Inflationary dynamics for matrix eigenvalue problems

Some Unusual Matrix Eigenvalue Problems

We survey some unusual eigenvalue problems arising in different applications. We show that all these problems can be cast as problems of estimating quadratic forms. Numerical algorithms based on the well-known Gauss-type quadrature rules and Lanczos process are reviewed for computing these quadratic forms. These algorithms reference the matrix in question only through a matrix-vector product op...

A New Inexact Inverse Subspace Iteration for Generalized Eigenvalue Problems

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.

Sign Wave Analysis in Matrix Eigenvalue Problems

Networked Consensus Agents Dynamics through Matrix Eigenvalue

The collective behavior system depends strongly on the efficiency of communication paths, in other words, network topology. Network connectivity affects the properties of networked agents. Synchronous behavior is also affected by the network structure. A consensus problem is also related to the problem of synchronization. A consensus algorithm is an interaction rule that specifies the informati...

Eigenvalue Dynamics and the Matrix Chain

We introduce a general method for transforming the equations of motion following from a Das-Jevicki-Sakita Hamiltonian, with boundary conditions, into a boundary value problem in one-dimensional quantum mechanics. For the particular case of a onedimensional chain of interacting N × N Hermitean matrices, the corresponding large N boundary value problem is mapped into a linear Fredholm equation w...