engleski

An Accurate SVD Algorithm for 2x2 Triangular Matrices

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.

singular value decomposition; triangular 2x2 matrix; accurate algorithm

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