Related papers: Recent Progress in Optimization of Multiband Elect…
The best uniform rational approximation of the \emph{sign} function on two intervals separated by zero was explicitly solved by E.I. Zolotar\"ev in 1877. This optimization problem is the initial step in the staircase of the so called…
A new optimized band-pass filter for wavelengths is proposed to increase the optical temporal coherence of thermal light. The choice of parameters for this filter is based on solving an optimization problem for finding the most intensely…
We propose and analyze new numerical methods to evaluate fractional norms and apply fractional powers of elliptic operators. By means of a reduced basis method, we project to a small dimensional subspace where explicit diagonalization via…
A new technique for reliably identifying point sources in millimeter/sub-millimeter wavelength maps is presented. This method accounts for the frequency dependence of noise in the Fourier domain as well as non-uniformities in the coverage…
Whenever we use devices to take measurements, calibration is indispensable. While the purpose of calibration is to reduce bias and uncertainty in the measurements, it can be quite difficult, expensive, and sometimes even impossible to…
The Einstein-Podolsky-Rosen~(EPR) model is an analogous model of the anti-ferromagnetic Heisenberg model or the equivalent quantum maximum-cut problem, proposed by R. King two years ago. Adjacent qubits in the model prefer symmetric…
This paper studies a nonlinear filtering problem over an infinite time interval. The signal to be estimated is driven by a stochastic partial differential equation involves unknown parameters. Based on discrete observation, strongly…
We are concerned with the numerical integration of functions from the Sobolev space $H^{r,\text{mix}}([0,1]^d)$ of dominating mixed smoothness $r\in\mathbb{N}$ over the $d$-dimensional unit cube. In 1976, K. K. Frolov introduced a…
The need to Fourier transform data sets with irregular sampling is shared by various domains of science. This is the case for example in astronomy or sismology. Iterative methods have been developed that allow to reach approximate…
The two-parameter Mittag-Leffler function $E_{\alpha, \beta}$ is of fundamental importance in fractional calculus. It appears frequently in the solutions of fractional differential and integral equations. Nonetheless, this vital function is…
In this paper we introduce a common problem in electronic measurements and electrical engineering: finding the first root from the left of an equation in the presence of some initial conditions. We present examples of electrotechnical…
The design of broad-band polarimeters with high performance is challenging due to the wavelength dependence of optical components. An efficient Genetic Algorithm (GA) computer code was recently developed in order to design and re-optimize…
We propose and analyze a new discretization technique for a linear-quadratic optimal control problem involving the fractional powers of a symmetric and uniformly elliptic second oder operator; control constraints are considered. Since these…
The Ensemble Kalman filter (EnKF) was introduced by Evensen in 1994 [10] as a novel method for data assimilation: state estimation for noisily observed time-dependent problems. Since that time it has had enormous impact in many application…
We present an efficient implementation of Wiener filtering of real-space linear field and optimal quadratic estimator of its power spectrum Band-powers. We first recast the field reconstruction into an optimization problem, which we solve…
The goal of this paper is to design compact support basis spline functions that best approximate a given filter (e.g., an ideal Lowpass filter). The optimum function is found by minimizing the least square problem ($\ell$2 norm of the…
We consider the problem of fusing an arbitrary number of multiband, i.e., panchromatic, multispectral, or hyperspectral, images belonging to the same scene. We use the well-known forward observation and linear mixture models with Gaussian…
Real-time identification of electrical equivalent circuit models is a critical requirement in many practical systems, such as batteries and electric motors. Significant work has been done in the past developing different types of algorithms…
We consider the problem of approximating optimal in the Minimum Mean Squared Error (MMSE) sense nonlinear filters in a discrete time setting, exploiting properties of stochastically convergent state process approximations. More…
This paper is concerned with the linear/nonlinear Kalman-like filtering problem under binary sensors. Since innovation represents new information in the sensor measurement and serves to correct the prediction for the Kalman-like filter…