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Shinya Miyajima 《Numerical Linear Algebra with Applications》2015,22(3):548-563
Fast algorithms for enclosing the minimum norm least squares solution of the matrix equation AXB = C are proposed. To develop these algorithms, theories for obtaining error bounds of numerical solutions are established. The error bounds obtained by these algorithms are verified in the sense that all the possible rounding errors have been taken into account. Techniques for accelerating the enclosure and obtaining smaller error bounds are introduced. Numerical results show the properties of the proposed algorithms. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献
997.
We consider the numerical solution of the continuous algebraic Riccati equation A*X + XA ? XFX + G = 0, with F = F*,G = G* of low rank and A large and sparse. We develop an algorithm for the low‐rank approximation of X by means of an invariant subspace iteration on a function of the associated Hamiltonian matrix. We show that the sought‐after approximation can be obtained by a low‐rank update, in the style of the well known Alternating Direction Implicit (ADI) iteration for the linear equation, from which the new method inherits many algebraic properties. Moreover, we establish new insightful matrix relations with emerging projection‐type methods, which will help increase our understanding of this latter class of solution strategies. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
998.
Numerical discretization-based kernel type estimation methods for ordinary differential equation models
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We consider the problem of parameter estimation in both linear and nonlinear ordinary differential equation(ODE) models. Nonlinear ODE models are widely used in applications. But their analytic solutions are usually not available. Thus regular methods usually depend on repetitive use of numerical solutions which bring huge computational cost. We proposed a new two-stage approach which includes a smoothing method(kernel smoothing or local polynomial fitting) in the first stage, and a numerical discretization method(Eulers discretization method, the trapezoidal discretization method,or the Runge–Kutta discretization method) in the second stage. Through numerical simulations, we find the proposed method gains a proper balance between estimation accuracy and computational cost.Asymptotic properties are also presented, which show the consistency and asymptotic normality of estimators under some mild conditions. The proposed method is compared to existing methods in term of accuracy and computational cost. The simulation results show that the estimators with local linear smoothing in the first stage and trapezoidal discretization in the second stage have the lowest average relative errors. We apply the proposed method to HIV dynamics data to illustrate the practicability of the estimator. 相似文献
999.
We consider uniform stability to a nontrivial equilibrium of a nonlinear fluid–structure interaction (FSI) defined on a two or three dimensional bounded domain. Stabilization is achieved via boundary and/or interior feedback controls implemented on both the fluid and the structure. The interior damping on the fluid combining with the viscosity effect stabilizes the dynamics of fluid. However, this dissipation propagated from the fluid alone is not sufficient to drive uniformly to equilibrium the entire coupled system. Therefore, additional interior damping on the wave component or boundary porous like damping on the interface is considered. A geometric condition on the interface is needed if only boundary damping on the wave is active. The main technical difficulty is the mismatch of regularity of hyperbolic and parabolic component of the coupled system. This is overcome by considering special multipliers constructed from Stokes solvers. The uniform stabilization result obtained in this article is global for the fully coupled FSI model. 相似文献
1000.
Separation of complex sugar mixtures on a hydrolytically stable bidentate urea‐type stationary phase for hydrophilic interaction near ultra high performance liquid chromatography
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Dorina Kotoni Alessia Ciogli Claudio Villani David S. Bell Francesco Gasparrini 《Journal of separation science》2014,37(5):527-535
A stationary phase bearing both bridged bis‐ureido and free amino groups (USP‐HILIC‐NH2–2.5SP) for high‐speed hydrophilic interaction liquid chromatography separations was prepared using a one‐pot two‐step procedure starting from 2.5 μm totally porous silica particles. Highly polar compounds, such as polyols, hydroxybenzoic acids, and sugars, were successfully analyzed in shorter times and with higher peak efficiency, when compared to results obtained with a bidentate urea‐type column packed with 5 μm particles. Increased sugarophilicity and better peak shape were attested for the USP‐HILIC‐NH2–2.5SP column (100 × 3.2 mm id) when compared with two commercially available UHPLC columns, namely an acquity BEH amide packed with totally porous 1.7 μm microparticles and a HILIC Kinetex column packed with core–shell 2.6 μm particles. Finally, the new column was employed in the separation of complex mixture of sugars (mono‐, di‐, and oligosaccharides) and in the analysis of beer samples. The resulting chromatograms showed good selectivity and overall resolution, while the catalyzing effect of the free amino moieties resulted in excellent peak shapes and in the absence of split peaks due to sugar anomerization phenomena. 相似文献