This research focuses on nding a large number of eigenvalues and eigenvectors of a sparse symmetric or Hermitian matrix, for example, nding 1000 eigenpairs of a 100,000 100,000 matrix. These eigenvalue problems are challenging because the matrix size is too large for traditional QR based algorithms and the number of desired eigenpairs is too large for most common sparse eigenvalue algorithms. I...

In this paper, a fundamentally new method, based on the denition, is introduced for numerical computation of eigenvalues, generalized eigenvalues and quadratic eigenvalues of matrices. Some examples are provided to show the accuracy and reliability of the proposed method. It is shown that the proposed method gives other sequences than that of existing methods but they still are convergent to th...

In this paper, we represent an inexact inverse subspace iteration method for computing a few eigenpairs of the generalized eigenvalue problem Ax = Bx [Q. Ye and P. Zhang, Inexact inverse subspace iteration for generalized eigenvalue problems, Linear Algebra and its Application, 434 (2011) 1697-1715 ]. In particular, the linear convergence property of the inverse subspace iteration is preserved.

In this paper, we propose an uniformly convergent adaptive finite element method with hybrid basis (AFEM-HB) for the discretization of singularly perturbed nonlinear eigenvalue problems under constraints with applications in Bose-Einstein condensation (BEC) and quantum chemistry. We begin with the time-independent Gross-Pitaevskii equation and show how to reformulate it into a singularly pertur...

a method for solving the descriptor discrete-time linear system is focused. for easily, it is converted to a standard discrete-time linear system by the definition of a derivative state feedback. then partial eigenvalue assignment is used for obtaining state feedback and solving the standard system. in partial eigenvalue assignment, just a part of the open loop spectrum of the standard linear s...

In this paper we extend the smoothing technique [7], [9] onto the problems of Semidefinite Optimization. For that, we develop a simple framework for estimating a Lipschitz constant for the gradient of some symmetric functions of eigenvalues of symmetric matrices. Using this technique, we can justify the Lipshitz constants for some natural approximations of maximal eigenvalue and the spectral ra...

Nonlinear PCA type learning has been recently suggested for signal subspace decomposition and sinusoidal frequencies tracking, which outperformed the linear PCA based methods and traditional least squares algorithms. Currently, nonlinear PCA algorithms are directly generalized from linear ones that based on gradient descent (GD) technique. The convergence behavior of gradient descent is depende...

The method of curve evolution is a popular method for recovering shape boundaries. However isotropic metrics have always been used to induce the flow of the curve and potential steady states tend to be difficult to determine numerically, especially in noisy or low-contrast situations. Initial curves shrink past the steady state and soon vanish. In this paper, anisotropic metrics are considered ...

The Schrödinger eigenvalue problem is solved with the imaginary time propagation technique. The separability of the Hamiltonian makes the problem suitable for the application of splitting methods. High order fractional time steps of order greater than two necessarily have negative steps and cannot be used for this class of diffusive problems. However, there exist methods which use fractional co...

Chaos synchronization in coupled chaotic oscillator systems with diffusive and gradient couplings forced by only one local feedback injection signal (boundary pinning control) is studied. By using eigenvalue analysis, we obtain controllable regions directly in control parameter space for different types of coupling links (including diagonal coupling and nondiagonal couplings). The effects of bo...