An Algebraic View on Finite Rank in 2D-SSA

On One-Sided Ideals of Rings of Linear Transformations

Shaped extensions of singular spectrum analysis

Extensions of singular spectrum analysis (SSA) for processing of non-rectangular images and time series with gaps are considered. A circular version is suggested, which allows application of the method to the data given on a circle or on a cylinder, e.g. cylindrical projection of a 3D ellipsoid. The constructed Shaped SSA method with planar or circular topology is able to produce low-rank appro...

A Fast Block Low-Rank Dense Solver with Applications to Finite-Element Matrices

1. Abstract. This article presents a fast dense solver for hierarchically off-diagonal low-rank (HODLR) matrices. This solver uses algebraic techniques such as the adaptive cross approximation (ACA) algorithm to construct the low-rank approximation of the off-diagonal matrix blocks. This allows us to apply the solver to any dense matrix that has an off-diagonal low-rank structure without any pr...

Influence of an Inclusion on Multi-Pass Copper Shaped-Wire Drawing by 2D Finite Element Analysis

The size and length effects of an inclusion on multi-pass copper shaped-wire drawing were investigated. For this purpose, an experimental investigation on optimal die half-angle was conducted. Based on experimental data of optimal die half-angle, wire and inclusion deformations, drawing and hydrostatic stress of copper shaped-wires that contain an inclusion were calculated by two-dimensional fi...

Finite-Difference Time-Domain Simulation of Light Propagation in 2D Periodic and Quasi-Periodic Photonic Structures

Ultra-short pulse is a promising technology for achieving ultra-high data rate transmission which is required to follow the increased demand of data transport over an optical communication system. Therefore, the propagation of such type of pulses and the effects that it may suffer during its transmission through an optical waveguide has received a great deal of attention in the recent years. We...