Search results for "matriisilaskenta"

Matriisin Hessenbergin muoto

2013

Electromagnetic wave propagation in non-homogeneous waveguides

2015

We investigate an electromagnetic waveguide, having several cylindrical ends. The waveguide is assumed to be empty and to have a perfectly conductive boundary. We study the electromagnetic field, excited in the waveguide in the presence of charges and currents. The field can be described as a solution of the stationary Maxwell system with conductive boundary conditions and “intrinsic” radiation conditions at infinity. We prove the problem to be well-posed. Electromagnetic waves propagation in the waveguide can be described by means of a scattering matrix. We introduce such a matrix for all values of the spectral parameter k in the waveguide continuous spectrum and study its properties. Moreove…

High-dimensional Big Data processing with dictionary learning and diffusion maps

2015

Algorithms for modern Big Data analysis deal with both massive amount of sam- ples and a large number of features (high-dimension). One way to cope with these challenges is to assume and discover the existence of localization in the data by uncovering its intrinsic geometry. This approach suggests that different data segments can be analyzed separately and then unified in order to gain an understanding of the whole phenomenon. Methods that utilize efficiently local- ized data are attractive for high-dimensional big data analysis, because they can be parallelized, and thus the computational resources, which are needed for their utilization, are realistic and affordable. These methods can explo…