It is important to develop computationally efficient algorithms to solve combinatorial optimization problems. Equally important, if not more so, is to find a way to reformulate the original combinatorial optimization ...
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It is important to develop computationally efficient algorithms to solve combinatorial optimization problems. Equally important, if not more so, is to find a way to reformulate the original combinatorial optimization problem, provided this is possible, so that the resulting equivalent problem can be solved easily and efficiently using commercially available codes. This paper proposes an equivalent formulation to deal basically with the linearization of nonlinear expressions in 0-1 variables. The equivalent formulation technique proposed in this paper linearizes a binary quadratic integer problem of n variables by introducing only n new linear constraints, whereas the most economical method in the literature requires the addition of 2n of such constraints. The same technique is extended to linearize the binary cubic expression of n variables, this time requiring the addition of at most 3n auxiliary linear constraints and 3n continuous variables. Also discussed in the paper is the computational superiority of the proposed method over the existing ones in the literature through a series of randomly generated test problems.
ROVIO is one of the state-of-the-art monocular visual inertial odometry algorithms. It uses an Iterative Extended Kalman Filter (IEKF) to align visual features and update the vehicle state simultaneously by including ...
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ROVIO is one of the state-of-the-art monocular visual inertial odometry algorithms. It uses an Iterative Extended Kalman Filter (IEKF) to align visual features and update the vehicle state simultaneously by including the feature locations in the state vector of the IEKF. This algorithm is single-core intensive, which allows the other cores to be used for other algorithms, such as object detection and path optimization. However, the computational cost of the algorithm grows rapidly with the maximum number of features to track. Each feature adds three new states (a 2D bearing vector and inverse depth), leading to bigger matrix multiplications that are computationally expensive. The main computational load of ROVIO is the iterative update step of the IEKF. In this work, we reduce the average computational cost of ROVIO by 40% on an NVIDIA Jetson TX2, without affecting the accuracy of the algorithm. This computational gain is mainly achieved by exploiting the sparse matrices in ROVIO. Furthermore, we reduce the computational peaks by pre-selecting new features based on their already calculated FAST score. The combination of both modifications allows us to run ROVIO on the computationally restricted Raspberry Pi Zero 2W.
When the additive noise vector in the discrete observation process of a system can be partitioned into uncorrelated subvectors, an iterative processing technique for updating the Kalman-filter covariance matrix can of...
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When the additive noise vector in the discrete observation process of a system can be partitioned into uncorrelated subvectors, an iterative processing technique for updating the Kalman-filter covariance matrix can often be used to increase computational efficiency. For standard typical programming algorithms and for a typical computer, the iterative processing technique can theoretically reduce the computational requirements of the covariance updating equation by over 50 percent. In practical situations, computational savings of over 30 percent are realizable, a significant amount particularly for real-time tracking applications in high-target-density environments. Furthermore, independent of the computational advantages, the iterative processing technique is useful for track management, permitting effective utilization of priority and interrupt schemes without disturbing the Kalman-filter operation.
We investigate the computational performance of various numerical methods for the integration of the equations of motion and the variational equations for some typical classical many-body models of condensed matter ph...
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We investigate the computational performance of various numerical methods for the integration of the equations of motion and the variational equations for some typical classical many-body models of condensed matter physics: the Fermi-Pasta-Ulam-Tsingou (FPUT) chain and the one- and two-dimensional disordered, discrete nonlinear Schrodinger equations (DDNLS). In our analysis we consider methods based on Taylor series expansion, Runge-Kutta discretization and symplectic transformations. The latter have the ability to exactly preserve the symplectic structure of Hamiltonian systems, which results in keeping bounded the error of the system's computed total energy. We perform extensive numerical simulations for several initial conditions of the studied models and compare the numerical efficiency of the used integrators by testing their ability to accurately reproduce characteristics of the systems' dynamics and quantify their chaoticity through the computation of the maximum Lyapunov exponent. We also report the expressions of the implemented symplectic schemes and provide the explicit forms of the used differential operators. Among the tested numerical schemes the symplectic integrators ABA864 and SRKN14a exhibit the best performance, respectively for moderate and high accuracy levels in the case of the FPUT chain, while for the DDNLS models s9ABC6 and s11ABC6 (moderate accuracy), along with s17ABC8 and s19ABC8 (high accuracy) proved to be the most efficient schemes.
作者：
Yuan, MinghuLu, RuiFeng, LiqiangChu, TianshuChinese Acad Sci
Dalian Inst Chem Phys State Key Lab Mol React Dynam Dalian 116023 Peoples R China Qingdao Univ
Coll Med Lab Pathogen Biol Qingdao 266071 Peoples R China Qingdao Univ
Growing Base State Key Lab Inst Computat Sci & Engn Lab New Fiber Mat & Modern Text Qingdao 266071 Peoples R China
We show that by introducing Wigner rotation technique into the solution of time-dependent Schrodinger equation in length gauge, computational efficiency can be greatly improved in describing atoms in intense few-cycle...
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We show that by introducing Wigner rotation technique into the solution of time-dependent Schrodinger equation in length gauge, computational efficiency can be greatly improved in describing atoms in intense few-cycle circularly polarized laser pulses. The methodology with Wigner rotation technique underlying our openMP parallel computational code for circularly polarized laser pulses is described. Results of test calculations to investigate the scaling property of the computational code with the number of the electronic angular basis function l as well as the strong field phenomena are presented and discussed for the hydrogen atom. (C) 2014 AIP Publishing LLC.
Fang's fourth-order finite-difference time-domain (FDTD) schemes are compared with conventional second-order Yee's FDTD scheme in terms of computational efficiency. A three-dimensional (3D) rectangular cavity ...
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Fang's fourth-order finite-difference time-domain (FDTD) schemes are compared with conventional second-order Yee's FDTD scheme in terms of computational efficiency. A three-dimensional (3D) rectangular cavity partially filled with a dielectric material is considered for the numerical experiments. A set of numerical boundary conditions, constructed consistently with the higher order accuracy of the schemes, enables a realistic assessment of the computational efficiencies of Fang's (4,4) and (2,4) schemes in the presence of metallic and dielectric boundaries. Numerical results show that both Fang's (4,4) and (2,4) schemes are more efficient than Yee's (2,2) scheme by more than two orders of magnitude in CPU time for a fixed error level in the L-2 norm. This comparative study verifies that Fang's explicit fourth-order FDTD methods, complemented with the proposed numerical boundary conditions at planar material interfaces, yield very accurate and computationally very efficient time-domain solvers for the numerical simulation of electromagnetic interactions in three-dimensional multi-material structures.
The heterogeneity induced by the federated edge learning execution environment poses many performance challenges. Indeed, a balance between efficient resource usage and inference accuracy must be found. Our work there...
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ISBN:
(纸本)9798350361261;9798350361278
The heterogeneity induced by the federated edge learning execution environment poses many performance challenges. Indeed, a balance between efficient resource usage and inference accuracy must be found. Our work therefore aims at characterizing the hyperparameter influence by creating a variety of simulated execution circumstances. We designed an experimentation platform to simulate the execution of a typical image recognition training workload to highlight tweaking opportunities. We particularly focus on participant selection as an important performance lever. Thus, our benchmarks vary the number of clients participating in the federated edge learning process within i.i.d. and non-i.i.d. environments, while illustrating real-world configurations based on heterogeneous edge systems. We identify computational efficiency facets in federated edge learning and propose a taxonomic methodology to approach the study. We demonstrate the impact of the number of clients selected to participate in the global model update of federated edge learning on the overall system computational efficiency in challenging environments. Thus, we propose an optimization formula to meet computational efficiency and accurate models in challenging federated edge learning environments.
This paper discusses the computational efficiency of some procedures for solving the inverse kinematics problem of serial-link manipulators with redundant DOF. Two procedures that the author has newly developed, are c...
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ISBN:
(纸本)0780372034
This paper discusses the computational efficiency of some procedures for solving the inverse kinematics problem of serial-link manipulators with redundant DOF. Two procedures that the author has newly developed, are compared to the most widely used SVD methods. One is called the fast similarity factorization (FSF) method, in which the symmetric matrix JJ(T) (J is the Jacobian of the manipulator) is factorized to GDG(T) (G is the orthogomal matrix and D is the diagonal matrix). Another procedure, that the author also developed, is a recursive formulation, in which the joint-variable variations are obtained n (the number of DOF of the manipulator) times recursive calculations. Both methods are fast and robust. The computer simulation for a seven DOF anthropomorphic type manipulator reveales the proposed methods are several times faster than the conventional algorithms based on the SVD.
In this article we apply the Matrix Pencil (MP) technique to extract the complex exponentials from truncated transient response data computed by the FDTD method. To obtain accurate parameters without further FDTD comp...
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ISBN:
(纸本)0780357434
In this article we apply the Matrix Pencil (MP) technique to extract the complex exponentials from truncated transient response data computed by the FDTD method. To obtain accurate parameters without further FDTD computations, the truncated time record is efficiently extended into the future by summing the complex exponentials with complex coefficients. Two examples are analyzed to illustrate the efficiency of the Matrix Pencil method.
This paper primarily deals with improving the computational efficiency of the continuation small signal stability analysis of a microgrid. The continuation (or iterative) small signal stability analysis is required to...
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ISBN:
(纸本)9781467366588
This paper primarily deals with improving the computational efficiency of the continuation small signal stability analysis of a microgrid. The continuation (or iterative) small signal stability analysis is required to carry out control parameter tuning based upon the system level study. In specific, tuning of droop coefficients and current feed-forward loop gains of voltage controllers in an islanded microgrid is addressed. A generalized system configuration with non-identical sources and arbitrary load placements is considered. The construction of the system state matrix for such generalized configuration is explained. Similarly to the existing approaches, the continuation small signal stability analysis is performed through exhaustive enumerations. However, the system state matrix is initially decomposed into components in the form of the coefficients of parameters to be tuned. Therefore, there is no need to entirely reconstruct the system matrix at each iteration. The computation time requirement can be further reduced by deploying the sparsity of each matrix component. A clear rule is also established for the tuning of multiple parameters. The effectiveness of the methodology proposed is verified through a detailed case study.
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