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The nonlinear Fourier transform (NFT) has recently gained significant attention in fiber optic communications and other engineering fields. Although several numerical algorithms for computing the NFT have been published, the design of…
In this work, we propose an innovative iterative direct sampling method to solve nonlinear elliptic inverse problems from a limited number of pairs of Cauchy data. It extends the original direct sampling method (DSM) by incorporating an…
We consider implementational aspects of the mixed finite element method for a special class of nonlinear problems. We establish the equivalence of the hybridized formulation of the mixed finite element method to a nonconforming finite…
Efficiently solving the continuous-time signal and discrete-time observation filtering problem for chaotic dynamical systems presents unique challenges in that the advected distribution between observations may encounter a separatrix…
By approximating posterior distributions with weighted samples, particle filters (PFs) provide an efficient mechanism for solving non-linear sequential state estimation problems. While the effectiveness of particle filters has been…
Iterative refinement -- start with a random guess, then iteratively improve the guess -- is a useful paradigm for representation learning because it offers a way to break symmetries among equally plausible explanations for the data. This…
This paper proposes a symbolic-numeric Bayesian filtering method for a class of discrete-time nonlinear stochastic systems to achieve high accuracy with a relatively small online computational cost. The proposed method is based on the…
We propose a successive one-sided Hodrick-Prescott (SOHP) filter from multiple time scale decomposition perspective to derive trend estimate for a time series. The idea is to apply the one-sided HP (OHP) filter recursively on the updated…
This paper introduces a modular, non-deep learning method for filtering and refining sparse correspondences in image matching. Assuming that motion flow within the scene can be approximated by local homography transformations, matches are…
In this paper has been considered probability-one global convergence of NFPH (Newton-Fixed Point Homotopy) algorithm for system of nonlinear equations and has been proposed a probability-one homotopy algorithm to solve a regularized…
We introduce the concept of homotopy iterators for performing polynomial homotopy continuation tasks in a memory efficient manner. The main idea is to push forward an iterator for the start solutions of a homotopy via the function which…
On an example of the open nonlinear electrodynamic system - transverse non-homogeneous, isotropic, nonlinear (a Kerr-like dielectric nonlinearity) dielectric layer, the algorithms of solution of the diffraction problem of a plane wave on…
Novel experimental modalities acquire spatially resolved velocity measurements for steady state and transient flows which are of interest for engineering and biological applications. One of the drawbacks of such high resolution velocity…
In the present article an endeavor is made to solve the variable order fractional diffusion equations using a powerful method viz., Homotopy Analysis method. It is demonstrated how the method can be used while solving approximately two…
In this paper we present an extension of standard iterative splitting schemes to multiple splitting schemes for solving higher order differential equations. We are motivated by dynamical systems, which occur in dynamics of the electrons in…
The underwater images usually suffers from non-uniform lighting, low contrast, blur and diminished colors. In this paper, we proposed an image based preprocessing technique to enhance the quality of the underwater images. The proposed…
We study the numerical solution of nonlinear partially observed optimal stopping problems. The system state is taken to be a multi-dimensional diffusion and drives the drift of the observation process, which is another multi-dimensional…
Particle Filter is an effective solution to track objects in video sequences in complex situations. Its key idea is to estimate the density over the possible states of the object using a weighted sample whose elements are called particles.…
This paper is concerned with differentiable resampling in the context of sequential Monte Carlo (e.g., particle filtering). Drawing on reparametrisation, we propose a new resampling method that is informative and instantly differentiable,…
In the paper we suggest the homotopy method for solving of the non linear evolution equation. This method consists of two steps. First is the analytical solution for the linearized version of the non-linear evolution deep in the saturation…