Applied Numerical Analysis & Computational Mathematics最新文献

The computation of the Greatest Common Divisor (GCD) of a set of more than two polynomials is a non-generic problem. There are cases where iterative methods of computing the GCD of many polynomials, based on the Euclidean algorithm, fail to produce accurate results, when they are implemented in a software programming environment. This phenomenon is very strong especially when floating-point data are being used. The ERES method is an iterative matrix based method, which successfully evaluates an approximate GCD, by performing row transformations and shifting on a matrix, formed directly from the coefficients of the given polynomials. ERES deals with any kind of real data. However, due to its iterative nature, it is extremely sensitive when performing floating-point operations. It succeeds in producing results with minimal error, if we combine both floating-point and symbolic operations. In the present paper we study the behavior of the ERES method using floating-point and exact symbolic arithmetic. The conclusions derived from our study are useful for any other algorithm involving extended matrix operations. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

In this work, we consider solving the radiosity equation using the collocation method. We develop analytic evaluation of the integrations which are needed to setup the linear system in solving the radiosity equation using the collocation method. These integrations are over triangular elements in R ³. Our approach is to use affine transformations to convert integrations over elements in R ³ to integrations over elements in R ² and then to use a change of variables. For this, we introduce functions H _{m ,n ,k} for m , n , k ∈ N ₀ and use these to give our analytic formulas. The analytic evaluations of H _{m ,n ,4} and other relevant integrations are given in detail for some values of m and n . Finally, a performance comparison of the analytic evaluation integration with that of other well-known numerical integration schemes is given. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Software is developed in Matlab to solve initial–boundary value problems for first order systems of hyperbolic partial differential equations (PDEs) in one space variable x and time t . (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

In this paper, we propose and analyze an orthogonal non-polynomial nodal basis on triangles for discontinuous spectral element methods (DSEMs) for solving Maxwell's equations. It is based on the standard tensor product of the Lagrange interpolation polynomials and a “collapsing” mapping between the standard square and the standard triangle. The basis produces diagonal mass matrices for the DSEMs and is easy to implement. Numerical results for electromagnetic scattering in heterogeneous media are provided to demonstrate the exponential convergence of the proposed basis, and its application to the simulation of optical coupling by whispering gallery modes between two microcylinders is presented as well. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

The numerical integration of Hamiltonian systems by symplectic modified partitioned Runge-Kutta methods with the trigonometrically fitted property is considered in this paper. We construct new symplectic modified Runge-Kutta method of second order with the trigonometrically fitted property. We apply our new method as well as other existing methods to the numerical integration of the harmonic oscillator, the two dimensional harmonic oscillator, the two-body problem and an orbit problem studied by Stiefel and Bettis. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

In this work, a general overview of the recent progress and the existing difficulties in the implementation of physical and biogeochemical models accompanied with advanced Kalman filtering techniques in regional and shelf areas of the Mediterranean Sea is presented. The hydrodynamics of these areas were simulated with realistic implementations of the Princeton Ocean Model (POM) while the biogeochemistry of the ecosystems was tackled with the European Regional Seas Ecosystem Model (ERSEM). On the other hand, the Singular Evolutive Extended Kalman (SEEK) filter and its ensemble-based variant called the SEIK filter was used to assimilate all physical and biogeochemical data into the models. In these filters the error statistics were parameterized by means of a suitable basis of empirical orthogonal functions (EOFs). This contribution falls into the framework of the ‘Mediterranean ocean Forecasting System: Toward Environmental Predictions (MFSTEP)’ project and synthetically presents the modeling efforts in conjunction with data assimilation techniques for the development of operational systems in regional and shelf areas of the Mediterranean Sea. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

The solution of the one-dimensional time-independent Schrödinger equation is considered by trigonometrically and exponentially fitted symplectic integrators. The Schrödinger equation is first transformed into a Hamiltonian canonical equation. Numerical results are obtained for the one-dimensional harmonic oscillator and the exponential potential. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Hydrodynamic numerical models nowadays offer great aid when studying the physical behavior of coastal waters. However, the calibration and furthermore the verification of such models, is a difficult process that should be applied carefully, especially when little direct hydrodynamic data has been collected from the study area. This paper suggests a methodology for indirect verification of mathematical coastal circulation models, by means of image processing and interpretation of Landsat's TM reflective bands 3 and 6 imagery. This approach is an efficient practice and is easily available even though no field survey was carried out. This method was successfully applied to Saronikos Gulf and in particular to gulf of Megara, located westwards of Salamis Island, where the dispersion of a plume formed by urban waste waters was examined. The satellite data processing derivatives were found to be in accordance with the results of the circulation simulation and thus the parameters used for the calibration of the model can be considered successfully selected. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Multiresolution transforms are powerful tools in video processing applications because of its flexibility in representing nonstationary signals. For a proper adaptation to the singularities, it is crucial to develop nonlinear schemes. In these applications where some coefficients are modified or discarded we need to have some stability properties. In this paper, three-dimensional multiresolution processing algorithms that ensure this stability are introduced. A prescribed accuracy in various norms is ensured by these strategies. Explicit error bounds are presented. Finally, a numerical experiment using linear and non-linear schemes is performed. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)