A novel orthogonalization-free method together with two specific algorithms is proposed to address extreme eigenvalue problems. On top of gradient-based algorithms, the modify multicolumn gradient such that earlier columns are decoupled from later ones. Locally, both converge linearly convergence rates depending on eigengaps. Momentum acceleration, exact linesearch, and column locking incorpora...

Stability problem of an axisymmetric swirling flow a viscous incompressible fluid with respect to nonaxisymmetric perturbations is considered. The system ordinary differential equations for the amplitude functions solved numerically by Runge-Kutta method and orthogonalization procedure. Solutions at neighborhood singular points are obtained Frobenius method. maximum amplification coefficients p...

Building on Koop, Pesaran and Potter (1996), we propose the `generalized' impulse response analysis for unrestricted vector autoregressive (VAR) and cointegrated VAR models. Unlike the traditional impulse response analysis, our approach does not require orthogonalization of shocks and is invariant to the ordering of the variables in the VAR. The approach is also used in the construction of orde...

Abstract: The paper reviews different methods of orthogonalization of constraints adopted in multibody dynamics formulations. A new approach, based on Schur decomposition, has been herein proposed. All the methods have been implemented in the MATLAB computing environnement and CPU times required for a simple simulation have been recorded.

Our randomized preprocessing of a matrix by means of augmentation counters its degeneracy and ill conditioning, uses neither pivoting nor orthogonalization, readily preserves matrix structure and sparseness, and leads to dramatic speedup of the solution of general and structured linear systems of equations in terms of both estimated arithmetic time and observed CPU time.

Our randomized preprocessing of a matrix by means of augmentation counters its degeneracy and ill conditioning, uses neither pivoting nor orthogonalization, readily preserves matrix structure and sparseness, and leads to dramatic speedup of the solution of general and structured linear systems of equations in terms of both estimated arithmetic time and observed CPU time.

We present a new batch learning algorithm for text classification in the vector space of document representations. The algorithm uses ellipsoid separation [3] in the feature space which leads to a semidefinite program. An approximation of the latent semantic feature extraction approach using Gram-Schmidt orthogonalization [2] is used for the feature extraction. Preliminary results demonstrate s...

We prove a determinantal formula for quantities related to the problem of enumeration of (semi-) meanders, namely the topologically inequivalent planar configurations of non-self-intersecting loops crossing a given (half-) line through a given number of points. This is done by the explicit Gram-Schmidt orthogonalization of certain bases of subspaces of the Temperley-Lieb algebra.