Generalized Kato Decomposition and Essential Spectra

Generalized essential matrix: Properties of the singular value decomposition

When considering non-central imaging devices, the computation of the relative pose requires the estimation of the rotation and translation that transform the 3D lines from one coordinate system to the second. In most of the state-ofthe-art methods, this transformation is estimated by the computing a 6× 6 matrix, known as the Generalized Essential Matrix. To allow a better understanding of this ...

Monadic generalized spectra

Generalized Filtering Decomposition

This paper introduces a new preconditioning technique that is suitable for matrices arising from the discretization of a system of PDEs on unstructured grids. The preconditioner satisfies a so-called filtering property, which ensures that the input matrix is identical with the preconditioner on a given filtering vector. This vector is chosen to alleviate the effect of low frequency modes on con...

Fast Generalized Bruhat Decomposition

The deterministic recursive pivot-free algorithms for the computation of generalized Bruhat decomposition of the matrix in the field and for the computation of the inverse matrix are presented. This method has the same complexity as algorithm of matrix multiplication and it is suitable for the parallel computer systems.

The generalized triangular decomposition

Given a complex matrix H, we consider the decomposition H = QRP∗, where R is upper triangular and Q and P have orthonormal columns. Special instances of this decomposition include the singular value decomposition (SVD) and the Schur decomposition where R is an upper triangular matrix with the eigenvalues of H on the diagonal. We show that any diagonal for R can be achieved that satisfies Weyl’s...