1 CERFACS, 42 Avenue Gaspard Coriolis, 31057 Toulouse Cedex 1, France ([email protected]). 2 The University of Tennessee, Department of Computer Science, 1122 Volunteer Blvd., Knoxville, TN 37996-3450, USA ([email protected]). 3 Institute of Computer Science, Academy of Sciences of the Czech Republic, Pod vodárenskou věž́ı 2, CZ-182 07 Prague 8, Czech Republic ([email protected]). 4 Heinrich-Heine-...

We discuss the general formation of complementary behaviors, functions and forms in biological species competing for resources. We call orthogonalization the related processes on macro and micro-level of a self-organized formation of correlations in the species properties. Orthogonalization processes could be, for example, easily observed in sympatric speciation, as we show in numerical studies...

An important geometric and linear algebraic problem denoted as vector orthogonalization, fundamental to handle contact detection and contact force descriptions in engineering applications, is here considered. The problem is to find a set of linearly independent vectors that span the entire R3 Euclidean space given only one of the base vectors. This paper contains the explanation on how theHouse...

A new inverse iteration algorithm that can be used to compute all the eigenvectors of a real symmetric tri-diagonal matrix on parallel computers is developed. The modified Gram-Schmidt orthogonalization is used in the classical inverse iteration. This algorithm is sequential and causes a bottleneck in parallel computing. In this paper, the use of the compact WY representation is proposed in the...

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 ...

We study decompositions of functions in the Hardy spaces into linear combinations of the basic functions in the orthogonal rational systems {Bn(x)} which can be obtained in the respective contexts through Gram-Schmidt orthogonalization process on shifted Cauchy kernels. Those lead to adaptive decompositions of quaternionic-valued signals of finite energy. This study is a generalization of the m...

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...