Related papers: Reduced projection method for photonic moir\'e lat…

We represent low dimensional quantum mechanical Hamiltonians by moderately sized finite matrices that reproduce the lowest O(10) boundstate energies and wave functions to machine precision. The method extends also to Hamiltonians that are…

We construct a local in time, exponentially decaying solution of the one-dimensional variable coefficient Schrodinger equation by solving a nonstandard boundary value problem. A main ingredient in the proof is a new commutator estimate…

We study the spectral properties of Schr\"{o}dinger operators on perturbed lattices. We shall prove the non-existence or the discreteness of embedded eigenvalues, the limiting absorption principle for the resolvent, construct a spectral…

Higher spatial resolution and larger imaging scene are always the goals pursued by advanced space-borne SAR system.High resolution and wide swath SAR imaging can provide more information about the illuminated scene of interest on one…

Using Fermat's least optical path principle the family of ray-trajectories through a special but common type of a gradient refractive index lens, n(r)=n_0+\Delta n R/r, is solved analytically. The solution, i.e. the ray-equation r(phi), is…

In this work we consider an iterative method for solving the quasi-convex feasibility problem. We firstly introduce the so-called star subgradient projection operator and present some useful properties. We subsequently obtain a convergence…

Fourier ptychographic microscopy enables gigapixel-scale imaging, with both large field-of-view and high resolution. Using a set of low-resolution images that are recorded under varying illumination angles, the goal is to computationally…

Image projection through scattering media has applications ranging from light delivery through multimode fiber to near-eye displays. Conventional methods utilize the transmission matrix (TM) measured by interfering with a reference beam.…

This paper presents a methodology that enables projection-based model reduction for black-box high-fidelity models such as commercial CFD codes. The methodology specifically addresses the situation where the high-fidelity model may be a…

We generate experimentally different types of two-dimensional self-trapped photonic lattices in a photorefractive medium and analyze the induced refractive index change using two different methods. One method gives the first experimental…

We introduce a new algorithm to solve a regularized spatial-spectral image estimation problem. Our approach is based on the linearized alternating directions method of multipliers (LADMM), which is a variation of the popular ADMM algorithm.…

We present a subgradient method for minimizing non-smooth, non-Lipschitz convex optimization problems. The only structure assumed is that a strictly feasible point is known. We extend the work of Renegar [5] by taking a different…

Due to quasicrystals having long-range orientational order but without translational symmetry, traditional numerical methods usually suffer when applied as is. In the past decade, the projection method has emerged as a prominent solver for…

In many modern imaging applications the desire to reconstruct high resolution images, coupled with the abundance of data from acquisition using ultra-fast detectors, have led to new challenges in image reconstruction. A main challenge is…

Recently, an open geometry Fourier modal method based on a new combination of an open boundary condition and a non-uniform $k$-space discretization was introduced for rotationally symmetric structures providing a more efficient approach for…

This paper investigates projection-free algorithms for stochastic constrained multi-level optimization. In this context, the objective function is a nested composition of several smooth functions, and the decision set is closed and convex.…

Random projection (RP) is a classical technique for reducing storage and computational costs. We analyze RP-based approximations of convex programs, in which the original optimization problem is approximated by the solution of a…

This paper is concerned with the Taylor-reduced basis method (Taylor-RBM) for the efficient approximation of eigenspaces of large scale parametric Hermitian matrices. The Taylor-RBM is a local model order reduction method, which constructs…

We present a new method for solving the Schrodinger equation using the Lossless Transmission Line Model (LTL). The LTL model although extensively used in fiber optics and optical fiber design, it has not yet found application in solid state…

A major challenge in single particle reconstruction methods using cryo-electron microscopy is to attain a resolution sufficient to interpret fine details in three-dimensional (3D) macromolecular structures. Obtaining high resolution 3D…