A restarted nonsymmetric Lanczos algorithm is given for computing eigenvalues and both right and left eigenvectors. The restarting limits the storage so that finding eigenvectors is practical. Restarting also makes it possible to deal with roundoff error in new ways. We give a scheme for avoiding near-breakdown and discuss maintaining biorthogonality. A system of linear equations can be solved ...

A deflated restarted Lanczos algorithm is given for both solving symmetric linear equations and computing eigenvalues and eigenvectors. The restarting limits the storage so that finding eigenvectors is practical. Meanwhile, the deflating from the presence of the eigenvectors allows the linear equations to generally have good convergence in spite of the restarting. Some reorthogonalization is ne...

Spatial-correlation properties of the wave functions (eigenvectors) of a spin-one eigenproblem for dipole interaction is studied for random geometries of the underlying system. This problem describes, in particular, polar excitations (“plasmons”) of large clusters. In contrast to Berry’s conjecture of quantum chaos for massive particles, we have found long-range spatial correlations for wave fu...

The ability of humans to perceive the spatial orientation of an occluded arm was investigated. It was hypothesized that this ability is tied to the arm's inertial eigenvectors, invariant mechanical parameters corresponding to a limb's axes of rotational symmetry. By breaking the coincidence between the eigenvectors of the arm and its longitudinal axis, 3 experiments were directed at the possibi...

This part describes the results obtained in the simulations and experiments reported in the previous sessions of this report. A) Statistical comparison of the principal component analysis in various spaces The cumulative contributions of the eigenvectors in each space are summarized for multiple-of-three numbers of eigenvectors in Tables I to III. Table I. Cumulative contribution of the eigenve...

Abstract We use the method of similar operators to study a mixed problem for first order differential equation with fractional integration operator. The operator defined by is transformed into that an orthogonal direct sum finite-rank operators. estimates eigenvalues, eigenvectors are obtained. result used construct group.

The complete knowledge of Laplacian eigenvalues and eigenvectors of complex networks plays an outstanding role in understanding various dynamical processes running on them; however, determining analytically Laplacian eigenvalues and eigenvectors is a theoretical challenge. In this paper, we study the Laplacian spectra and their corresponding eigenvectors of a class of deterministically growing ...

For the one-dimensional XXX model under the periodic boundary conditions, we discuss two types of eigenvectors, regular eigenvectors which have finite-valued rapidities satisfying the Bethe ansatz equations, and non-regular eigenvectors which are descendants of some regular eigenvectors under the action of the SU(2) spin-lowering operator. It was pointed out by many authors that the non-regular...

This paper proposes a spectral clustering method using k-means and weighted Mahalanobis distance (Referred to as MDLSC) enhance the degree of correlation between data points improve accuracy Laplacian matrix eigenvectors. First, we used coefficient weight calculate any two constructed set; then, based on matrix, K-nearest neighborhood (KNN) algorithm construct similarity matrix. Secondly, regul...

We study certain function algebras and their operator algebra completions on r-discrete abelian groupoids, the corresponding conditional expectations, maximal abelian subalgebras (masa) and eigen-functionals. We give a semidirect product decomposition for an abelian groupoid. This is done through a matched pair and leads to a C*-diagonal (for a special case). We use this decomposition to study ...