Search

Copyright of Przegląd Elektrotechniczny is the property of Przeglad Elektrotechniczny and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

This work focuses on weighted Lagrange interpolation on an unbounded domain and analyzes the Lebesgue constant for a sequence of weighted Leja points. The standard Leja points are a nested sequence of points defined on a compact subset of the real line and can be extended to unbounded domains with the introduction of a weight function |$w:\mathbb{R}\rightarrow [0,1]$|⁠. Due to a simple recursive formulation in one dimension, such abscissas provide a foundation for high-dimensional approximation methods such as sparse grid collocation, deterministic least squares and compressed sensing. Just as in the unweighted case of interpolation on a compact domain, we use results from potential theory to prove that the Lebesgue constant for the Leja points grows subexponentially with the number of interpolation nodes. [ABSTRACT FROM AUTHOR]

Copyright of Coal Science & Technology (0253-2336) is the property of Coal Science & Technology and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

In this paper we investigate the numerical solution of Cauchy bisingular integral equations of the first kind on the square. We propose two different methods based on a global polynomial approximation of the unknown solution. The first one is a discrete collocation method applied to the original equation and then is a "direct" method. The second one is an "indirect" procedure of discrete collocation-type since we act on the so-called regularized Fredholm equation. In both cases, the convergence and the stability of the method is proved in suitable weighted spaces of functions, and the well conditioning of the linear system is showed. In order to illustrate the efficiency of the proposed procedures, some numerical tests are given. [ABSTRACT FROM AUTHOR]

Abstract Pulse height measurement is one of the most important step in ionizing radiation spectroscopy. However, the conventional analog and digital peak detection methods may be limited due to their high complexity and cost. In this work, a simple and novel mathematical approach based on Lagrange interpolation has been developed to precisely extract pulse height from a sequence of samples recorded at a low rate (2 MS/s). This has been implemented in an ARM-based micro-controller to construct a full functionality multi-channel analyzer. The results showed that the multi-channel analyzer has a very good integral linearity response (<0.1 %) and reasonable full width at half maximum (3.4 channels) over the entire analog-to- digital converter range. The pulse height spectrum, which was recorded using an HPGe detector, demonstrated high performance of multi-channel analyzer in the spectroscopy experiments, leading to a resolution of about 0.2 % at 1332.5 keV. [ABSTRACT FROM AUTHOR]

Dispersion relation reflects the dependence of wave frequency on its wave vector when the wave passes through certain materials. It demonstrates the properties of this material and thus it is critical. However, dispersion relation reconstruction is very time-consuming and expensive. To address this bottleneck, we propose in this paper an efficient dispersion relation reconstruction scheme based on global polynomial interpolation for the approximation of two-dimensional photonic band functions. Our method relies on the fact that the band functions are piecewise analytic with respect to the wave vector in the Brillouin zone. We utilize suitable sampling points in the Brillouin zone at which we solve the eigenvalue problem involved in the band function calculation, and then employ Lagrange interpolation to approximate the band functions on the whole Brillouin zone. Numerical results show that our proposed method can significantly improve the computational efficiency. [ABSTRACT FROM AUTHOR]

The aim of this paper is to study the Lagrange interpolation on the unit circle taking only into account the separation properties of the nodal points. The novelty of this paper is that we do not consider nodal systems connected with orthogonal or paraorthogonal polynomials, which is an interesting approach because in practical applications this connection may not exist. A detailed study of the properties satisfied by the nodal system and the corresponding nodal polynomial is presented. We obtain the relevant results of the convergence related to the process for continuous smooth functions as well as the rate of convergence. Analogous results for interpolation on the bounded interval are deduced and finally some numerical examples are presented.

In numerous implementations of modern telecommunications and digital audio systems there is a need for sampling rate change of the system input signal. When the relation between signal input and output sampling frequencies is a fraction of two large integer numbers, Lagrange interpolation based on Farrow structure can be used for the efficient realization of the resample block. This paper highlights efficient realization and estimation of necessary resources for polynomial cubic Lagrange interpolation in the case of the demand for the signal sampling rate change with the factor 160/147 on Field-Programmable Gate Array architecture (FPGA). [Projekat Ministarstva nauke Republike Srbije, br. TR-32023 i br. TR-32028]

In this article, we propose an efficient approach for inverting computationally expensive cumulative distribution functions. A collocation method, called the Stochastic Collocation Monte Carlo sampler (SCMC sampler), within a polynomial chaos expansion framework, allows us the generation of any number of Monte Carlo samples based on only a few inversions of the original distribution plus independent samples from a standard normal variable.We will show that with this path-independent collocation approach the exact simulation of the Heston stochastic volatility model, as proposed in Broadie and Kaya [Oper. Res., 2006, 54, 217-231], can be performed efficiently and accurately. We also show how to efficiently generate samples from the squared Bessel process and perform the exact simulation of the SABR model. [ABSTRACT FROM AUTHOR]

The aim of this paper is to construct an interpolatory polynomial (0,1;0) with special types of boundary conditions. Here the nodes ... and ... are the roots of P(k)n(x) and P(k+1)n-1(x) respectively, where P(k)n(x is the Ultraspherical polynomial of degree n. In this paper, we prove, existence, explicit representation and order of convergence of the interpolatory polynomial. [ABSTRACT FROM AUTHOR]

Abstract A low-complexity post-processing algorithm to estimate and compensate for timing skew error in a four-channel time-interleaved analog to digital converter (TIADC) is presented in this paper, together with its hardware implementation. The Lagrange interpolator is used as the reconstruction filter which alleviates online interpolator redesign by using a simplified representation of coefficients. Simulation results show that the proposed algorithm can suppress error tones for input signal frequency from 0 to 0.4 f s. The proposed structure has, at least, 41% reduction in the number of required multipliers. Implementation of the algorithm, for a four-channel 10-bit TIADC, show that, for a 0.4 f s input signal frequency, the Signal to Noise and Distortion Ratio (SNDR) and Spurious-Free Dynamic Range (SFDR) are improved 31.26 dB and 43.7 dB, respectively. Our proposed approximation technique does not degrade the performance of system, resulting in the same SNDR and SFDR as the exact coefficient values. In addition, the proposed structure provides an acceptable performance in the presence of wideband signals. [ABSTRACT FROM AUTHOR]

In this paper, a numerical solution of fractional-order time-varying delayed differential systems using Lagrange interpolation is investigated. Based on Lagrange interpolation method, the Adams-Bashforth-Moulton algorithm has been extended to solve fractional-order time-varying delayed differential systems. Furthermore, a detailed error analysis of this algorithm is presented. A fractional-order time-varying delayed Hopfield neural network as numerical example is given. In addition, the different parameters in the fractional-order time-varying delayed neural network are considered. Finally, some simple and direct numerical methods which are compared with Lagrange interpolation method in the fractional-order time-varying delayed neural network are discussed. The example with numerical simulation clearly illustrated that the present method is reliable. [ABSTRACT FROM AUTHOR]

In this paper, an iterative finite element model updating method in structural dynamics is proposed. This uses information matrices and element connectivity matrices to reconstruct the corrected model by reproducing the frequency response at measured degrees of freedom. Indicators have been proposed to quantify the mismodelling errors based on a development in Lagrange matrix interpolation. When applied on simulated truss structures, the model gives satisfactory results by detecting and quantifying the defaults of the initial model. [ABSTRACT FROM AUTHOR]

Highlights • A high-order simplified thermal lattice Boltzmann method (HSTLBM) is proposed. • HSTLBM incorporates the high-order interpolation into formulations of STLBM. • Parametric study is given to decide optimal parameters in application. • Overall the third-order of accuracy can be achieved by HSTLBM. • HSTLBM is more efficient than STLBM when giving comparable results. Abstract A high-order simplified thermal lattice Boltzmann method (HSTLBM) is developed in this paper for accurate and efficient simulation of incompressible thermal flows. The derivation of HSTLBM stems from the recently developed simplified thermal lattice Boltzmann method (STLBM) and incorporates high-order interpolation algorithms, which reflects an effective combination of local second-order reconstruction and global high-order scheme. By introducing virtual streaming nodes, HSTLBM decouples the streaming distance from the mesh spacing and then correlates them through high-order interpolation scheme. Delicate parametric studies indicate that adopting 5-point Lagrange interpolation and setting the streaming distance as 0.2 times of the mesh spacing could give optimal results which balances computational accuracy, stability, and efficiency well; and third-order of global accuracy can be achieved. HSTLBM inherits various merits of STLBM, especially its nice numerical stability. As a result, HSTLBM can give accurate and stable solutions on coarser meshes for problems at high Reynolds/Rayleigh numbers. Higher efficiency and lower memory cost can thus be expected. A series of benchmark tests are provided for comprehensive evaluation of HSTLBM in modelling two- and three-dimensional problems and on uniform/non-uniform meshes. [ABSTRACT FROM AUTHOR]

The paper is devoted to studying a Pál-type interpolation problem on the roots of Ultraspherical polynomials of degree n-1 with parameter k+1 on the closed interval -1 to 1. The aim of this paper is to find a unique interpolatory polynomial of degree at most m equal to 2n+2k+3 satisfying the interpolatory conditions that is, function values of the polynomial of degree m at the zeros of the function values of the ultraspherical polynomials and the first derivative values of the polynomial of degree m at the zeros of the first derivative values of the ultraspherical polynomials. We will use the special type of Hermite-boundary conditions at the end points of interval -1 to 1, which are defined by, the lth derivative of the polynomial of degree m at the zeros of the boundary point 1, where l goes from 0 to k+1 and the lth derivative of the polynomial of degree m at the zeros of the boundary point -1, where l goes from 0 to k+2. Further, we will prove the existence,uniqueness and explicit representation of the interpolatory polynomial. For, the prove of order of convergence of the interpolatory polynomial, we will prove the order of convergence of the first derivative of the first kind fundamental polynomials and order of convergence of the first derivative of the second kind fundamental polynomials. [ABSTRACT FROM AUTHOR]

Copyright of Hydrographic Surveying & Charting / Haiyang Cehui is the property of Hydrographic Surveying & Charting Editorial Board and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

To simplify the key management processes, data transmission protocols for vehicular ad-hoc networks typically use identity-based cryptography for protecting the transmitted data. However, current identity-based data transmission protocols are mainly based on the bilinear map technique, which requires high computation costs on vehicles and road-side units, resulting in high latency. At the same time, to provide location privacy protection, data transmission protocols typically use pseudonyms instead of vehicles’ real identities, resulting in complicated pseudonym management processes. To address these issues, we present a novel identity-based data transmission protocol called EIBDT. Similar to the protocols of this field, EIBDT can provide integrity and confidentiality protections for the transmitted data. However, compared to other well-known approaches, EIBDT uses Lagrange interpolation instead of bilinear map for integrity protection, which employs only a few modular exponentiation operations. Since modular exponentiation is much more efficient than bilinear pairing, EIBDT can reduce the computation costs of vehicles and RSUs significantly. Moreover, for location privacy protection, EIBDT encrypts real identities of vehicles using an algebraic-signature-and-identity-based algorithm which is highly efficient. Therefore, the complicated pseudonym management process is avoided and the computation costs are reduced. Experimental results show that the proposed protocol is feasible for real applications. [ABSTRACT FROM AUTHOR]

In the calculation of water application in mobile sprinkler machines, various interpolation and fitting methods have been applied to describe the radial water distribution pattern of sprinklers. However, few studies have been carried out related to the accuracy and applicability of these methods. In this study, the radial water distribution curves were obtained by adopting cubic spline interpolation, Lagrange interpolation, least-squares polynomial fitting, and simplified geometric curves, respectively. The mobile spraying water distribution and spray uniformity coefficients were calculated based on these radial water distribution curves. The results indicated that the cubic spline curve and the least-squares polynomial fitting reflected the water distribution characteristics accurately, with the maximum deviation between the calculated values and the measured values being less than 10%. The existence of Runge's phenomenon in the Lagrange interpolation method led to sharp oscillations at both ends of the radial water distribution curve, resulting in large inconsistencies between the calculated value and the measured value of irrigation depth. The curves of the simplified geometric method were too simple to accurately characterise water application. Although the cubic spline interpolation showed high calculation accuracy, the large number of interpolation polynomial coefficients hinder its practical application. The least-squares based polynomial fitting curve showed both sufficient calculation accuracy and simple expression form, while the number of polynomial coefficients is only one more than the degree of polynomial. The recommended degree of polynomial fitting was six in this study. Highlights • A variety of methods to obtain sprinkler radial water distribution was analyzed. • For methods with high calculation accuracy, the ease of application was discussed. • A simple and feasible radial water distribution approach method was proposed. [ABSTRACT FROM AUTHOR]

Copyright of Transactions of Beijing Institute of Technology is the property of Beijing University of Technology and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The micro-electro-mechanical inertial measurement unit (MEMS-IMU) has gradually become a research hotspot in the field of mid-low navigation, because of its advantages of low cost, small size, light weight, and low power consumption (CSWap). However, the performance of MEMS-IMUs can be severely degraded when subjected to temperature changes, especially gyroscopes. In order to make full use of the navigation accuracy, this paper proposes an optimized error calibration method for a tri-axial MEMS gyroscope across a full temperature range. First of all, a calibration error model is established which includes package misalignment error, sensor-to-sensor non-orthogonality error, scale factor, and bias. Then, a simple three-position positive/reversed test is undertaken by carrying out a single-axis temperature-controlled turntable at different reference temperature points. Lastly, the error compensation vector is obtained using the least squares method to establish an error matrix. It is worth mentioning that the error compensation vector at a known temperature point can be calculated through Lagrange interpolation; then, the outputs of the tri-axial MEMS gyroscope can be well compensated, eliminating the need for a recalibration step. The experimental results confirm the effectiveness of the proposed method, which is feasible and operational in engineering applications, and has a certain reference value. [ABSTRACT FROM AUTHOR]

Secret image sharing (SIS) is a technique to decompose a secret image into multiple shadows distributed to the corresponding participants. Only qualified subsets of the shadows can reveal the secret image. Usually all shadows have the same importance. However, in some application scenario, some shadows are accorded with the special privilege due to the status or importance of the corresponding participants. A ( t , k , n ) essential secret image sharing (ESIS) scheme share a secret image into n shadows including t essential shadows and n – t non-essential shadows. A qualified subset of the shadows should contain at least k shadows including all t essential shadows. In this paper, we propose a construction method of ( t , k , n ) essential secret image sharing (ESIS) scheme. In our scheme, all shadows have the size 1/ k times of the secret image. It also resolves the problems in the previous ESIS schemes, such as different shadow sizes, concatenation of sub-shadows, using multiple SIS schemes and so on. Theoretical analyses and experimental results show that the proposed scheme is secure and effective. [ABSTRACT FROM AUTHOR]

This paper presents a developed predictor formulation for performing the time-series power-flow simulation of balanced and unbalanced distribution systems. The developed technique uses the changes in reactive and active powers of loads during the 24 hr in order to predict the updated voltage magnitudes and phase angles, respectively. The Lagrange linear interpolation is used as a predictor approach in the developed formulation. The developed technique is compared with the traditional technique that uses the previous solution as predictor values for the next solution. The conventional and developed techniques are implemented into forward/backward sweep for the three-phase radial distribution power-flow algorithm. The iterations number and computation time of the power-flow algorithm are significantly reduced in the case of using the developed technique compared with the previous solution technique. To prove its effectiveness, the developed technique is adopted for IEEE test systems, such as the radial balanced 69-node and unbalanced IEEE 123-node feeder. All calculations are performed using C++ programming. [ABSTRACT FROM AUTHOR]

In this paper, we are concerned with stability of numerical methods for linear neutral systems with multiple delays. Delay-dependent stability of Runge-Kutta methods is investigated, i. e., for delay-dependently stable systems, we ask what conditions must be imposed on the Runge-Kutta methods in order that the numerical solutions display stability property analogous to that displayed by the exact solutions. By means of Lagrange interpolation, Runge-Kutta methods can be applied to neutral differential systems with multiple delays. Based on the argument principle, sufficient conditions for delay-dependent stability of Runge-Kutta methods combined with Lagrange interpolation are presented. Numerical examples are given to illustrate the main results. [ABSTRACT FROM AUTHOR]

In this paper, using the piecewise linear and quadratic Lagrange interpolation functions, we propose a novel numerical approximate method for the Caputo fractional derivative. For the obtained explicit recursion formula, the truncation error is investigated, which shows the involved convergence order isO(τ3−β) withβ∈(0,1). As an application, we use this proposed numerical approximation to solve the time fractional diffusion equations by the barycentric rational interpolations in space. The resultant systems of algebraic equations, truncation error, convergence, and stability are analyzed. Theoretical analysis and numerical examples show this constructed method enjoys accuracy of, wheredis the degree of the rational polynomial. [ABSTRACT FROM AUTHOR]

Copyright of Chinese Journal of Liquid Crystal & Displays is the property of Chinese Journal of Liquid Crystal & Displays and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

In this paper, a new reversible data hiding scheme has been proposed using lagrange’s interpolating polynomial on interpolated sub-sampled images. First, we generate sub-sampled images from original image and enlarge its size using image interpolation. Now, we convert secret message using lagrange interpolating polynomial and generate new secret message. The new secret message is divided and stored within interleaved pixel of each interpolated sub-sampled images. At the receiver end, new secret message is extracted from interleaved pixel of each sub-sampled stego images and then lagrange’s interpolation is applied to generate original secret message. The security has been enhanced due to the distributive nature of hidden data within multiple images. The original pixels are not effected during data embedding which assure reversibility. The proposed scheme provides average embedding capacity with good visual quality measured by peak signal to noise ratio (PSNR) which is greater than 50 dB. It is observed that the proposed scheme provides better performance than other existing data hiding schemes in terms of data embedding capacity, visual quality and security. We have analyzed our stego images through RS analysis, calculate relative entropy, standard deviation and correlation coefficient of original and stego image to show the robustness under various steganographic attacks. [ABSTRACT FROM AUTHOR]

In an image secret sharing scheme (ISSS), two main categories are discussed. One is the polynomial-style image secret sharing scheme (PISSS), and the other is the visual secret sharing (VSS). It is interesting to combine the main properties of these two schemes. When the encoded secret images are received, we can decode them by combining these two schemes’ properties, utilizing the VSS property to seek the secret immediately by human visual system (HVS) and the PISSS property to recover the secret perfectly with a decoding machine. This paper combines PISSS and random grids-based VSS to remove all the drawbacks existing in the previous works including 1) distortion by compressing a secret image, 2) non-perfect reconstructed image, 3) distortion of pixel expansion, and 4) size-reduced halftone image. The experimental results demonstrate the proposed scheme does work well. [ABSTRACT FROM AUTHOR]

The Lebesgue constant is a measure for the stability of the Lagrange interpolation. The decomposition of the Lagrange interpolation operator in their even and odd parts with respect to the last variable can be used to find a relation between the Lebesgue constant for a space of polynomials and the corresponding Lebesgue constants for subspaces of even and odd polynomials. It is shown that such a decomposition preserves the stability properties of the Lagrange interpolation operator. We use the Lebesgue functions to provide pointwise quantitative measures of the stability properties and illustrate with examples the behaviour in simple cases. [ABSTRACT FROM AUTHOR]

Based on the interpolation of the Lagrange series and the Finite Block Method (FBM), the formulations of the Boundary Node Petrov–Galerkin Method (BNPGM) are presented in the weak form in this paper and their applications are demonstrated to the elasticity of functionally graded materials, subjected to static and dynamic loads. By introducing the mapping technique, a block of quadratic type is transformed from the Cartesian coordinate to the normalized coordinate with 8 seeds for two-dimensional problems. The first-order partial differential matrices of boundary nodes are obtained in terms of the nodal values of the boundary node, which can be utilized to determine the tractions on the boundary. Time-dependent partial differential equations are analyzed in the Laplace transformed domain and the Durbin’s inversion method is applied to determine the physical values in the time domain. Illustrative numerical examples are given and comparison has been made with the analytical solutions, the Boundary Element Method (BEM) and the Finite Element Method (FEM). [ABSTRACT FROM AUTHOR]