相关论文: H-infinity Optimal Approximation for Causal Spline…

The Numerical Recipes series of books are a useful resource, but all the algorithms they contain cannot be used within open-source projects. In this paper we develop drop-in alternatives to the two algorithms they present for cubic spline…

This paper presents a universal numerical scheme tailored for tackling linear integral, integro-differential, and both initial and boundary value problems of ordinary differential equations. The numerical scheme is readily adapted for…

This paper introduces a $H_\infty$-like methodology of coherent filtering for equalization of passive linear quantum systems to help mitigate degrading effects of quantum communication channels. For such systems, which include a wide range…

We present novel model reduction methods for rapid solution of parametrized nonlinear partial differential equations (PDEs) in real-time or many-query contexts. Our approach combines reduced basis (RB) space for rapidly convergent…

In this paper, the $\mathcal{H}_{2}$ optimal approximation of a $n_{y}\times{n_{u}}$ transfer function $\mathbf{G}(s)$ by a finite dimensional system $\hat{\mathbf{H}}_{d}(s)$ including input/output delays, is addressed. The underlying…

A common goal throughout science and engineering is to solve optimization problems constrained by computational models. However, in many cases a high-fidelity numerical emulation of systems cannot be optimized due to code complexity and…

This paper proposes an image interpolation algorithm exploiting sparse representation for natural images. It involves three main steps: (a) obtaining an initial estimate of the high resolution image using linear methods like FIR filtering,…

The Topological Signal Processing (TSP) framework has been recently developed to analyze signals defined over simplicial complexes, i.e. topological spaces represented by finite sets of elements that are closed under inclusion of subsets…

A numerical method is developed to solve linear semi-infinite programming problem (LSIP) in which the iterates produced by the algorithm are feasible for the original problem. This is achieved by constructing a sequence of standard linear…

In this paper, we investigate the optimal $\mathcal{H}_2$ model reduction problem for single-input single-output (SISO) continuous-time linear time-invariant (LTI) systems. A semi-definite relaxation (SDR) approach is proposed to determine…

This paper is concerned with the fuzzy $H_{\infty}$ filter design issue for nonlinear systems with time-varying delay. To overcome the shortcomings of the conventional methods with matched preconditions, the fuzzy $H_{\infty}$ filter to be…

Computing accurate splines of degree greater than three is still a challenging task in today's applications. In this type of interpolation, high-order derivatives are needed on the given mesh. As these derivatives are rarely known and are…

The primary focus of this paper is on designing an inexact first-order algorithm for solving constrained nonlinear optimization problems. By controlling the inexactness of the subproblem solution, we can significantly reduce the…

In simulation technology, computationally expensive objective functions are often replaced by cheap surrogates, which can be obtained by interpolation. Full grid interpolation methods suffer from the so-called curse of dimensionality,…

We consider the interpolation problem for a class of radial basis functions (RBFs) that includes the classical polyharmonic splines (PHS). We show that the inverse of the system matrix for this interpolation problem can be approximated at…

This paper introduces a quasi-interpolation operator for scalar- and vector-valued finite element spaces constructed on affine, shape-regular meshes with some continuity across mesh interfaces.This operator gives optimal estimates of the…

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…

The analysis of complex nonlinear systems is often carried out using simpler piecewise linear representations of them. A principled and practical technique is proposed to linearize and evaluate arbitrary continuous nonlinear functions using…

The purpose of this work is to introduce and analyze a numerical scheme to efficiently solve boundary value problems involving the spectral fractional Laplacian. The approach is based on a reformulation of the problem posed on a…

In this work, we introduce a novel numerical method for solving initial value problems associated with a given differential. Our approach utilizes a spline approximation of the theoretical solution alongside the integral formulation of the…