1,721,051 research outputs found
Regularization of a Fourier Series Method for the Laplace Transform inversion with real data
No full textWe propose a numerical method for computing a function, given its Laplace transform function on the real axis. The inversion algorithm is based on the Fourier series expansion of the unknown function and the Fourier coefficients are approximated using a Tikhonov regularization method. The key point of this approach is the use of the regularization scheme in order to improve the conditioning of the discrete problem: the value of the regularization parameter is that giving a tradeoff between the discretization error, including the regularization error, and the conditioning of the discrete problem
High Performance Algorithms and Software for Nonlinear Optimization, Computational Optimization and Applications (special issue)
No full textFWT based preconditioners for Image restoration problems
No full textThe problem of removing or minimizing degradations in a blurred and noisy image is known as image restoration. The computational kernel of many image restoration problems is the solution of the following inverse problem: Hf=g+η where where the n2-vectors f and g represent the real and the observed image, respectively. The n2 vector η is an additive noise which is usually unknown. The n 2× n2-matrix H is the point spread function matrix and it represents the blurring process. The inverse problem consists in the computation of an approximation to the original image vector f, from known values of g and H. In such cases the restoration problem typically leads to a discrete ill-posed inverse problem. The classical way to compute a reasonable solution is to regularize the discrete problem. We explore the possible use of the fast wavelet transform-based preconditioners for the efficient solution of image restoration problem
A Parallel Software System for the Numerical Simulation of Air Pollution
No full textWe report on our research activity devoted to the development of numerical algorithms and software for the simulation of the transport and the photochemical transformations of air pollutants in urban-scale domains. A parallel software package has been produced, named Parallel Naples Airshed Model (PNAM), for the simulation of air pollution episodes in the Naples area, using parallel distributed memory machines. We describe the work that has lead to PNAM, focusing on the choice of numerical methods and parallelization techniques, and present results of numerical experiments performed with a realistic test case
Error analysis of a Collocation method for numerically inverting a Laplace transform in case of real samples
No full textIn [S. Cuomo, L. D’Amore, A. Murli, M.R. Rizzardi, Computation of the inverse Laplacetransform based on acollocationmethod which uses only real values, J. Comput. Appl. Math., 198 (1) (2007) 98–115] the authors proposed aCollocationmethod (C-method) for real inversion of Laplacetransforms (Lt), based on the truncated Laguerre expansion of the inverse function.
The computational kernel of a C-method is the solution of a Vandermonde linear system, where the right hand side is obtained evaluating the Lt on the real axis. The Bjorck Pereira algorithm has been used for solving the Vandermonde linear system, providing a computable componentwise error bound on the solution.
For an inversion problem on discrete data F is known on a pre-assigned set of points (we refer to these points as samples of F) only and the major challenge is to deal with a significative loss of information. A natural approach to overcome this intrinsic difficulty is to construct a suitable fitting model that approximates the given data. In this case, we show that such approach leads to a C-method with perturbed right hand side, and then we use again the Bjorck Pereira algorithm.
Starting from the error introduced by the fitting model, we study its propagation in order to determine the maximum attainable accuracy on fN. Moreover we derive a computable error bound that allows to get the suitable value of the parameter N that gives the maximum attainable accurac
An Extension of the Henrici Formula for the Laplace Transform Inversion
No full textAbstract. Under certain conditions, starting from the Riemann inversion formula, which gives an explicit representation of the inverse Laplace transform in the complex form, we derive an integral equation, of convolution type, whose solution is the inverse Laplace transform function. This formula can be used if the Laplace transform has a finite number of singularities, located everywhere in the complex plane, and provided that their corresponding residues are known. It only requires the knowledge of the Laplace transform function on the real negative axis. Preliminary numerical experiments illustrating the reliability of the inversion algorithm are described
Image Sequence Inpainting: a numerical approach for blotch detection and removal via motion estimation
No full textNumerical methods for data assimilation: Kalman filter
No full textThe Kalman filter (KF) dates back to 1960, when R. E. Kalman [4] provided a recursive algorithm to compute the solution of a (linear) data filtering and prediction problem, proving to be much more efficient than the N. Wiener’s approach, introduced in 1949 in [5].
Data filtering is a simple example of Data Assimilation problem which can be regarded as a least squares approximation problem and, more precisely, as an inverse ill-posed problem.
In this paper we review and discuss KF in the context of numerical regularization methods aimed to solve ill-posed inverse problems such those arising in Data Assimilation applications
- …
