The phase-retrieval problem, fundamental in applied physics and engineering, addresses the question of how to determine the phase of a complex-valued function from modulus data and additional a priori information. Recently we identified two important methods for phase retrieval, namely, Fienup's basic input-output and hybrid input-output (HIO) algorithms, with classical convex projection method...

This is the second of a series of papers on the subject of projection methods for viscous incompressible flow calculations. The purpose of the present paper is to explain why the accuracy of the velocity approximation is not affected by (1) the numerical boundary layers in the approximation of pressure and the intermediate velocity field, and (2) the non-commutativity of the projection operator...

We study the cohomology and hence K-theory of the aperiodic tilings formed by the so called ‘cut and project’ method, i.e., patterns in d dimensional Euclidean space which arise as sections of higher dimensional, periodic structures. They form one of the key families of patterns used in quasicrystal physics, where their topological invariants carry quantum mechanical information. Our work devel...

Isotop is a new neural method for nonlinear projection of high-dimensional data. Isotop builds the mapping between the data space and a projection space by means of topology preservation. Actually, the topology of the data to be projected is approximated by the use of neighborhoods between the neural units. Isotop is provided with a piecewise linear interpolator for the projection of generaliza...

In this paper, we propose a method for finding certain eigenvalues of a generalized eigenvalue problem that lie in a given domain of the complex plane. The proposed method projects the matrix pencil onto a subspace associated with the eigenvalues that are located in the domain via numerical integration. The projection produces a small pencil with Hankel matrices.

This paper describes a new nonlinear projection method. The aim is to design a user-friendly method, tentativ ely as easy to use as the linear PCA (Principal Component Analysis). The method is based on CCA (Curvilinear Component Analysis). This paper presen ts tw o improvements with respect to the original CCA: a better beha vior in the projection of highly nonlinear databases (like spirals) an...

The stereographic projection is a popular method for viewing spherical panoramas because of its ability to represent the scene as a “little planet” with a simulated overhead view. However, the stereographic projection does not work well for indoor scenes. In this paper, we present a method for producing a counterpart to the stereographic projection for indoor scenes. The main innovation of our ...

Various methods for numerically solving Stokes Flow, where a small Reynolds number is assumed to be zero, are investigated. If pressure, horizontal velocity, and vertical velocity can be decoupled into three different equations, the numerical solution can be obtained with significantly less computation cost than when compared to solving a fully coupled system. Two existing methods for numerical...

We show that the continuous (in time) form of the projection-3 scheme proposed in [2] is not a proper approximation of the unsteady Navier-Stokes equations. Hence the projection-3 scheme and its variants are not appropriate for the numerical computation of the Navier-Stokes equations. The projection-3 scheme in [2] was proposed as a possible improvement over the projection-1 and projection-2 sc...