientific Computing: 洋書: Raymond H. Chan,Tony F. Chan,Gene H. Golub Iterative methods are an important and fundamental class of solution algorithms that are used by scientists and engineers. Because of the rapid evolution of the development of this field, as well as the fact that iterative methods are not often developed in a generic form for general applications, there is a lack of published materials that treat the topic properly and fully. These lectures from the Winter School on Iterative Methods in Scientific Computing and their Applications aims to bridge such gap in the literature. www.amazon.co.jp /Iterative-Methods-Scientific-Computing-Raymond/dp/9813083085   (300 words)

 Workshop on Scalable Iterative Methods   (Site not responding. Last check: ) Iterative methods for the solution of linear and nonlinear systems of equations are commonly used in large scientific computations because of their relative efficiency for problems of large size. These methods have been very successful, but as both the depth of the memory hierarchies within each compute node and the total number of compute nodes increases, it becomes increasingly difficult to maintain high levels of overall performance. This workshop seeks to bring together researchers and practitioners in parallel iterative methods to share recent results and ideas. www.mcs.anl.gov /~gropp/events/wscim02   (210 words)

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