Naslov
Two-sided hyperbolic singular value decomposition

Autori
Šego, Vedran

Vrsta, podvrsta i kategorija rada
Ocjenski radovi, doktorska disertacija

Fakultet
PMF - Matematički odjel

Mjesto
Zagreb

Datum
25.09

Godina
2009

Stranica
124

Mentor
Singer, Sanja ; Singer, Saša

Ključne riječi
SVD; hyperbolic scalar products

Sažetak
The aim of this work is construction of a singular value decomposition of a given matrix A with regards to a hyperbolic scalar product induced by J (called two-sided SVD or, shortly, just 2HSVD), maintaining the properties similar to those of a traditional singular value decomposition. In the first chapter an overview of the thesis and known results in the indefinite linear algebra are given. Some of the plethora of the variations of the singular value decomposition are given. The third chapter brings the main theoretical results: 2HSVD itself, its variant for J-nonnegative matrices, relation to a semidefinite J-polar decomposition and its properties similar or equal to those in Euclidean case. Two algorithms -- two- and one-sided Jacobi-like -- along with their numerical properties are discussed in the fourth chapter. The next chapter shows one application of 2HSVD to a generalization of a Zakrajšek-Vidav decomposition of block-unitary matrices. The final chapter discusses further generalizations of such decomposition to more general scalar product spaces.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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