Two method for computation of the spectra certain infinite graphs are suggested. The first one can be viewed as a reversed Gram--Schmidt orthogonalization procedure. It relies heavily on spectral theory Jacobi matrices. second is related to Schur complement block A number examples including with tails, chains cycles and ladders worked out in detail.

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.

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...

in this paper, a numerical scheme for solving singular initial/boundary value problems presented.by applying the reproducing kernel hilbert space method (rkhsm) for solving these problems,this method obtained to approximated solution. numerical examples are given to demonstrate theaccuracy of the present method. the result obtained by the method and the exact solution are foundto be in good agr...

Eigen values evaluation is an integral but computation-intensive part for many image and signal processing applications. Modified Gram-Schmidt Orthogonalization (MGSO) is an efficient method for evaluating the Eigen values in face recognition algorithms. MGSO applies normalization of vectors in its iterative orthogonal process and its accuracy depends on the accuracy of normalization. Using sof...

The advent of supercomputers with hierarchical memory systems has imposed the use of block algorithms for the linear algebra algorithms. Although block algorithms may result in impressive improvements in performance, their numerical properties are quite different from their scalar counterpart and deserve an in-depth study. In this paper, the numerical stability ofblock Gram-Schmidt orthogonaliz...

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-...