Naslov
An Accurate SVD Algorithm for 2x2 Triangular Matrices

Autori
Hari, Vjeran ; Matejaš, Josip

Vrsta, podvrsta i kategorija rada
Radovi u zbornicima skupova, cjeloviti rad (in extenso), znanstveni

Izvornik
ICNAAM, International Conference on Numerical Analysis and Applied Mathematics 2006 / Simos, T., E. et al. - Weinheim : Wiley-VCH, 2006, 143-146

Skup
International Conference on Numerical Analysis and Applied Mathematics 2006

Mjesto i datum
Hersonissos, Grčka, 15.09.2006. - 19.09.2006

Vrsta sudjelovanja
Predavanje

Vrsta recenzije
Međunarodna recenzija

Ključne riječi
singular value decomposition; triangular 2x2 matrix; accurate algorithm

Sažetak
In this paper we present ideas that are used to define an accurate algorithm for computing the singular value decomposition of two-by-two triangular matrices and for proving the ppropriate accuracy bounds. The angle formulas, originally proposed by Voevodin, are modified to become relatively accurate in floating point arithmetics. The rounding error analysis uses natural assumptions which fully comply with the IEEE floating point standards. A subtle analysis is used to express the final errors as functions of errors of some beginning or intermediate quantities. This enables to prove much sharper final error bounds, especially in the case when the initial matrix is nearly diagonal.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA