algorithms for computing the inverse Laplace transform that consist essentially in choosing a series expansion for the original function are particularly effective in many cases and are widely used. The main purpose o...
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algorithms for computing the inverse Laplace transform that consist essentially in choosing a series expansion for the original function are particularly effective in many cases and are widely used. The main purpose of this paper is to review these algorithms in the context of regularization. We relate this viewpoint to the design of reliable algorithms destined to be run on finite precision arithmetic systems.
We consider the computational questions which arise when analyzing quasi-birth-death processes with a continuous phase set. We develop a framework based on the wavelet transform and we propose a numerical algorithm fo...
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We consider the computational questions which arise when analyzing quasi-birth-death processes with a continuous phase set. We develop a framework based on the wavelet transform and we propose a numerical algorithm for computing the steady-state probabilities based on the fast orthogonal wavelet transform. We conclude with a few examples to illustrate the effectiveness of our numerical algorithm. (c) 2014 Elsevier Inc. All rights reserved.
A mathematical model of the dynamics of the Baltic Sea is considered. A problem of variational assimilation of sea surface temperature (SST) data is formulated and studied. Based on variational assimilation of satelli...
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A mathematical model of the dynamics of the Baltic Sea is considered. A problem of variational assimilation of sea surface temperature (SST) data is formulated and studied. Based on variational assimilation of satellite observation data, an algorithm solving the inverse problem of heat flux restoration on the interface of two media is proposed. The results of numerical experiments reconstructing the heat flux functions in the problem of variational assimilation of SST observation data are presented. The influence of SST assimilation on other hydrodynamic parameters of the model is considered.
The control of a parabolic equation is considered. The solution of this equation is assumed to be measured inaccurately. An algorithm is described for finding a feedback control function such that the solution of this...
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The control of a parabolic equation is considered. The solution of this equation is assumed to be measured inaccurately. An algorithm is described for finding a feedback control function such that the solution of this equation tracks the solution of another equation generated by an unknown right-hand side.
The method of enforcing sparsity during magnetic resonance imaging reconstruction has been successfully applied to partially parallel imaging (PPI) techniques to reduce noise and artifact levels and hence to achieve e...
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The method of enforcing sparsity during magnetic resonance imaging reconstruction has been successfully applied to partially parallel imaging (PPI) techniques to reduce noise and artifact levels and hence to achieve even higher acceleration factors. However, there are two major problems in the existing sparsity-constrained PPI techniques: speed and robustness. By introducing an auxiliary variable and decomposing the original minimization problem into two subproblems that are much easier to solve, a fast and robust numerical algorithm for sparsity-constrained PPI technique is developed in this work. The specific implementation for a conventional Cartesian trajectory data set is named self-feeding Sparse Sensitivity Encoding (SENSE). The computational cost for the proposed method is two conventional SENSE reconstructions plus one spatially adaptive image denoising procedure. With reconstruction time approximately doubled, images with a much lower root mean square error (RMSE) can be achieved at high acceleration factors. Using a standard eight-channel head coil, a net acceleration factor of 5 along one dimension can be achieved with low RMSE. Furthermore, the algorithm is insensitive to the choice of parameters. This work improves the clinical applicability of SENSE at high acceleration factors. Magn Reson Med 64:1078-1088, 2010. (C) 2010 WileyLiss, Inc.
In order to solve a class of linear nonlocal boundary value problems, a new reproducing kernel space satisfying nonlocal conditions is constructed carefully. This makes it easy to solve the problems. Furthermore, the ...
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In order to solve a class of linear nonlocal boundary value problems, a new reproducing kernel space satisfying nonlocal conditions is constructed carefully. This makes it easy to solve the problems. Furthermore, the exact solutions of the problems can be expressed in series form. The numerical results demonstrate that the new method is quite accurate and efficient for solving fourth-order nonlocal boundary value problems. (C) 2010 Elsevier Ltd. All rights reserved.
We develop a general notion of orthogonal wavelets 'centered' on an irregular knot sequence. We present two families of orthogonal wavelets that are continuous and piecewise polynomial. We develop efficient al...
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We develop a general notion of orthogonal wavelets 'centered' on an irregular knot sequence. We present two families of orthogonal wavelets that are continuous and piecewise polynomial. We develop efficient algorithms to implement these schemes and apply them to a data set extracted from an ocelot image. As another application, we construct continuous, piecewise quadratic, orthogonal wavelet bases on the quasi-crystal lattice consisting of the tau-integers where tau is the golden ratio. The resulting spaces then generate a multiresolution analysis of L-2(R) with scaling factor tau.
A previously formulated new approach to the consideration of systems of quasilinear hyperbolic equations on the basis of variational principles is described in more detail in the case of special systems of three equat...
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A previously formulated new approach to the consideration of systems of quasilinear hyperbolic equations on the basis of variational principles is described in more detail in the case of special systems of three equations. It is shown that each field of characteristics can be represented as a solution of a variational problem. Moreover, the Rankine-Hugoniot relations at the corner points of the characteristics or at the intersections of the characteristics of a single family hold automatically. In the simplest case of the Hopf equation, a numerical algorithm is constructed on the basis of a variational principle.
In this paper, we present a toolbox for structured model reduction developed for MATLAB. In addition to structured model reduction methods using balanced realizations of the subsystems, we introduce a numerical algori...
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ISBN:
(纸本)9783952426937
In this paper, we present a toolbox for structured model reduction developed for MATLAB. In addition to structured model reduction methods using balanced realizations of the subsystems, we introduce a numerical algorithm for structured model reduction using a subgradient optimization algorithm. We briefly present the syntax for the toolbox and its features. Finally, we demonstrate the applicability of various model reduction methods in the toolbox on a structured mass-spring mechanical system.
This paper presents a new theory and algorithm regarding on optimal control based on natural computation. This natural algorithm simulates the survival and competition of multi-races and multi-individuals in the astro...
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ISBN:
(纸本)9781467376792
This paper presents a new theory and algorithm regarding on optimal control based on natural computation. This natural algorithm simulates the survival and competition of multi-races and multi-individuals in the astrospace which consists of all races and individuals. This super-intelligent natural algorithm covers most of current optimization algorithms for dynamic and static parameters, and is applicable to a variety of fields and disciplines. In the natural running process, all races and individuals can compete for its own interests, and the final results must be optimal for the overall situation. Some numerical simulation results show that this new theory and algorithm of optimal control are correct and feasible, as well as superior for the multilateral confrontations problem.
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