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2017 Practice and Experience in Advanced Research Computing, PEARC 2017

作者： Malaya, Nicholas McDougall, Damon Michoski, Craig Lee, Myoungkyu Simmons, Christopher S. Institute for Computational Engineering and Sciences 201 East 24th St AustinTX78712-1229 United States

ISBN: (纸本)9781450352727

This paper presents experiences using Intel's KNL MIC platform on hardware that will be available in the Stampede 2 cluster launching in Summer 2017. We focus on 1) porting of existing scientific software;2) observing performance of this software. Additionally, we comment on both the ease of use of KNL and observed performance of KNL as compared to previous generation "Knights Ferry" and "Knights Corner" Xeon Phi MICs [32]. Fortran, C, and C++ applications are chosen from a variety of scientific disciplines including computational fiuid dynamics, numerical linear algebra, uncertainty quantification, finite element methods, and computational chemistry. © 2017 Copyright is held by the owner/author(s).

关键词： numerical methods

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Operator-theoretic approach to minimal-norm bandlimited interpolation of nonuniform samples 12

Operator-theoretic approach to minimal-norm bandlimited inte...

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12th International conference on Sampling theory and applications (SAMPTA)

作者： Thao, Nguyen T. Rzepka, Dominik CUNY City Coll New York Dept EE New York NY 10031 USA AGH Univ Sci & Tech Dept Elect Krakow Poland

ISBN: (纸本)9781538615652

methods for the minimal-norm bandlimited interpolation of nonuniform samples are known to have serious numerical issues even though this interpolation is mathematically well defined. Moreover, they have been formulated only for finite numbers of samples. By a rigorous revisit of this problem from an operator-theoretic viewpoint in Hilbert spaces, we devise an algorithm for this interpolation that applies to an infinite number of samples with no condition, with guaranteed stability at least for finite numbers of samples, and with a recursive part that can be rigorously implemented in discrete time.

关键词： nonuniform sampling bandlimited signals interpolation minimal norm least squares algorithm stability linear operator pseudoinverse frame

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Fields of values of linear pencils and spectral inclusion regions 1

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International conference on Matrix Analysis and its applications, MAT-TRIAD 2015

作者： Bebiano, Natália da Providência, João Nata, Ana da Providência, João P. Department of Mathematics CMUC University of Coimbra Coimbra3001-454 Portugal Department of Physics CFisUC University of Coimbra Coimbra3004-516 Portugal Department of Mathematics CMUC Polytechnic Institute of Tomar Tomar2300-313 Portugal Department of Physics University of Beira Interior Covilhã6201-001 Portugal

ISBN: (数字)9783319499840

ISBN: (纸本)9783319499826

We propose efficient methods for the numerical approximation of the field of values of the linear pencil A − λB, when one of the matrix coefficients A or B is Hermitian and λ ∈ ℂ. Our approach builds on the fact that the field of values can be reduced under compressions to the bidimensional case, for which these sets can be exactly determined. The presented algorithms hold for matrices both of small and large size. Furthermore, we investigate spectral inclusion regions for the pencil based on certain fields of values. The results are illustrated by numerical examples. We point out that the given procedures complement the known ones in the literature. © Springer International Publishing AG 2017.

关键词： Matrix algebra

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Advances in implementation, theoretical motivation, and numerical results for the nested iteration with range decomposition algorithm

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numerical linear algebra WITH applications 2018年第3期25卷

作者： Mitchell, Wayne Manteuffel, Tom Univ Colorado 526 UCB Boulder CO 80309 USA

This paper studies a low-communication algorithm for solving elliptic PDEs on high-performance machines, the nested iteration with range decomposition (NIRD) algorithm. Previous work has shown that NIRD converges to a high level of accuracy within a small, fixed number of iterations (usually one or two) when applied to simple elliptic problems. This paper makes some improvements to the NIRD algorithm (including the addition of adaptivity during preprocessing, wider choice of partitioning functions, and modified error measurement) that enhance the method's accuracy and scalability, especially on more difficult problems. In addition, an updated convergence proof is presented based on heuristic assumptions that are supported by numerical evidence. Furthermore, a new performance model is developed that shows increased performance benefits for NIRD when problems are more expensive to solve using traditional methods. Finally, extensive testing on a variety of elliptic problems provides additional insight into the behavior of NIRD and additional evidence that NIRD achieves excellent convergence on a wide class of elliptic PDEs and, as such, should be a very competitive method for solving PDEs on large parallel computers.

关键词： elliptic PDE solvers low-communication nested iteration range decomposition

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Complexity Analysis and Efficient Measurement Selection Primitives for High-Rate Graph SLAM

Complexity Analysis and Efficient Measurement Selection Prim...

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IEEE International conference on Robotics and Automation

作者： Kristoffer M. Frey Ted J. Steiner Jonathan P. How Department of Aeronautics and Astronautics MIT Cambridge MA USA Technical Staff at Draper Cambridge MA USA

Sparsity has been widely recognized as crucial for efficient optimization in graph-based SLAM. Because the sparsity and structure of the SLAM graph reflect the set of incorporated measurements, many methods for sparsification have been proposed in hopes of reducing computation. These methods often focus narrowly on reducing edge count without regard for structure at a global level. Such structurally-naive techniques can fail to produce significant computational savings, even after aggressive pruning. In contrast, simple heuristics such as measurement decimation and keyframing are known empirically to produce significant computation reductions. To demonstrate why, we propose a quantitative metric called elimination complexity (EC) that bridges the existing analytic gap between graph structure and computation. EC quantifies the complexity of the primary computational bottleneck: the factorization step of a Gauss-Newton iteration. Using this metric, we show rigorously that decimation and keyframing impose favorable global structures and therefore achieve computation reductions on the order of r~2/9 and r~3, respectively, where r is the pruning rate. We additionally present numerical results showing EC provides a good approximation of computation in both batch and incremental (iSAM2) optimization and demonstrate that pruning methods promoting globally-efficient structure outperform those that do not.

关键词： Simultaneous localization and mapping Complexity theory Optimization Sparse matrices Extraterrestrial measurements linear algebra

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Lanczos version of BCR algorithm for solving the generalised second-order Sylvester matrix equation EVF plus GVH plus BVC = DWE plus M

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IET CONTROL theory AND applications 2017年第2期11卷 273-281页

作者： Hajarian, Masoud Shahid Beheshti Univ Fac Math Sci Dept Math Gen Campus Tehran 19839 Iran

It is well known that the biconjugate residual (BCR) algorithm and its variants are powerful procedures to find the solution of large sparse non-symmetric systems equation. In this study, the authors develop the Lanczos version of BCR algorithm for computing the solution pair of the generalised second-order Sylvester matrix equation EVF + GVH + BVC = DWE + M which includes the second-order Sylvester, Lyapunov and Stein matrix equations as special cases. The convergence results show that the algorithm with any initial matrices converges to the solutions within a finite number of iterations in the absence of round-off errors. Finally, two numerical examples are provided to support the theoretical findings and to testify the effectiveness and usefulness of the algorithm.

关键词： matrix algebra iterative methods pole assignment observers generalised second-order Sylvester matrix equation biconjugate residual algorithm Stein matrix equations Lanczos version BCR algorithm pole assignment eigenstructure assignment robust fault detection Luenberger-type observer design second-order linear system

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Optimal-Dimensionality Sampling on the Sphere: Improvements and Variations 12

Optimal-Dimensionality Sampling on the Sphere: Improvements ...

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12th International conference on Sampling theory and applications (SAMPTA)

作者： Nafees, Wajeeha Khalid, Zubair Kennedy, Rodney A. McEwen, Jason D. Lahore Univ Management Sci Sch Sci & Engn Lahore 54792 Pakistan Australian Natl Univ Res Sch Engn Canberra ACT 2601 Australia Univ Coll London Mullard Space Sci Lab Dorking RH5 6NT Surrey England

ISBN: (纸本)9781538615652

For the accurate representation and reconstruction of band-limited signals on the sphere, an optimal-dimensionality sampling scheme has been recently proposed which requires the optimal number of samples equal to the number of degrees of freedom of the signal in the spectral (harmonic) domain. The computation of the spherical harmonic transform (SHT) associated with the optimal-dimensionality sampling requires the inversion of a series of linear systems in an iterative manner. The stability of the inversion depends on the placement of iso-latitude rings of samples along co-latitude. In this work, we have developed a method to place these iso-latitude rings of samples with the objective of improving the well-conditioning of the linear systems involved in the computation of the SHT. We also propose a multi-pass SHT algorithm to iteratively improve the accuracy of the SHT of band-limited signals. Furthermore, we review the changes in the computational complexity and improvement in accuracy of the SHT with the embedding of the proposed methods. Through numerical experiments, we illustrate that the proposed variations and improvements in the SHT algorithm corresponding to the optimal-dimensionality sampling scheme significantly enhance the accuracy of the SHT.

关键词： unit sphere sampling spherical harmonic transform optimal-dimensionality condition number minimization harmonic analysis

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Solving differential equations by steel structures 11

Solving differential equations by steel structures

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11th International conference on Inspection, Appraisal, Repairs and Maintenance of Structures

作者： Yilmaz, Levent Technical University of Istanbul Turkey

ISBN: (纸本)9789810581923

The ordinary linear differential equations with constant coefficients can be solved by the algebraic methods and the solutions are obtained by elementary functions. In practice, the class of this kind of differential equations is rather narrow. The most of the differential equations met in mathematics, physics and engineering sciences remain out of this class. In such cases, it is searched for solutions in form of infinite series. A new theory of functions named as higher transcendant functions or special functions were set up. The Legendre and Bessel equations are of this type. They appear in problems on vibrations, electric field, heat conduction, fluid flow etc. In this paper the authors intend to show by means of four interesting applications from the field of structural and mechanical engineering how still a powerful tool is the method of series solutions, beside the algebraic and numerical methods;how easy can the problems be handled by this method using the computer softwares prepared especially for mathematics. The results are compared with the numerical solutions.

关键词： numerical methods

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Collocation-quadrature methods and fast summation for Cauchy singular integral equations with fixed singularities

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linear algebra AND ITS applications 2016年 491卷 187-238页

作者： Junghanns, P. Kaiser, R. Potts, D. Tech Univ Chemnitz Fac Math Reichenhainer Str 39 D-09107 Chemnitz Germany

Basing on recent results on the stability of collocation methods applied to Cauchy singular integral equations with additional fixed singularities we give necessary and sufficient conditions for the stability of collocation-quadrature methods for such equations. These methods have the advantage that the respective system of equations has a very simple structure and allows to apply fast summation methods which results in a fast algorithm with (O(n log n) complexity. We present numerical results of the application of the proposed collocation quadrature methods to the notched half plane problem of two-dimensional elasticity theory. (C) 2015 Elsevier Inc. All rights reserved.

关键词： Cauchy singular integral equation Collocation-quadrature method C*-algebra techniques

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Exploiting Hidden Structure in Matrix Computations: Algorithms and applications Cetraro, Italy 2015

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2017年

作者： Michele Benzi Dario Andrea Bini Daniel Kressner Hans Z Munthe-Kaas Charles Francis van Loan Valeria Simoncini

ISBN: (纸本)9783319498867

Focusing on special matrices and matrices which are in some sense `near to structured matrices, this volume covers a broad range of topics of current interest in numerical linear algebra. Exploitation of these less obvious structural properties can be of great importance in the design of efficient numerical methods, for example algorithms for matrices with low-rank block structure, matrices with decay, and structured tensor computations. applications range from quantum chemistry to queuing theory. Structured matrices arise frequently in applications. Examples include banded and sparse matrices, Toeplitz-type matrices, and matrices with semi-separable or quasi-separable structure, as well as Hamiltonian and symplectic matrices. The associated literature is enormous, and many efficient algorithms have been developed for solving problems involving such matrices. The text arose from a C.I.M.E. course held in Cetraro (Italy) in June 2015 which aimed to present this fast growing field to young researchers, exploiting the expertise of five leading lecturers with different theoretical and application perspectives.

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