The occurrence of collinearity in fMRI-based GLMs (general linear models) may reduce power or produce unreliable parameter estimates. It is commonly believed that orthogonalizing collinear regressors in the model will solve this problem, and some software packages apply automatic orthogonalization. However, the effects of orthogonalization on the interpretation of the resulting parameter estima...

In this article we present a fast recursive orthogonalization scheme for two important subspaces of the Macaulay matrix: its row space and null space. It requires a graded monomial ordering and exploits the resulting structure of the Macaulay matrix induced by this graded ordering. The resulting orthogonal basis for the row space will retain a similar structure as the Macaulay matrix and is as ...

This paper focuses on the empirical autocovariance operator of H-valued periodically correlated processes. It will be demonstrated that the empirical estimator converges to a limit with the same periodicity as the main process. Moreover, the rate of convergence of the empirical autocovariance operator in Hilbert-Schmidt norm is derived.

A new inverse iteration algorithm that can be used to compute all the eigenvectors of a real symmetric tridiagonal matrix on parallel computers is developed. In the classical inverse iteration algorithm, the modified GramSchmidt orthogonalization is used, and this causes a bottleneck in parallel computing. In this paper, the use of the compact WY representation is proposed in the orthogonalizat...

In this short note we show that for a Markovian open quantum system it is always possible to construct a unique set of perfectly consistent Schmidt paths, supporting quasi-classicality. Our Schmidt process, elaborated several years ago, is the ∆t → 0 limit of the Schmidt chain constructed very recently by Paz and Zurek.

This paper describes modeling discrete event systems in Metropolis using one of the key concepts employed by Metropolis, orthogonalization of design aspects, which in this particular case, is the orthogonalization between capability and cost. To support the orthogonalization, quantity annotation mechanism is introduced. This paper formally analyzes simulation strategies for quantity annotation ...

two symmetric matrices, where one matrix has a restricted rank. A comparison of the two cases reveals a remarkable similarity between Eckhart-Young theorem and Ky Fan’s maximum principle. The extremum principles of Ky Fan consider sums and products of eigenvalues of Hermitian matrices. The third part of the talk derives extended rules for rectangular matrices. In this case singular values take ...

All-electron calculations play an important role in density functional theory, which improving computational efficiency is one of the most needed and challenging tasks. In model formulations, both nonlinear eigenvalue problem total energy minimization pursue orthogonal solutions. Most existing algorithms for solving these two models invoke orthogonalization process either explicitly or implicit...