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4 edition of On the optimality of an additive iterative refinement method found in the catalog.

On the optimality of an additive iterative refinement method

by Maksymilian Dryja

  • 66 Want to read
  • 26 Currently reading

Published by Courant Institute of Mathematical Sciences, New York University in New York .
Written in English


Edition Notes

Statementby Maksymilian Dryja, Olof B. Widlund.
ContributionsWidlund, Olof B.
The Physical Object
Pagination11 p.
Number of Pages11
ID Numbers
Open LibraryOL17866193M

We describe an iterative refinement procedure for computing extended-precision or exact solutions to linear programming (LP) problems. Arbitrarily precise solutions can be computed by solving a sequence of closely related LPs with limited-precision arithmetic. The LPs solved share the same constraint matrix as the original problem instance and are transformed only by modification of the Cited by: Topology Optimization Mathematics for Design Homogenization Design Method Convergence History of Iteration. 21 Mesh Refinement. 23 Change Volumes. 24 Design Constraint Load case 2 area Design area Topology Optimization Methods • Commercial Codes have been developed in USA, Europe, and Pacific Regions.

Purchase Computer Solution of Large Linear Systems, Volume 28 - 1st Edition. Print Book & E-Book. ISBN , Iterative methods for solving general, large sparse linear systems have been gaining popularity in many areas of scientific computing. Until recently, direct solution methods were often preferred to iterative methods in real applications because of their robustness and predictable by:

3. The Additive Preconditioning Method, the Schur Aggregation and the Extended Iterative Refinement or Improvement Algorithm The Additive Preconditioning Method Definition For a pair of matrices of size and of size, both having full rank r > 0, the matrix of rank r is an additive preprocessor (APP) of rank r for any matrix. Approximate Multi-matroid Intersection via Iterative Refinement. In V. Nagarajan, & A. Lodi (Eds.), Integer Programming and Combinatorial Optimization: 20th International Conference, IPCO , Ann Arbor, MI, USA, May 22–24, , Proceedings (pp. ). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Author: André Linhares, Neil Olver, Chaitanya Swamy, Rico Zenklusen.


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On the optimality of an additive iterative refinement method by Maksymilian Dryja Download PDF EPUB FB2

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Occupy Wall Street TV NSA Clip : The economics of iterative refinement are favourable for solvers based on a factorization of A, because the factorization used to compute x̑ can be reused in the second step of the refinement.

Traditionally, iterative refinement is used with Gaussian elimination (GE), and r is computed in extended precision before being rounded to working precision.

Iterative refinement for GE was used in the. Dryja, M. and Widlund, O.B. ( a), ‘On the optimality of an additive iterative refinement method’, in Proc. Fourth Copper Mountain Conf. on Multigrid Methods Cited by: Optimality of local multilevel methods on adaptively refined meshes for elliptic boundary value problems Article in Journal of Numerical Mathematics 18(1) April with 21 Reads.

Publication Data. A general formulation of the additive correction methods of Poussin [4] and Watts [7] is presented. The methods are applied to the solution of finite difference equations resulting from elliptic and parabolic partial differential equations. A new method is developed for anisotropic and heterogeneous by: Abstract.

Many parallel iterative algorithms for solving symmetric, positive definite problems proceed by solving in each iteration, a number of independent systems on subspaces. The convergence of such methods is determined by the spectrum of the sums of orthogonal projections on those subspaces, while the convergence of a related sequential method Cited by: maximization methods and Fourier inversion.

Certain topics in the book will be appropriate for an undergraduate class, but generally the book is aimed at a graduate-level audience. Some of the chapters end with a section devoted to exercises. In ad-dition, throughout the book there are.

Taheri, A., Suresh, K."Adaptive w-refinement: a new paradigm in isogeometric analysis", Submitted to Computer Methods in Applied Mechanics and Engineering, January Kumar, T., Suresh, K." A density-and-strain based K-clustering approach to microstructural topology optimization", Struct Multidisc Op – ().

conjugate gradient method and the DIRECT algorithm). We aim for clarity and brevity rather than complete generality and confine our scope to algorithms that are easy to implement (by the reader!) and understand. One consequence of this approach is that the algorithms in this book are often special cases of more general ones in the literature.

The flowchart of the proposed method is shown in Fig. First, in order to avoid very thin parts and isolated islands, small features of the topology optimization results are identified. Second, boundary refinement is executed along with characteristics preservation, in Cited by: Iterative Methods for Optimization does more than cover traditional gradient-based optimization: it is the first book to treat sampling methods, including the Hooke-Jeeves, implicit filtering, MDS, and Nelder-Mead schemes in a unified by: 1.

Introduction The fast adaptive composite grid method (FAC; cf. []) is a multilevel technique for efficient adaptive solution of partial differential equations. A fairly extensive convergence theory exists for FAC (cf. [2,]), but with two exceptions Cited by: We propose iterative refinement techniques, as well as an adaptive reformulation of the quadratic problem, that can greatly reduce these errors without incurring high computational overheads.

Numerical results illustrating the efficacy of the proposed approaches are : I M GouldNicholas, E HribarMary, NocedalJorge. Iterative refinement is an iterative method proposed by James H.

Wilkinson to improve the accuracy of numerical solutions to systems of linear equations. When solving a linear system Ax = b, due to the presence of rounding errors, the computed solution x̂ may sometimes deviate from the exact solution x *.

Domain Decomposition Methods for Partial Differential Equations. Abstract. Domain decomposition methods are iterative methods for the solution of linear or nonlinear systems that use explicit information about the geometry, discretization, and/or partial differential equations that underlie the discrete by: The optimality of the FAC method when spectrally equivalent inexact solvers are used is also proved by using similar techniques.

We next consider multilevel additive Schwarz methods with partial refinement. These algorithms are generalizations of the multilevel additive Schwarz methods developed by Dryja and Widlund and many others. Abstract: High-quality real-time stereo matching has the potential to enable various computer vision applications including semi-automated robotic surgery, teleimmersion, and 3-D video surveillance.

A novel real-time stereo matching method is presented that uses a two-pass approximation of adaptive support-weight aggregation, and a low-complexity iterative disparity refinement by: Before deriving our iterative Linear-Quadratic-Gaussian (ILQG) method, we give a more detailed overview of what is new here.

(1) Most dynamic programming methods use quadratic approximations to the optimal cost-to-go function. All such methods are ‘‘blind’’ to additive noise.

However, in many problems of interest the noiseCited by: Method: High Way Reduction in Three Dimensions and Convergence with Inexact Solvers, C.

Douglas and J. Mandel; On the Optimality of an Additive Iterative Refinement Method, M. Dryja and O.B. Widlund; A Multigrid-Like Semi-Iterative Algorithm for the Massively Parallel Solution ofLarge Scale Finite Element Systems, C.

Farhat. To overcome this difficulty, various heuristic methods, including progressive methods and iterative refinement methods (4–6), have been proposed to date. They are mostly based on various combinations of successive two-dimensional DP, which takes CPU time proportional to N by:.

In this paper, we will be evaluating numerical methods for direct and iterative solvers of linear systems. From class we have discussed the various methods; Gauss elimination with pivoting techniques, Jacobi Iterative Method, Gauss-Seidel Iterative Method, Successive Over-Relaxation Method, Iterative Refinement Method, and Conjugate Gradient Method.Building on recent work on iterative refinement for p-norm optimization [2], we develop a high accuracy algorithm for a large family of flow optimization problems on undirected graphs.There is more to say about iterative refinement.

See Nick Higham's SIAM book and, especially, the TOMS paper by Demmel, Kahan and their Berkeley colleagues.

A preprint is available from Kahan's web site. References.