This article uses the projected gradient method (PG) for a non-negative matrix factorization problem (NMF), where one or both factors must have orthonormal columns rows. We penalize orthonormality constraints and apply PG via block coordinate descent approach. means that at certain time factor is fixed other updated by moving along steepest direction computed from penalized objective function p...

We present a class of orthogonal non-regular in a sense of Kalnins and Miller (hence nonStäckel) coordinates which are R-separable in 3-dim. Helmholtz equation. One family of parametric surfaces consists of parallel Dupin cyclides, the other two consist of circular cones. This coordinate system is used to simplify derivation of Friedlander’s formulae for a general ”simple progressive solution o...

In this paper, a new finite-difference time-domain (FDTD) algorithm is investigated to analyze electromagnetic structures with curved boundaries using a Cartesian coordinate system. The new algorithm is based on a nonorthogonal FDTD method. However, only those cells near the curved boundaries are calculated by nonorthogonal FDTD formulas; most of the grid is orthogonal and can be determined by ...

A computational code has been developed for analyzing 3-D radiation problems in curved geometries. To accomplish this, a suitable formulation is developed considering Maxwell equations in a general coordinate system and numerically solved by the use of a parallel curvilinear finite-difference time-domain (FDTD) method. In order to validate the computational code, the method analyzes a microstri...

In this paper we introduce a new set of hp nite element expansions for use in hybrid domains using hexahedrons, prisms, pyramids and tetrahedrons. The expansions are explained in terms of a uniied notation which incorporates the standard hexahedral hp nite element expansion. The new bases are motivated from a set of orthogonal polynomial expansions within each of the hybrid domains. The polynom...

We present here a brief description of a numerical technique suitable for solving axisymmetric (or two-dimensional) free-boundary problems of fluid mechanics. The technique is based on a finite-difference solution of the equations of motion on an orthogonal curvilinear coordinate system, which is also constructed numerically and always adjusted so as to fit the current boundary shape. The overa...

Computer-aided surgery intensively uses the concept of navigation: after having collected CT data from a patient and transferred them to the operating room coordinate system, the surgical instrument (a puncture needle for instance) is localized and its position is visualized with respect to the patient organs which are not directly visible. This approach is very similar to the GPS paradigm. Tra...

A common problem for experimental space physicists is the determination of the "attitude matrix" T which transforms vectors between representations in X and Xl coordinate systems according to Vx = TXX' VXI. Solution of this problem using the standard Eulerian angle techniques is in general tedious and circuitous. A straightforward, simple, and efficient solution for the transformation matrix is...