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Optimal rate of convergence of the Bence-Merriman-Osher algorithm for motion by mean curvature

SIAM JOURNAL ON MATHEMATICAL ANALYSIS 2005年第3期37卷 841-866页

作者： Ishii, K Kobe Univ Fac Maritime Sci Kobe Hyogo 6580022 Japan

Bence, Merriman, and Osher proposed an algorithm for computing the motion a hypersurface by mean curvature in terms of solutions of the usual heat equation, continually reinitialized after short time steps. In this paper, applying some techniques of asymptotic analysis for the Allen-Cahn equation, we give a rate of convergence of their algorithm for the motion of a smooth and compact hypersurface by mean curvature. We also consider the special case of a circle evolving by curvature and show that our rate is optimal.

关键词： motion by mean curvature numerical algorithm rate of convergence optimality

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A Sensitivity-Based algorithm Approach in Reconstructing Images in Electrical Impedance Tomography

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IEEE ACCESS 2024年 12卷 146560-146574页

作者： Alas, Rose Anne D. Velasco, Arrianne Crystal T. Univ Philippines Diliman Inst Math Quezon City 1101 Philippines

Electrical impedance tomography (EIT) is a medical imaging technique used to reconstruct images inside the domain of interest. EIT collects data on the boundary of the domain to infer the conductivity distribution inside the domain. The conductivity distribution will then be used to produce a tomographic image of the inside of the domain. This paper aims to recover geometric properties of a spherical perturbation in the conductivity inside a domain using sensitivity values of the electric potential on the boundary of the domain. The continuum model for EIT is first considered, as it holds more boundary information compared to other models of EIT. A change on the conductivity inside the domain is applied, and the impact on the electric potential is studied. The inverse EIT problem is then solved by formulating relations between the sensitivity values on the boundary and the geometric properties of the spherical perturbation: the radius and the projection onto the boundary and depth of its center. A reconstruction method using these relations is proposed and the method is examined by performing numerical simulations on different domains to model the head and the thorax. Lastly, the proposed method is applied to the complete electrode model of the EIT problem to analyze the performance of the method when the boundary data is limited on the electrodes.

关键词： Electrical impedance tomography gateaux derivative image reconstruction numerical algorithm sensitivity gateaux derivative image reconstruction numerical algorithm sensitivity

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Matrix partitioning on a virtual shared memory parallel machine

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IEEE TRANSACTIONS ON PARALLEL AND DISTRIBUTED SYSTEMS 1996年第4期7卷 343-355页

作者： Charny, B Audre Inc. San Diego CA USA

The general problem considered in the paper is partitioning of a matrix operation between processors of a parallel system in an optimum load-balanced way without potential memory contention. The considered parallel system is defined by several features the main of which is availability of a virtual shared memory divided into segments. if partitioning of a matrix operation causes parallel access to the same memory segment with writing data to the segment by al least one processor, then contention between processors arises which implies performance degradation. To eliminate such situation, a restriction is imposed on a class of possible partitionings, so that no two processors would write data to the same segment. On the resulting class of contention-free partitionings, a load-balanced optimum partitioning is defined as satisfying independent minimax criteria. The main result of the paper is an algorithm for finding the optimum partitioning by means of analytical solution of respective minimax problems. The paper also discusses implementation and performance issues related to the algorithm, on the basis of experience at Kendall Square Research Corporation, where the partitioning algorithm was used for creating high-performance parallel matrix libraries.

关键词： basic matrix operations matrix partitioning minimax criteria numerical algorithm optimum load balance parallel multiprocessor performance virtual shared memory

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An eigen-mode method in kinematic shakedown analysis

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INTERNATIONAL JOURNAL OF PLASTICITY 2002年第1期18卷 71-90页

作者： Zhang, TG Raad, L Univ Alaska Dept Civil Engn Fairbanks AK 99775 USA

The kinematic shakedown theorem is formulated for some deformation processes as a kinematic extremum problem based on a polyhedral load domain and a deformation mode domain. An eigen-mode method is used to construct the deformation mode domain. Every kinematically admissible strain field within some time interval can be derived from the deformation domain and used in the proposed shakedown formulation to determine the safety load factor. Several simple shakedown problems are examined by using this proposed methodology. These numerical results are discussed and compared with available analytical and other numerical results. (C) 2002 Elsevier Science Ltd. All rights reserved.

关键词： kinematic shakedown deformation domain eigen-mode method numerical algorithm

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On the Wiberg algorithm for matrix factorization in the presence of missing components

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INTERNATIONAL JOURNAL OF COMPUTER VISION 2007年第3期72卷 329-337页

作者： Okatani, Takayuki Deguchi, Koichiro Tohoku Univ Grad Sch Informat Sci Sendai Miyagi 9808579 Japan

This paper considers the problem of factorizing a matrix with missing components into a product of two smaller matrices, also known as principal component analysis with missing data (PCAMD). The Wiberg algorithm is a numerical algorithm developed for the problem in the community of applied mathematics. We argue that the algorithm has not been correctly understood in the computer vision community. Although there are many studies in our community, almost every one of which refers to the Wiberg study, as far as we know, there is no literature in which the performance of the Wiberg algorithm is investigated or the detail of the algorithm is presented. In this paper, we present derivation of the algorithm along with a problem in its implementation that needs to be carefully considered, and then examine its performance. The experimental results demonstrate that the Wiberg algorithm shows a considerably good performance, which should contradict the conventional view in our community, namely that minimization-based algorithms tend to fail to converge to a global minimum relatively frequently. The performance of the Wiberg algorithm is such that even starting with random initial values, it converges in most cases to a correct solution, even when the matrix has many missing components and the data are contaminated with very strong noise. Our conclusion is that the Wiberg algorithm can also be used as a standard algorithm for the problems of computer vision.

关键词： matrix factorization singular value decomposition principal component analysis with missing data (PCAMD) structure from motion numerical algorithm

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Dynamic thermo-mechanical coupled response of random particulate composites:A statistical two-scale method

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Chinese Physics B 2014年第7期23卷 605-616页

作者：杨自豪陈云杨志强马强 Department of Applied Mathematics Northwestern Polytechnical University College of Computer Science Fujian Agriculture and Forestry University LSEC ICMSECAcademy of Mathematics and Systems ScienceChinese Academy of Sciences

This paper focuses on the dynamic thermo-mechanical coupled response of random particulate composite materials. Both the inertia term and coupling term are considered in the dynamic coupled problem. The formulation of the problem by a statistical second-order two-scale （SSOTS） analysis method and the algorithm procedure based on the finite-element difference method are presented. numerical results of coupled cases are compared with those of uncoupled cases. It shows that the coupling effects on temperature, thermal flux, displacement, and stresses are very distinct, and the micro- characteristics of particles affect the coupling effect of the random composites. Furthermore, the coupling effect causes a lag in the variations of temperature, thermal flux, displacement, and stresses.

关键词： random particulate composites statistical second-order two-scale (SSOTS) analysis method,thermo-mechanical coupling effect numerical algorithm

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Fast Toeplitz eigenvalue computations, joining interpolation-extrapolation matrix-less algorithms and simple-loop theory: The preconditioned setting

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APPLIED MATHEMATICS AND COMPUTATION 2024年 466卷

作者： Bogoyaa, M. Serra-Capizzano, S. Vassalos, P. Univ Valle Dept Matemat Cali Colombia Univ Insubria Dipartimento Sci & Alta Tecnol Como Italy Uppsala Univ Dept Informat Technol Div Sci Comp Uppsala Sweden Athens Univ Econ & Business Sch Informat Sci & Technol Dept Informat Athens Greece

Under appropriate technical assumptions, the simple-loop theory allows to derive various types of asymptotic expansions for the eigenvalues of Toeplitz matrices T-n (f) generated by a function f. Unfortunately, such a theory is not available in the preconditioning setting, that is for matrices of the formT(n)(-1)(g)T-n(l) with g,l real-valued, g nonnnegative and not identically zero almost everywhere. Independently and under the milder hypothesis that f = l/g is even and monotonic over [0, pi], matrix-less algorithms have been developed for the fast eigenvalue computation of large preconditioned matrices of the type above, within a linear complexity in the matrix order: behind the high efficiency of such algorithms there are the expansions as in the case g = 1, combined with the extrapolation idea, and hence we conjecture that the simple-loop theory has to be extended in such a new setting, as the numerics strongly suggest. Here we focus our attention on a change of variable, followed by the asymptotic expansion of the new variable, and we consider new matrix-less algorithms ad hoc for the current case. numerical experiments show a much higher accuracy till machine precision and the same linear computational cost, when compared with the matrix-less procedures already proposed in the literature.

关键词： Toeplitz matrix Spectra Preconditioned matrix Asymptotic expansion numerical algorithm

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Optimal harvesting for periodic age-dependent population dynamics

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SIAM JOURNAL ON APPLIED MATHEMATICS 1998年第5期58卷 1648-1666页

作者： Anita, S Iannelli, M Kim, MY Park, EJ Univ Al I Cuza Fac Math Iasi 6600 Romania Univ Trent Dept Math I-38050 Trent TN Italy Univ Wyoming Dept Math Laramie WY 82071 USA

Here we investigate the optimal harvesting problem for some periodic age-dependent population dynamics;namely, we consider the linear Lotka-McKendrick model with periodic vital rates and a periodic forcing term that sustains oscillations. Existence and uniqueness of a positive periodic solution are demonstrated and the existence and uniqueness of the optimal control are established. We also state necessary optimality conditions. A numerical algorithm is developed to approximate the optimal control and the optimal harvest. Some numerical results are presented.

关键词： population dynamics age structure periodic solutions Volterra integral equation optimal harvesting optimality conditions numerical algorithm finite differences

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Multi-cell Optimal Downlink Beamforming algorithm with Per-base Station Power Constraints

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WIRELESS PERSONAL COMMUNICATIONS 2012年第4期62卷 893-906页

作者： Huang, Fan Wang, Yafeng Geng, Jian Yang, Dacheng Beijing Univ Posts & Telecommun Wireless Theories & Technol Lab WT&T Beijing 100088 Peoples R China Beijing Univ Posts & Telecommun Sch Informat & Telecommun Beijing 100088 Peoples R China Beijing Univ Posts & Telecommun Qualcomm Joint Res Ctr Beijing 100088 Peoples R China

We consider a problem of optimizing multi-cell downlink throughput in multiple-input single-output (MISO) beamforming with single user per sub-channel in the wireless communication system. Previous work based on the generalization of uplink-downlink duality has already reformulated the maximum achievable downlink throughput into dual uplink throughput maximization problem. Since the dual uplink problem is nonconvex, it is difficult to find its optimal solution. The main contribution of this paper is a novel practical algorithm based on heuristic to find the solution of beamforer design satisfying the necessary optimality conditions of the dual uplink problem. Meanwhile the converged beamforming vectors can in turn improve the system sum rate significantly. As the dual problem is a mixed optimization, we also provide algorithms for its two sub-optimal problems. Simulation results validate the convergence and the efficiency of proposed algorithms.

关键词： Multi-cell Downlink beamforming Throughput maximization Power constraint numerical algorithm

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About the algebraic solutions of smallest enclosing cylinders problems

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APPLICABLE ALGEBRA IN ENGINEERING COMMUNICATION AND COMPUTING 2012年第3-4期23卷 151-164页

作者： Petitjean, Michel Univ Paris 07 INSERM MTi UMR S 973 F-75205 Paris 13 France

Given n points in Euclidean space E (d) , we propose an algebraic algorithm to compute the best fitting (d-1)-cylinder. This algorithm computes the unknown direction of the axis of the cylinder. The location of the axis and the radius of the cylinder are deduced analytically from this direction. Special attention is paid to the case d = 3 when n = 4 and n = 5. For the former, the minimal radius enclosing cylinder is computed algebrically from constrained minimization of a quartic form of the unknown direction of the axis. For the latter, an analytical condition of existence of the circumscribed cylinder is given, and the algorithm reduces to find the zeroes of an one unknown polynomial of degree at most 6. In both cases, the other parameters of the cylinder are deduced analytically. The minimal radius enclosing cylinder is computed analytically for the regular tetrahedron and for a trigonal bipyramids family with a symmetry axis of order 3.

关键词： Best fitting cylinder Smallest enclosing cylinder Minimal cylinder Circumscribed cylinder through five points numerical algorithm

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