Search results for "interpolation."

Application of elastostatic Green function tensor technique to electrostriction in cubic, hexagonal and orthorhombic crystals

2002

The elastostatic Green function tensor approach, which was recently used to treat electrostriction in numerical simulation of domain structure formation in cubic ferroelectrics, is reviewed and extended to the crystals of hexagonal and orthorhombic symmetry. The tensorial kernels appearing in the expressions for effective nonlocal interaction of electrostrictive origin are derived explicitly and their physical meaning is illustrated on simple examples. It is argued that the bilinear coupling between the polarization gradients and elastic strain should be systematically included in the Ginzburg-Landau free energy expansion of electrostrictive materials.

Cell-Average Multiwavelets Based on Hermite Interpolation

2007

Adaptive rational interpolation for cell-average

2020

Abstract In this paper, we extend the rational interpolation introduced by G. Ramponi et al. (1997, 1998, 1996, 1995) to the cell average setting. We propose a new family of non linear interpolation operator. It consists on constructing new approximations using a non linear weighted combination of polynomials of degree 1 or 2 to obtain new interpolations of degree 2 or 4 respectively. New weights are proposed and analyzed. Gibbs phenomenon is studied and some experiments are performed comparing the new methods with classical linear and non linear interpolation as Weighted Essentially Non-Oscillatory (WENO).

Optimal extension of multispectral image demosaicking algorithms for setting up a one-shot camera video acquisition system

2022

Multispectral images are acquired using multispectral cameras equipped with CCD or CMOS sensors which sample the visible or near infrared spectrum according to specific spectral bands. A mosaic of multispectral MSFA filters is superimposed on the surface of the sensors to acquire a raw image called an MSFA image. In the MSFA image, only one spectral band is available per pixel, the demosaicking process is necessary to estimate the multispectral image at full spatio-spectral resolution. Motivated by the success of single-sensor cameras capturing the image in a single exposure that use CFA filters, we performed a comparative study of a few recent color image demosaicking algorithms and experi…

Circolazione e sviluppo di un modello metodologico. La critica testuale delle fonti giuridiche romane fra Otto Gradenwitz e Salvatore Riccobono

2018

La ricerca delle interpolazioni, cominciata con la Scula culta, viene ripresa in Germania alla fine del XIX secolo. Fra quanti misero a punto un metodo storico-critico per lo studio delle fonti giuridiche romane va menzionato anche Gradenwitz, che – insieme ad altri studiosi tedeschi – sarebbe stato uno dei maestri di Riccobono. La prima produzione scientifica di Riccobono, che si riconosce nel nuovo indirizzo storico-critico affermatosi in Germania, si avvale dei metodi appresi dai maestri tedeschi. Lungo questo solco, tuttavia, comincia l’elaborazione di un metodo più raffinato, che distingue fra interpolazioni formali e interpolazioni sostanziali e recupera gradualmente altri strumenti d…

Sparse Image Representation by Directionlets

2010

Despite the success of the standard wavelet transform (WT) in image processing in recent years, the efficiency and sparsity of its representation are limited by the spatial symmetry and separability of its basis functions built in the horizontal and vertical directions. One-dimensional discontinuities in images (edges or contours), which are important elements in visual perception, intersect too many wavelet basis functions and lead to a non-sparse representation. To capture efficiently these elongated structures characterized by geometrical regularity along different directions (not only the horizontal and vertical), a more complex multidirectional (M-DIR) and asymmetric transform is requi…

A note on the Banach space of preregular maps

2011

The aim of this paper is to give simple proofs for Jeurnink's characterizations of preregular maps in terms of Θ-maps acting between Banach lattices. For Banach lattices E and F, we achieve our goal by considering the space Lβ(E, F) of all those linear maps T: E → F for which there exists a constant K such that {double pipe}Vn i=1 {pipe}Txi{pipe} ≤ K {double pipe}Vn i=1{pipe}xi for all finite sequences x1, ..., xn e{open}E. We show that, if Lβ(E; F), and the spaces L Θ (E; F) of Θ -map and Lpr(E; F) of preregular maps are respectively endowed with their canonical norms, then they are identical Banach spaces

Computational Aspects in Spaces of Bivariate Polynomial of w-Degree n

2005

Multivariate ideal interpolation schemes are deeply connected with H-bases. Both the definition of a H-basis and of an ideal interpolation space depend of the notion of degree used in the grading decomposition of the polynomial spaces. We studied, in the case of bivariate polynomials, a generalized degree, introduced by T. Sauer and named w-degree. This article give some theoretical results that allow us to construct algorithms for calculus of the dimension of the homogeneous spaces of bivariate polynomials of w – degree n. We implemented these algorithms in C++ language. The analysis of the results obtained, leads us to another theoretical conjecture which we proved in the end.

Guaranteed error bounds for a class of Picard-Lindelöf iteration methods

2013

We present a new version of the Picard-Lindelof method for ordinary dif- ¨ ferential equations (ODEs) supplied with guaranteed and explicitly computable upper bounds of an approximation error. The upper bounds are based on the Ostrowski estimates and the Banach fixed point theorem for contractive operators. The estimates derived in the paper take into account interpolation and integration errors and, therefore, provide objective information on the accuracy of computed approximations. peerReviewed

Banach spaces which are somewhat uniformly noncreasy

2003

AbstractWe consider a family of spaces wider than r-UNC spaces and we give some fixed point results in the setting of these spaces.