Search results for "Orthogonalization"
showing 5 items of 5 documents
A two-center-oscillator-basis as an alternative set for heavy ion processes
1977
The two-center-oscillator-basis, which is constructed from harmonic oscillator wave functions developing about two different centers, suffers from numerical problems at small center separations due to the overcompleteness of the set. In order to overcome these problems we admix higher oscillator wave functions before the orthogonalization, or antisymmetrization resp. This yields a numerically stable basis set at each center separation. The results obtained for the potential energy surface are comparable with the results of more elaborate models.
Null Space Based Image Recognition Using Incremental Eigendecomposition
2011
An incremental approach to the discriminative common vector (DCV) method for image recognition is considered. Discriminative projections are tackled in the particular context in which new training data becomes available and learned subspaces may need continuous updating. Starting from incremental eigendecomposition of scatter matrices, an efficient updating rule based on projections and orthogonalization is given. The corresponding algorithm has been empirically assessed and compared to its batch counterpart. The same good properties and performance results of the original method are kept but with a dramatic decrease in the computation needed.
In silico prediction of central nervous system activity of compounds. Identification of potential pharmacophores by the TOPS–MODE approach
2004
The central nervous system (CNS) activity has been investigated by using a topological substructural molecular approach (TOPS-MODE). A discriminant analysis to classify CNS and non-CNS drugs was developed on a data set (302 compounds) of great structural variability where more than 81% (247/302) were well classified. Randic's orthogonalization procedures was carried out to allow the interpretation of the model and to avoid the collinearity among descriptors. The discriminant model was assessed by a leave-n-out (when n varies from 2 to 20) cross-validation procedure (79.94% of correct classification), an external prediction set composed by 78 CNS/non-CNS drugs (80.77% of correct classificati…
Computation of a few smallest eigenvalues of elliptic operators using fast elliptic solvers
2001
The computation of a few smallest eigenvalues of generalized algebraic eigenvalue problems is studied. The considered problems are obtained by discretizing self-adjoint second-order elliptic partial differential eigenvalue problems in two- or three-dimensional domains. The standard Lanczos algorithm with the complete orthogonalization is used to compute some eigenvalues of the inverted eigenvalue problem. Under suitable assumptions, the number of Lanczos iterations is shown to be independent of the problem size. The arising linear problems are solved using some standard fast elliptic solver. Numerical experiments demonstrate that the inverted problem is much easier to solve with the Lanczos…
Improved reliability estimates for the serial color-word test
1978
Starting from Lennart Sjoberg's serial scoring of the Color-Word Test and his critical review of the test, the possibilities of attaining better reliability estimates are briefly surveyed. As a simple step, the orthogonalization of the regression model is suggested. Ways of maximizing the reliability estimate are demonstrated. On the basis of 261 subjects from five differing subsamples, clinical and control groups, the reliability estimates of the oblique system of the orthogonalized system and of the maximum reliability solutions are compared empirically. The significance of the results for test theoretic evaluation of the Color-Word Test is discussed.