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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]

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]

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]