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| 2. |
- Holmström, Kenneth, et al.
(författare)
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A review of the parameter estimation problem of fitting positive exponential sums to empirical data
- 2002
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Ingår i: Applied Mathematics and Computation. - : Elsevier. - 0096-3003 .- 1873-5649. ; 126:1, s. 31-61
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Tidskriftsartikel (refereegranskat)abstract
- Exponential sum models are used frequently: in heat diffusion, diffusion of chemical compounds, time series in medicine, economics, physical sciences and technology. Thus it is important to find good methods for the estimation of parameters in exponential sums. In this paper we review and discuss results from the last forty years of research. There are many different ways of estimating parameters in exponential sums and model a fit criterion, which gives a valid result from the fit. We find that a good choice is a weighted two-norm objective function, with weights based on the maximum likelihood (ML) criterion. If the number of exponential terms is unknown, statistical methods based on an information criterion or cross-validation can be used to determine the optimal number. It is suitable to use hybrid Gauss–Newton (GN) and quasi-Newton algorithms to find the unknown parameters in the constrained weighted nonlinear least-squares (NLLS) problem formulated using an maximal likelihood (ML) objective function. The problem is highly ill conditioned and it is crucial to find good starting values for the parameters. To find the initial parameter values, a modified Prony method or a method based upon rewriting partial sums as geometrical sums is proposed.
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| 3. |
- Knisevskaja, L., et al.
(författare)
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Singular integral equations method for computations of the scattering characteristics of a model heart exposed to electromagnetic radiation
- 2003
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Ingår i: Applied Mathematics and Computation. - 0096-3003 .- 1873-5649. ; 138:2-3, s. 545-553
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Tidskriftsartikel (refereegranskat)abstract
- The singular integral equations method elaborated in this paper allows us to solve accurately the Maxwell’s equations for a three-dimensional (3D) model heart exposed to electromagnetic radiation in the frequency range SHF and EHF. To test our algorithm we have computed the back scattering cross-section for a metal disc. Our computations are in good agreement with experiment given in literature. To demonstrate the usefulness of the algorithm we have computed the scattering characteristics of a simplified model of the human heart. This model is composed of the myocardium, the right and left atria and ventricles. All surfaces of the model are defined a triangular mesh in 3D covering the heart surfaces and normals to the triangles.
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| 4. |
- Zorzano, María Paz, et al.
(författare)
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Numerical solution of two dimensional Fokker-Planck equations
- 1999
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Ingår i: Applied Mathematics and Computation. - : Elsevier. - 0096-3003 .- 1873-5649. ; 98:2-3, s. 109-117
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Tidskriftsartikel (refereegranskat)abstract
- We present a robust finite difference scheme for the integration of the Fokker-Planck (FP) equation with two variables plus time. The scheme is checked with problems where analytical solutions exist and it is compared with finite element codes, as well as with simulations of the associated Stochastic Differential Equation (SDE). The precision and stability of the scheme are verified.
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| 5. |
- Ögren, Petter, et al.
(författare)
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Vaccination Strategies for Epidemics in Highly Mobile Populations
- 2002
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Ingår i: Applied Mathematics and Computation. - : Elsevier. - 0096-3003 .- 1873-5649. ; 127:2-3, s. 261-276
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Tidskriftsartikel (refereegranskat)abstract
- Our goal is to calculate optimal vaccination patterns for a rapidly spreading disease in an urbanized highly mobile population. The goal being to determine if vaccination can effect a disease for which there is low immunity in the population. Different types of structured SIR models are investigated. We construct a model appropriate for a traveling urbanized population and introduce a control in terms of a vaccination program. Linear constraints, a quadratic cost on the control and a linear cost on the number of infected are imposed. In this setting we calculate optimal vaccination patterns using the maximum principle of Pontryagin. The numerics are performed using Matlab.
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| 6. |
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| 7. |
- Ahmed, E, et al.
(författare)
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On Bertrand duopoly game with differentiated goods
- 2015
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Ingår i: Applied Mathematics and Computation. - : Elsevier. - 0096-3003 .- 1873-5649. ; 251, s. 169-179
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Tidskriftsartikel (refereegranskat)abstract
- The paper investigates a dynamic Bertrand duopoly with differentiated goods in which boundedly rational firms apply a gradient adjustment mechanism to update their price in each period. The demand functions are derived from an underlying CES utility function. We investigate numerically the dynamical properties of the model. We consider two specific parameterizations for the CES function and study the Nash equilibrium and its local stability in the models. The general finding is that the Nash equilibrium becomes unstable as the speed of adjustment increases. The Nash equilibrium loses stability through a period-doubling bifurcation and the system eventually becomes chaotic either through a series of period-doubling bifurcations or after a Neimark–Sacker bifurcation.
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| 8. |
- Anco, S., et al.
(författare)
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Solutions of gasdynamic equations associated with classical and new conservation laws
- 2015
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Ingår i: Applied Mathematics and Computation. - : Elsevier. - 0096-3003 .- 1873-5649. ; 268, s. 52-58
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Tidskriftsartikel (refereegranskat)abstract
- Exact solutions of the one-dimensional gasdynamic equations are constructed by applying the method of conservation laws to all point-wise conserved vectors of the equations under consideration. © 2015 Elsevier Inc.
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| 9. |
- Arjmand, Doghonay, 1987-, et al.
(författare)
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A note on the Taylor s decomposition on four points for a third-order differential equation
- 2007
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Ingår i: Applied Mathematics and Computation. - : Elsevier. - 0096-3003 .- 1873-5649. ; 188:2, s. 1483-1490
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Tidskriftsartikel (refereegranskat)abstract
- Taylor's decomposition on four points is presented. three-step difference schemes generated by the Taylor's decomposition on fourpoints for the numerical solutions of an initial-value problem, a boundary-value problem, and a nonlocal boundary-value problem for a third-order ordinary differential equation are constructed. Numerical examples are given.
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| 10. |
- Armerin, Fredrik, 1971-
(författare)
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Optimal stopping of a killed exponentially growing process
- 2019
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Ingår i: Applied Mathematics and Computation. - : ELSEVIER SCIENCE INC. - 0096-3003 .- 1873-5649. ; 353, s. 208-214
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Tidskriftsartikel (refereegranskat)abstract
- We consider a finite horizon optimal stopping problem with a gain function equal to the call option's. The value of the underlying process grows exponentially until a Poisson process jumps for the first time, at which the process jumps to zero and stays there forever. As applications of this model we consider valuing real options and options written on the stock of a start-up company.
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