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recursive algorithms FOR DISTRIBUTED FORESTS OF OCTREES

SIAM JOURNAL ON SCIENTIFIC COMPUTING 2015年第5期37卷 C497-C531页

作者： Isaac, Tobin Burstedde, Carsten Wilcox, Lucas C. Ghattas, Omar Univ Texas Austin Inst Computat Engn & Sci Austin TX 78712 USA Univ Bonn Inst Numer Simulat D-53115 Bonn Germany Naval Postgrad Sch Dept Appl Math Monterrey CA 93943 USA Univ Texas Austin Dept Mech Engn Jackson Sch Geosci Austin TX 78712 USA Univ Texas Austin Inst Computat Engn & Sci Austin TX 78712 USA

The forest-of-octrees approach to parallel adaptive mesh refinement and coarsening has recently been demonstrated in the context of a number of large-scale PDE-based applications. Efficient reference software has been made freely available to the public both in the form of the standalone p4est library and more indirectly by the general-purpose finite element library deal. II, which has been equipped with a p4est backend. Although linear octrees, which store only leaf octants, have an underlying tree structure by definition, it is not fully exploited in previously published mesh-related algorithms. This is because tree branches are not explicitly stored and because the topological relationships in meshes, such as the adjacency between cells, introduce dependencies that do not respect the octree hierarchy. In this work, we combine hierarchical and topological relationships between octants to design efficient recursive algorithms that operate on distributed forests of octrees. We present three important algorithms with recursive implementations. The first is a parallel search for leaves matching any of a set of multiple search criteria, such as leaves that contain points or intersect polytopes. The second is a ghost layer construction algorithm that handles arbitrarily refined octrees that are not covered by previous algorithms, which require a 2: 1 condition between neighboring leaves. The third is a universal mesh topology iterator. This iterator visits every cell in a partition, as well as every interface (face, edge, and corner) between these cells. The iterator calculates the local topological information for every interface that it visits, taking into account the nonconforming interfaces that increase the complexity of describing the local topology. To demonstrate the utility of the topology iterator, we use it to compute the numbering and encoding of higher-order C-0 nodal basis functions used for finite elements. We analyze the complexity of the new recursive a

关键词： forest of octrees parallel adaptive mesh refinement Morton code recursive algorithms large-scale scientific computing

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recursive algorithms for the computation of the potential harmonic coefficients of a constant density polyhedron

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JOURNAL OF GEODESY 2009年第10期83卷 925-942页

作者： Tsoulis, Dimitrios Jamet, Olivier Verdun, Jerome Gonindard, Nicolas Aristotle Univ Thessaloniki Dept Geodesy & Surveying Thessaloniki 54124 Greece IGN Lab Rech Geodesie F-94160 St Mande France ENSG F-77455 Marne La Vallee France

The gravitational potential of a constant density general polyhedron can be expressed both in terms of a closed analytical expression and as a series expansion involving the corresponding spherical harmonic coefficients. The latter can be obtained from two independent algorithms, which differ not only in their algorithmic architecture but in their efficiency and overall performance, especially when computing the coefficients of higher degree and order. In the present paper a comparative study of all these three approaches is carried out focusing on the numerical implementation of the recursive relations appearing in the two algorithms for the computation of the polyhedral potential harmonic coefficients. The performed numerical investigations show that the linear algorithm proposed by Jamet and Thomas (Proceedings of the second international GOCE user workshop, 'GOCE, The Geoid and Oceanography', ESA-ESRIN, Frascati, Italy, 8-10 March 2004, ESA SP-569, 2004), but so far not implemented, achieves a reasonable accuracy at a computational expense that opens to practical applications, for instance in the field of satellite gravimetry/gradiometry interpretation. The convergence behavior of the linear recursion algorithm is studied thoroughly and a computational procedure is proposed that enables the stable computation of potential harmonic coefficients up to degree 60 when referring to an arbitrarily shaped polyhedral body.

关键词： Gravitational potential General polyhedron Spherical harmonics Analytical expression recursive algorithms

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recursive algorithms, urn processes and chaining number of chain recurrent sets

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ERGODIC THEORY AND DYNAMICAL SYSTEMS 1998年第1期18卷 53-87页

作者： Benaim, M Univ Toulouse 3 Dept Math F-31062 Toulouse France

This paper investigates the dynamical properties of a class of urn processes and recursive stochastic algorithms with constant gain which arise frequently in control, pattern recognition, learning theory, and elsewhere. It is shown that, under suitable conditions, invariant measures of the process tend to concentrate on the Birkhoff center of irreducible (i.e. chain transitive) attractors of some vector field F : R-d --> R-d obtained by averaging. Applications are given to simple situations including the cases where F is Axiom A or Morse-Smale, F is gradient-like, F is a planar vector field, F has finitely many alpha and omega limit sets.

关键词： linearly ordered set recursive algorithms Chaining SETTING Irreducible Vector field Process Measures Fluorine (F)

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recursive algorithms for unbalanced banded Toeplitz systems

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NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS 2009年第7期16卷 561-587页

作者： Favati, P. Lotti, G. Menchi, O. Univ Pisa Dept Comp Sci I-56127 Pisa Italy Univ Parma Dept Math I-43100 Parma Italy IIT CNR Pisa Pisa Italy

Direct recursive algorithms for the solution of band Toeplitz systems are considered here. They exploit the displacement rank properties, which allow a large reduction of computational efforts and storage requirements. Their use of the Sherman-Morrison-Woodbury formula turns out to be particularly suitable for the case of unbalanced bandwidths. The computational costs of the algorithms under consideration are compared both in a theoretical and practical setting. Some stability issues are discussed as well. Copyright (C) 2009 John Wiley & Sons, Ltd.

关键词： recursive algorithms banded Toeplitz systems displacement rank

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Screw and Lie group theory in multibody dynamics recursive algorithms and equations of motion of tree-topology systems

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MULTIBODY SYSTEM DYNAMICS 2018年第2期42卷 219-248页

作者： Mueller, Andreas Johannes Kepler Univ Linz Inst Robot Altenberger Str 69 A-4040 Linz Austria

Screw and Lie group theory allows for user-friendly modeling of multibody systems (MBS), and at the same they give rise to computationally efficient recursive algorithms. The inherent frame invariance of such formulations allows to use arbitrary reference frames within the kinematics modeling (rather than obeying modeling conventions such as the Denavit-Hartenberg convention) and to avoid introduction of joint frames. The computational efficiency is owed to a representation of twists, accelerations, and wrenches that minimizes the computational effort. This can be directly carried over to dynamics formulations. In this paper, recursive Newton-Euler algorithms are derived for the four most frequently used representations of twists, and their specific features are discussed. These formulations are related to the corresponding algorithms that were presented in the literature. Two forms of MBS motion equations are derived in closed form using the Lie group formulation: the so-called Euler-Jourdain or "projection" equations, of which Kane's equations are a special case, and the Lagrange equations. The recursive kinematics formulations are readily extended to higher orders in order to compute derivatives of the motions equations. To this end, recursive formulations for the acceleration and jerk are derived. It is briefly discussed how this can be employed for derivation of the linearized motion equations and their time derivatives. The geometric modeling allows for direct application of Lie group integration methods, which is briefly discussed.

关键词： Multibody system dynamics Relative coordinates recursive algorithms O(n) Screws Lie groups Newton-Euler equations Lagrange equations Kane's equations Euler-Jourdain equations Projection equations Lie group integration Linearization

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Fast recursive algorithms for morphological operators based on the basis matrix representation

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IEEE TRANSACTIONS ON IMAGE PROCESSING 1996年第6期5卷 1073-1077页

作者： Ko, SJ Morales, A Lee, KH PENN STATE UNIV COLL ENGNDU BOISPA 15801

A real-time implementation method for the most general morphological system, the so-called grayscale function processing (FP) system is presented. The proposed method is an extension of our previous works [5], [6] using the matrix representation of the FP system with a basis matrix (BM) and a block basis matrix (BBM) composed of grayscale structuring elements (GSE). In order to further improve the computational efficiency of the basis matrix representation, we propose recursive algorithms based on the observation of the BM and BBM. The efficiency of the proposed algorithms is gained by avoiding redundant steps in computing overlapping local maximum or minimum operations. It is shown that, with the proposed scheme, both opening and closing can be determined in real time by 2N - 2 additions and 2N - 2 comparisons, and OC and CO by 4N - 4 additions and 4N - 4 comparisons, when the size of the GSE is equal to N. It is also shown that the proposed recursive opening and dosing require only 3N - 3 memory elements.

关键词： recursive algorithms Matrix representation basis matrix Computational efficiency Local Maximum Grey scale CTLA4 gene morphological operator

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Efficient recursive algorithms for detection of abrupt changes in signals and control systems

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IEEE TRANSACTIONS ON AUTOMATIC CONTROL 1999年第5期44卷 952-966页

作者： Lai, TL Shan, JZL Stanford Univ Dept Stat Stanford CA 94305 USA Hewlett Packard Labs Palo Alto CA 94304 USA

This paper addresses a number of open problems concerning the generalized likelihood ratio (GLR) rules for online detection of faults and parameter changes in control systems. It is shown that with an appropriate choice of the threshold and window size, these GLR rules are asymptotically optimal, The rules are also extended to nonlikelihood statistics that are widely used in monitoring adaptive algorithms for system identification and control by establishing Gaussian approximations to these statistics when the window size is chosen suitably. recursive algorithms are developed for practical implementation of the procedure, and importance sampling techniques are introduced for determining the threshold of the rule to satisfy prescribed bounds on the false alarm rate.

关键词： GLR rules Kullback-Leibler information online detection recursive algorithms

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Large deviations for a class of recursive algorithms

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STATISTICS & PROBABILITY LETTERS 1996年第2期26卷 135-140页

作者： Zajic, T STANFORD UNIV DEPT OPERAT RESSTANFORDCA 94305

The large deviation principle is shown to hold for a class of stochastic recursive algorithms based on a sequence of random variables satisfying an appropriate mixing condition.

关键词： large deviations strong mixing recursive algorithms

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Mixed time scale recursive algorithms

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IEEE TRANSACTIONS ON SIGNAL PROCESSING 2001年第8期49卷 1824-1830页

作者： Bucklew, JA Kurtz, TG Univ Wisconsin Dept Elect & Comp Engn Madison WI 53706 USA Univ Wisconsin Dept Math Madison WI 53706 USA

In this paper, we investigate the behavior of certain types of mixed time scale adaptive algorithms. These systems comprise a "fast" or quickly changing algorithm mutually coupled to a "slow" or slowly changing algorithm, They arise naturally in a variety of adaptive environments such as in IIR system identification, the training of recurrent neural networks, decision feedback equalization, and others. [These algorithms (despite their title) should not be confused with the mixed time scales of wavelet transforms or other algorithms associated with multiresolution signal processing.] We give conditions for when the system can be analyzed from the framework of a simpler "frozen state" system, This analysis extends some of the previous work of Solo and his coworkers.

关键词： mixed time scales nonlinear signal processing algorithms recursive algorithms

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Bounded-error parameter estimation: Noise models and recursive algorithms

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AUTOMATICA 1996年第7期32卷 985-999页

作者： Bai, EW Nagpal, KM Tempo, R HKUST DEPT EEE HONG KONG HONG KONG UNIV MICHIGAN DEPT ELECT ENGN & COMP SCI ANN ARBOR MI 48109 USA POLITECN TORINO CENS CNR I-10129 TURIN ITALY

This paper deals with some issues involving a parameter estimation approach that yields estimates consistent with the data and the given a priori information. The first part of the paper deals with the relationships between various noise models and the 'size' of the resulting membership set, the set of parameter estimates consistent with the data and the a priori information. When there is some flexibility about the choice of the noise model, this analysis can be helpful for noise model selection so that the resulting membership set yields a better estimate of the unknown parameter. The second part of the paper presents algorithms for various commonly encountered noise models that have the following properties: (a) they are recursive and easy to implement;and (b) after a finite 'learning period', the estimates provided by these algorithms are guaranteed to be in (or very 'close' to) the membership set. In general, the interpolatory algorithms, that produce an estimate in the membership set, do not possess nice statistical and worst-case properties similar to those of classical approaches such as least mean squares (LMS) and least squares (LS) algorithms. In the third part of the paper, we propose an algorithm that is optimal in a certain worst-case sense but gives an estimate that is in (or is 'close' to) the membership set. Copyright (C) 1996 Elsevier Science Ltd.

关键词： system identification parameter estimation bounded noise modelling identifier estimator recursive algorithms

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