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A novel class of quasi-polynomials orthogonal with respect to the fractional integration operator has been developed in this paper. The related Gaussian quadrature formulas for numerical evaluation of fractional order integrals have also been proposed. By allowing the commensurate order of quasi-polynomials to vary independently of the integration order, a family of fractional quadrature formulas has been developed for each fractional integration order, including novel quadrature formulas for numerical approximation of classical, integer order integrals. A distinct feature of the proposed quadratures is high computational efficiency and flexibility, as will be demonstrated in the paper. As auxiliary results, the paper also presents methods for Lagrangian and Hermitean quasi-polynomial interpolation and Hermitean fractional quadratures. The development is illustrated by numerical examples. [ABSTRACT FROM AUTHOR]

A. Horn's problem concerns finding two self adjoint matrices, so that A , B , and A + B have prescribed spectrum. In this paper, we show how it connects to an interpolation problem for two variable real zero polynomials and a tracial moment problem. In addition, we outline an algorithm to construct a pair ( A , B ) . [ABSTRACT FROM AUTHOR]

The aim of this paper is a construction of parametric polynomial interpolants of a circular arc possessing maximal geometric smoothness. Two boundary points of a circular arc are interpolated together with higher order geometric data. Construction of interpolants is done via a complex factorization of the implicit unit circle equation. The problem is reduced to solving only one nonlinear equation determined by a monotone function and the existence of the solution is proven for any degree of the interpolating polynomial. Precise starting points for the Newton–Raphson type iteration methods are provided and the best solutions are then given in a closed form. Interpolation by parametric polynomials of degree up to six is discussed in detail and numerical examples confirming theoretical results are included. [ABSTRACT FROM AUTHOR]

Interpolation operators are important for many applications in scientific computing. During numerical simulations and especially in the context of anisotropic mesh adaptation, with highly stretched elements, the interpolation step is crucial. However, it reduces conservation of important physical quantities and leads to errors that spoil the solution accuracy. In this paper we present a globally conservative method suitable for both interpolations on unstructured fixed and adaptive anisotropic meshes. It consists in combining an a posteriori error estimator that minimizes the interpolation error of the finite element solution followed by an interpolation with restrictions method that conserves physical properties of the field being interpolated. Several numerical examples, in 2D and 3D, are presented and validated to illustrate the efficiency of the approach. [ABSTRACT FROM AUTHOR]

Simultaneous source shooting is a modern marine acquisition technology that accelerates field acquisition tremendously. However, we need to carefully remove the spike-like noise in the recorded seismic data, the process of which is called deblending. Considering the field obstacles, the recorded data may also contain missing traces. In this paper, we propose a very efficient way to simultaneously remove the spike-like noise to separate simultaneous sources and fill the data gaps in the recorded data. We propose to apply structure-oriented median and mean filters to reject the spike-like noise and restore the missing data. The commonly used median and mean filters guarantee the efficiency and convenience of the proposed algorithm framework. We use a robust slope estimation method to calculate the local slope of the structure patterns in the seismic data. Both synthetic and field data examples demonstrate the successful performance of the proposed algorithm. When compared with the state-of-the-art FK transform based projection onto convex sets (POCS) method, the presented method can obtain better performance with much less computational cost. [ABSTRACT FROM AUTHOR]

We present a simple and effective Chebyshev polynomial scheme (CPS) combined with the method of fundamental solutions (MFS) and the equilibrated collocation Trefftz method for the numerical solutions of inhomogeneous elliptic partial differential equations (PDEs). In this paper, CPS is applied in a two-step approach. First, Chebyshev polynomials are used to approximate a particular solution of a PDE. Chebyshev nodes which are the roots of Chebyshev polynomials are used in the polynomial interpolation due to its spectral convergence. Then the resulting homogeneous equation is solved by boundary type methods including the MFS and the equilibrated collocation Trefftz method. Numerical results for problems on various irregular domains show that our proposed scheme is highly accurate and efficient. [ABSTRACT FROM AUTHOR]

Image resolution enhancement or super-resolution (SR) problem generates a high resolution (HR) image from one or a set of low resolution (LR) images. In the past two decades, a wide variety of resolution enhancement algorithms have been proposed. These methods are confined to small scaling factors. This paper presents a novel single image resolution enhancement algorithm in wavelet domain which operates at high scaling factors. First, we perform subband decomposition on the input LR image by using discrete wavelet transform (DWT). It decomposes the LR image into different frequency subbands namely low-low (LL), low-high (LH), high-low (HL) and high-high (HH). In parallel we apply sparse representation based interpolation method on the LR image. Next, we process the three high frequency subbands in wavelet domain by applying bicubic interpolation. Finally, the interpolated high frequency subbands in addition to the sparse recovered solution are combined to produce a HR image using inverse discrete wavelet transform (IDWT). Experiments on different LR test images demonstrate that our approach produces relatively less artifacts compared to the existing methods. [ABSTRACT FROM AUTHOR]

Video frame-rate up-conversion (FRUC) is one of the common temporal-domain operations. From the earlier frame repetition and linear interpolation, FRUC has been developed to motion compensated frame interpolation (MCFI), which effectively overcomes the temporal jerkiness and ghosting shadows. In a broad sense, FRUC can be regarded as a video forgery operation. By experiments, it is observed that FRUC still leads to edge dis-continuity or over-smoothing artifacts around object boundaries. In this paper, an edge-intensity based passive forensics approach is proposed to detect the possible FRUC operation in candidate video. After computing the edge intensities of every frame, Kaufman adaptive moving average (KAMA) is exploited to define an adaptive threshold to distinguish the interpolating frames by FRUC from the original frames. Moreover, the original frame-rate of up-converted video can be inferred. Experimental results show that the proposed approach is not only effective for simple frame repetition and linear interpolation, but also valid for advanced FRUC techniques such as MCFI. The detection accuracy is up to 94.5% on average. Its computation is simple as well. [ABSTRACT FROM AUTHOR]

In this paper we present an algorithm for monotone interpolation of monotone data on a rectangular mesh by piecewise bicubic functions. Carlton and Fritsch (1985) develop conditions on the Hermite derivatives that are sufficient for such a function to be monotone. Here we extend our results of Aràndiga (2013) to obtain nonlinear approximations to the first partial and first mixed partial derivatives at the mesh points that allow us to construct a monotone piecewise bicubic interpolants. We analyze its order of approximation and present some numerical experiments. [ABSTRACT FROM AUTHOR]

In this paper we propose two fast localized radial basis function fitting algorithms for solving large-scale scattered data interpolation problems. For each given point in the given data set, a local influence domain containing a small number of nearest neighboring points is established and a global interpolation is performed within this restricted domain. A sparse matrix is formulated based on the global interpolation in these local influence domains. The proposed methods have achieved both low computational cost and minimal memory storage. In comparison with the compactly supported radial basis functions, the proposed fitting algorithms are highly accurate. The numerical examples have provided strong evidence that the two proposed algorithms are indeed highly efficient and accurate. In the two proposed algorithms, we have successfully solved a large-scale interpolation problem with 225,000 interpolation points in two dimensional space. [ABSTRACT FROM AUTHOR]

We construct Weakly Admissible polynomial Meshes (WAMs) on circular sections, such as symmetric and asymmetric circular sectors, circular segments, zones, lenses and lunes. The construction resorts to recent results on subperiodic trigonometric interpolation. The paper is accompanied by a software package to perform polynomial fitting and interpolation at discrete extremal sets on such regions. [ABSTRACT FROM AUTHOR]

Using reversible data hiding (RDH) we can hide our secret data into a cover image and the receiver can restore both the secret data and the original image. It has wide application in medical imagery, military imagery where no distortion of original cover is allowed. Hong and Chen proposed a RDH scheme based on interpolation and histogram shifting. In their scheme reference pixels are not used for data embedding which leads to low capacity. Huang et al. modified this scheme and proposed a high capacity RDH scheme in which prediction errors are used for data embedding. In this paper we propose a further modification to the scheme of Huang et al. based on directional interpolation. Directional interpolation yields a better approximation to the original pixel which improves the capacity of embedding. The effectiveness of the proposed scheme is tested using standard test images and the proposed scheme gives better results in terms of embedding capacity and visual quality compared to Huang et al. scheme. [ABSTRACT FROM AUTHOR]

This paper presents a method to design servo controllers for flexible ball screw drives with time-varying dynamics, which are mainly due to the time-varying table position and the workpiece mass. A gain-scheduled H∞ loop shaping controller is designed to achieve high tracking performance against the dynamic variations. H∞ loop shaping design procedure incorporates open loop shaping by a set of compensators to obtain performance/robust stability tradeoffs. The interpolating gain-scheduled controller is obtained by interpolating the state space model of the linear time-invariant (LTI) controllers estimated for fixed values of the scheduling parameters and a linear least squares problem can be solved. The proposed controller has been compared with P/PI with velocity and acceleration feedforward and adaptive backstepping sliding mode control experimentally. The experimental results indicate that the tracking performance has been improved and the robustness for time-varying dynamics has been achieved with the proposed scheme. [ABSTRACT FROM AUTHOR]