Using transfer matrix method to solve 3D Ising model is generalized straightforwardly from 2D case. We follow the B.Kaufman's approach. No approximation is made except the largest eigenvalue cannot be identified. This problem comes from the fact that we follow the choice of directions of 2-dimensional rotations in direct product space of 2D Ising model such that all eigenvalue equations reduce ...

A structure preserving Sort-Jacobi algorithm for computing eigenvalues or singular values is presented. The proposed method applies to an arbitrary semisimple Lie algebra on its (−1)-eigenspace of the Cartan involution. Local quadratic convergence for arbitrary cyclic schemes is shown for the regular case. The proposed method is independent of the representation of the underlying Lie algebra an...

1. Page 2741, caption of Fig. 2: three occurrences of ‘‘commutator’’ instead of ‘‘commutor’’, i.e. the caption should read Fig. 2. Eigenvalue decomposition of the commutor for the CDFT: (a) sorted eigenvalues of the commutor T1 for N 1⁄4 128. (b) Selected symmetric and skew-symmetric eigenvectors of the commutor for k 1⁄4 0,1, 2, 3. 2. Page 2743, fourth sentence after Eq. (14): ‘‘commutator’’ i...

In a frequency selective slow-fading channel in a MIMO system, the channel matrix is of the form of a block matrix. We propose a method to calculate the limit of the eigenvalue distribution of block matrices if the size of the blocks tends to infinity. We will also calculate the asymptotic eigenvalue distribution of HH ∗, where the entries of H are jointly Gaussian, with a correlation of the fo...

In this paper we develop descriptor techniques for modeling swirling hydrodynamic structures. Using the descriptor notation we obtain the generalized eigenvalue formulation for differential-algebraic equations describing the spatial stability of the fluid flow. We describe the general framework for spatial stability investigation of vortex structures in both viscous and inviscid cases. The disp...

We present a new numerical method for computing selected eigenvalues and eigenvectors of the two-parameter eigenvalue problem. The method does not require good initial approximations and is able to tackle large problems that are too expensive for methods that compute all eigenvalues. The new method uses a two-sided approach and is a generalization of the Jacobi– Davidson type method for right d...

A method for the computation of eigenfrequencies and eigenmodes of fractal drums is presented. The approach involves first mapping the unit disk to a polygon approximating the fractal and then solving a weighted eigenvalue problem on the unit disk by a spectral collocation method. The numerical computation of the complicated conformal mapping was made feasible by the use of the fast multipole m...

In this paper, we consider the sparse eigenvalue problem wherein the goal is to obtain a sparse solution to the generalized eigenvalue problem. We achieve this by constraining the cardinality of the solution to the generalized eigenvalue problem and obtain sparse principal component analysis (PCA), sparse canonical correlation analysis (CCA) and sparse Fisher discriminant analysis (FDA) as spec...

This paper presents adaptive algorithms for eigenvalue problems associated with non-selfadjoint partial differential operators. The basis for the developed algorithms is a homotopy method which departs from a wellunderstood selfadjoint problem. Apart from the adaptive grid refinement, the progress of the homotopy as well as the solution of the iterative method are adapted to balance the contrib...

In this paper, we present a new approach for the solution to a series of slightly perturbed symmetric eigenvalue problems (A + BSi BT) t = X E, 0 5 i 5 m, where A = AT f 72 nxn, B E 7Znx*, and Si = q E 7ZPx*, p < n. The matrix B is assumed to have full column rank, The main idea of our approach lies in a specific choice of starting vectors used in the block Lanczos algorithm so that the effect ...