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Patchwork algorithm for the parallel computation of the Green's function in open systems

JOURNAL OF COMPUTATIONAL ELECTRONICS 2013年第2期12卷 123-133页

作者： Girao, Eduardo Costa Meunier, Vincent Univ Fed Piaui Dept Fis BR-64049550 Teresina Piaui Brazil Rensselaer Polytech Inst Dept Phys Appl Phys & Astron Troy NY 12180 USA

The efficient calculation of the Green's function is a central issue for assessing electronic transport at the nanoscale. In a near-to-equilibrium description, it can be obtained from a matrix inversion, combined with iterative algorithms developed in the 80s. However, this procedure becomes computationally challenging when dealing with very large systems. A set of algorithms (known as knitting and sewing) based on the recursive application of Dyson's equation were recently proposed, where the Green's function elements are obtained in a selective way and without the need of explicit matrix inversion, by including one matrix element at a time. Here we propose a variation of these algorithms adapted to parallel computing. The approach is based on the division of the system in a set of domains whose individual Green's functions are computed independently. The domains are then merged to yield the necessary elements of the Green's function for subsequent evaluation of the electronic transport properties. Promising scaling behavior is found, depending on the details of the domain decomposition.

关键词： Electronic transport Green's function Dyson's equation recursive algorithms

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SQUARE ROOT FILTERING VIA COVARIANCE AND INFORMATION EIGENFACTORS

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AUTOMATICA 1986年第5期22卷 599-604页

作者： OSHMAN, Y BARITZHACK, IY Department of Aeronautical Engineering Technion - Israel Institute of Technology Haifa 32000 Israel

Two new square root Kalman filtering algorithms are presented. Both algorithms are based on the spectral V − Λ of the covariance matrix where V is the matrix whose columns are the eigenvectors of the covariance and Λ is the diagonal matrix of its eigenvalues. The algorithms use the covariance mode in the time propagation stage and the information mode in the measurement update stage. This switch between modes, which is trivial in the V − Λ representation, increases the efficiency of the algorithms. In the first algorithm, which is a continuous/discrete one, the V and Λ 1 2 matrices are propagated in time in a continuous manner, while the measurement update is a discrete time procedure. In the second algorithm, which is a discrete/discrete one, the time propagation of the V − Λ 1 2 factors is performed in discrete time too, using a procedure which is similar to the one used for the discrete measurement update. The discrete propagation and the measurement update are based on singular value decomposition algorithms. The square root nature of the algorithms is demonstrated numerically through a typical example. While promising all the virtues of square root routines, the V − Λ filters are also characterized by their ability to exhibit singularities as they occur.

关键词： (Square root filtering) decomposition eigenvalues filtering Kalman filters numerical methods recursive algorithms signal processing state estimation

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recursive NONLINEAR ESTIMATION - GEOMETRY OF A SPACE OF POSTERIOR DENSITIES

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AUTOMATICA 1992年第2期28卷 313-323页

作者： KULHAVY, R Institute of Information Theory and Automation Czechoslovak Academy of Sciences 182 08 Prague Pod vodarenskou vezi 4 Czech Republic

The paper establishes a geometric formulation for nonlinear parameter estimation using reduced statistics. If a reduced, rather than sufficient statistic is used in estimation, an equivalence class of densities, [p(t)], rather than the true posterior density p(t) is determined. Two questions arise in this connection: (1) What kind of a reduced statistic allows recursive computations? (2) What is the appropriate representative p(t) of the equivalence class [p(t)? Typically, the first question is not posed at all and the second one is resolved by heuristic considerations. The present paper attempts to cast the problem into a solid mathematical structure. It closely follows the differential-geometric approach suggested in Kulhavy (Automatica, 26, 545-555, 1990) but goes into more detail. Roughly, admissible statistics are characterized here as homomorphisms of a group containing all possible likelihoods. A representative of the pertinent equivalence class is constructed by a projection along this class onto an orthogonal submanifold going through a prespecified density p* and imbedded in the manifold of possible posteriors. The obtained projection p(t) has attractive extremal properties: it minimizes the Kullback-Leibler distance from the "reference" point p* and, at the same time, the dual Kullback-Leibler distance from the true point p(t).

关键词： PARAMETER ESTIMATION SAMPLED DATA SYSTEMS BAYESIAN STATISTICS recursive algorithms APPROXIMATION THEORY DIFFERENTIAL GEOMETRY

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A recursive formulation of Cholesky factorization of a matrix in packed storage

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ACM TRANSACTIONS ON MATHEMATICAL SOFTWARE 2001年第2期27卷 214-244页

作者： Andersen, BS Wasniewski, J Gustavson, FG Tech Univ Denmark UNIC Danish Comp Ctr Res & Educ DK-2800 Lyngby Denmark IBM Corp Thomas J Watson Res Ctr Yorktown Hts NY 10598 USA

A new compact way to store a symmetric or triangular matrix called RPF for recursive Packed Format is fully described. Novel ways to transform RPF to and from standard packed format are included. A new algorithm, called RPC for recursive Packed Cholesky, that operates on the RPF format is presented. Algorithm RPC is based on level-3 BLAS and requires variants of algorithms TRSM and SYRK that work on RPF. We call these RP_TRSM and RP_SYRK and find that they do most of their work by calling GEMM. It follows that most of the execution time of RPC lies in GEMM. The advantage of this storage scheme compared to traditional packed and full storage is demonstrated. First, the RPC storage format uses the minimal amount of storage for the symmetric or triangular matrix. Second, RPC gives a level-3 implementation of Cholesky factorization whereas standard packed implementations are only level 2. Hence, the performance of our RPC implementation is decidedly superior. Third, unlike fixed block size algorithms, RPC requires no block size tuning parameter. We present performance measurements on several current architectures that demonstrate improvements over the traditional packed routines. Also SMP parallel computations on the IBM SMP computer are made. The graphs that are attached in Section 7 show that the RPC algorithms are superior by a factor between 1.6 and 7.4 for order around 1000, and between 1.9 and 10.3 for order around 3000 over the traditional packed algorithms. For some architectures, the RPC performance results are almost the same or even better than the traditional full-storage algorithm results.

关键词： algorithms performance BLAS real symmetric matrices complex Hermitian matrices positive definite matrices Cholesky factorization and solution recursive algorithms novel packed matrix data structures

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A generalization of Cattaneo-Mindlin for thin strips

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JOURNAL OF APPLIED MECHANICS-TRANSACTIONS OF THE ASME 1999年第4期66卷 1034-1037页

作者： Jäger, J IBAMA D-91058 Erlangen Germany

In this paper, a generalization of the Cuttaneo-Mindlin solution is derived for thin bonded layers with arbitrary surfaces. We assume that equal layers are in contact, and show that the normal and tangential stress displacement equations are uncoupled and of the same form. In this case the stick condition Sor tangential shift is identical with the contact condition in normal direction, and the tangential problem can be reduced to the normal problem. Finally, a recursive algorithm for general load cases is proposed We believe that this model illustrates typical features of elastic bodies with friction. It call also serve as a model for memory effects, employing the elastic superposition technique.

关键词： thin strip recursive algorithms Tangential stresses normal direction Generalization BOND COATS Identical elastic bodies Memory effect friction Superposition technique Normal

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recursive SOLUTION OF GENERALIZED PREDICTIVE CONTROL AND ITS EQUIVALENCE TO RECEDING HORIZON TRACKING CONTROL

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AUTOMATICA 1992年第6期28卷 1235-1238页

作者： KWON, WH CHOI, H BYUN, DG NOH, S Engineering Research Center for Advanced Control and Instrumentation Seoul National University Seoul 151-742 San 56-1 Silim-dong Kwanak-gu South Korea

In this paper, a recursive solution of Generalized Predictive Control (GPC) for I/O models is suggested. Also the GPC algorithm for state space model is introduced and shown to be identical to GPC for I/O models when each model represents the same system. It is shown by using the recursive solution of GPC that GPC for I/O models is identical to Receding Horizon Tracking Control (RHTC) for state space models when they are applied to. the same system. Some new stability results of GPC for I/O models are introduced, which originated from the stability properties of RHTC.

关键词： PREDICTIVE CONTROL STABILITY OPTIMAL CONTROL recursive algorithms STATE SPACE STEP RESPONSE

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AN FFT ALGORITHM BASED FAST ALGORITHM FOR ARBITRARY POLYNOMIAL TRANSFORMATION

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IEEE TRANSACTIONS ON ACOUSTICS SPEECH AND SIGNAL PROCESSING 1989年第10期37卷 1612-1614页

作者： KRISHNA, H Department of Electrical and Computer Engineering Syracuse University Syracuse NY USA

A fast algorithm for the arbitrary polynomial transformation is described. This algorithm is based on the fast Fourier transform (FFT) algorithm and reduces the computational complexity of a recently proposed recursiv... 详细信息

关键词： Arbitrary recursive algorithms complexity classes Fasting FFT algorithm algorithms Polynomial

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Generating De Bruijn sequences: An efficient implementation

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IEEE TRANSACTIONS ON COMPUTERS 1997年第2期46卷 198-200页

作者： Annexstein, FS Dept. of Electr. & Comput. Eng. Cincinnati Univ. OH USA Abstract Authors References Cited By Keywords Metrics Similar Download Citation Email Print Request Permissions

This paper presents a concise and efficient implementation of a method of producing De Bruijn sequences. The implementation is based on a recursive method due to Lempel [5]. We provide code for a function that for each pair of integers n greater than or equal to 2 and 0 less than or equal to x < 2(n-2) returns a unique De Bruijn sequence of order-n. The implementation requires only 0(2(n)) bit operations.

关键词： shift register sequences De Bruijn graphs computational complexity recursive algorithms NESL programming language

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Application of simplified line searches in the design of adaptive envelope-constrained filters

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IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I-FUNDAMENTAL THEORY AND APPLICATIONS 1996年第10期43卷 854-857页

作者： Zheng, WX Department of Mathematics University of Western Sydney Nepean NSW Canada

Envelope-constrained (EC) filtering is to design a finite impulse response filter such that the output of the filter is guaranteed to lie within a prescribed output pulse mask with respect to a given input pulse. The standard unconstrained least mean squares (LMS) or recursive least squares (RLS) algorithms are not applicable to this kind of adaptive filtering problem coupled with inequality constraints. A new type of recursive algorithms were proposed recently for designing an adaptive EC filter, and the corresponding convergence properties were established. In this paper, it is shown that faster convergence can be achieved by incorporating a simplified line search into the developed recursive algorithms. The modified recursive algorithms are very efficient, and very simple to implement.

关键词： recursive algorithms input pulse Levamisole Infinite impulse response filters Self tuning Filters learning management system inequality constraint Dosage Form Not Applicable line retrieval

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ON THE ABSENCE OF POSITIVE REALNESS CONDITIONS IN SELF-TUNING REGULATORS BASED ON EXPLICIT CRITERION MINIMIZATION

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AUTOMATICA 1987年第2期23卷 259-260页

作者： MOSCA, E ZAPPA, G Dipartimento di Sistemi e Informatica Universita' di Firenze Via S. Marta 3 50139 Firenze Italy

Local convergence properties of an adaptive control algorithm that, under suitable assumptions, is known to be globally convergent to the optimal LQ regulator, are studied. In this connection, it is shown that, as in more standard adaptive controllers, a “transfer function” H ( q ), depending on the innovation C ( q )-polynomial, plays a central role. The peculiarity of the algorithm under consideration is that the special form of the corresponding H ( q ) implies its positive realness. The interest of this result is in the relationship that it allows one to establish between the algorithm under consideration and other adaptive controllers, viz. MUSMAR, whose local convergence properties are known to be described by the same H ( q ).

关键词： Adaptive control convergence linear optimal control recursive algorithms self-tuning regulators

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