Applied Numerical Analysis & Computational Mathematics最新文献

We provide a local as well as a semilocal convergence analysis for two-point Newton methods under very general conditions. Our equation contains a Fréchet differentiable operator F and another operator G whose differentiability is not assumed. Using more precise majorizing sequences than before we provide sufficient convergence conditions for Newton methods to a locally unique solution of equation F (x) + G(x) = 0. In the semilocal case we show under weaker conditions that our error estimates on the distances involved are finer and the information on the location of the solution at least as precise as in earlier results [17]. In the local case a larger radius of convergence is obtained [21]. Several applications are provided to show that our results compare favorably with earlier ones [11]–[14], [17], [21], [23], [25]. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

The least-squares linear estimation problem of discrete-time signals using measurements perturbed by additive white plus coloured noises is solved. It is supposed that the measurements are arrived in time or delayed by one sampling time and the delay is modelled by a sequence of independent Bernoulli random variables whose values, one or zero, indicate if there exists or not delay. The estimation algorithms only use the covariance information about the signal and the observation noises and the delay probabilities. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

In this paper we consider a method for finding several eigenvalues and corresponding eigenvectors of large-scale generalized eigenvalue problems. In this method, a small matrix pencil that has only the desired eigenvalues is derived using complex moments obtained via numerical integration. Since the process to derive the moments can be performed in parallel and we do not need to exchange data between processes, the presented method is suitable for master-worker programming models. We have implemented and tested the proposed method in a grid RPC (remote procedure call) system. Numerical examples illustrate the properties of our approach. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

The back propagation of error in multi-layer perceptrons when used for supervised training is a non-local algorithm in space, that is it needs the knowledge of the network topology. On the other hand, learning rules in biological systems with many hidden units, seem to be local in both space and time. In this work, a local learning algorithm is proposed which makes no distinction between input, hidden and output layers. Simulation results are presented and compared with other well known training algorithms. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Short term accurate wind and wave forecasts can be used for optimal ship routing. In this work, a method is presented for manipulating the POSEIDON [1] system forecasts for the Greek seas and for producing optimal routes for small and medium size ships. The method is composed from a geometrical calculation of all possible routes between two points and from an iterative algorithm which approximates the optimal (or an almost optimal) route. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

In a series of articles [9, 10, 11] about the numerical computation of orthogonal polynomials on a subset of the real line, Gautschi shows that computing orthogonal polynomials starting from the moments μ_k = ∫ x^kdμ(x) of the measure is generally an ill-conditioned problem. However, in [10] an alternative approach is presented, based on so-called modified moments, which works better in certain situations. In this paper we generalize these results to the computation of orthogonal rational functions and provide a new modified moment algorithm, based on the connection between modified moments and interpolatory quadrature. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

In this paper, we present a preconditioning method based on Incomplete Cholesky Decomposition (ICD) combined with a band-diagonalization strategy which enables an efficient ICD. The performance of the ICD preconditioner for sparse symmetric systems has a close relationship to the number of fill-ins of the exact Cholesky decomposition and the number can be decreased by the band-diagonalization. We consider an implicit surface reconstruction as a typical problem which has a property that the coefficient matrix can be transformed into a band-diagonal structure at a low computational cost. The effectiveness of the preconditioning is shown as a result of some numerical experiments. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

In this paper an advanced interpolatory graphical display algorithm based on cardinal B-spline functions is provided. It is well-known that B-spline functions are a flexible tool to design various scale rapresentations of a signal. The proposed method allows to display without recursion a function at any desiderable resolution so that only initial data and opportune vectors weight are involved. In this way the structure of the algorithm is independent across the scale and a computational efficiency is reached. In this paper mono and bi-dimensional vectors weight generated by means of centered cubic cardinal B-spline functions have been supplied. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

A concept of the characteristic technique used to obtain a generalized solution of the scalar one-dimensional nonlinear advection equation with the non-convex flow function is presented. Two grids: characteristic and Eulerian are used to obtain numerical solution. A characteristic grid is adaptive both to the properties of the initial distribution function and to the properties of the boundary condition function. This allows: development of the algorithm for obtaining a numerical solution on characteristic grid using the properties of the solution of nonlinear advection equation in smooth region; to reproduce spatial location and solution value at the discontinuity points and extreme points at the accuracy determined by interpolation and approximation of initial values and boundary condition functions. For the non-convex flow function, algorithms are proposed for the definition of the sequence of Riemann problems (strong discontinuity) and for their solving. Refined expressions are derived for the velocity of a strong non-stationary discontinuity. Construction of the solution with satisfying of integral preservation law for the non-convex flow function is presented. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

“Without Mathematics almost everything is zilch”, a scientific maxim, is the kernel for this mathematical piece of research. The basic notion is to formulate mathematical models for devices and circuits deployed in state of the art electronic gadgets. The article searches for a tool to perform the aforementioned operation and finally accouters its models with well known mathematical approximation tools called Interpolators. The analysis of these models is carried out using MATLAB and the simulations are obtained for both frequency dependent and independent device characteristics. The scheme could result in some predicted merits when it allies with Very Large Scale and Ultra Large Scale Integration [VLSI,ULSI] techniques employed in the Electronic chip design industry and Artificial Intelligence. The quondam alliance could result in device miniaturization and the latter may result in the design of robots enabled in the control of electronic environments. However, the latter could be an application [for Robots] or an alliance where the principles of neural networks could be applied for the purpose of mathematical modelling. Thus, the article reveals a solution for how mathematics be applied to engineering and science. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)