In this paper, we present a novel structure for adap-tive noise ltering based on subspace methods. Our approach requires no eigenvalue or singular value decomposition to obtain the principal signal components. In addition, only the noisy signal, and no reference signal is needed. A modiied RLS adaptive algorithm is proposed which approximately performs the principal component analysis of the no...

This paper establishes an improved NDIF method for the eigenvalue extraction of two-dimensional acoustic cavities with arbitrary shapes. The NDIF method, which was introduced by the authors in 1999, gives highly accurate eigenvalues despite employing a small number of nodes. However, it needs the inefficient procedure of calculating the singularity of a systemmatrix in the frequency range of in...

Separation into spectral and nonlinear complex-eigenvalue problems is shown to be an effective and flexible approach to soliton laser models. The simplest such model, a complex Ginzburg-Landau model with cubic nonlinearity, has no stable solitonic solutions. We show that coupling it to a resonant linear system is a simple and general route to stabilization, which encompasses several previous in...

Based on the scalar Helmholtz equation and the finite-difference approximation, we formulate a matrix eigenvalue problem for the calculation of propagation constants, β(ω), in micro-structured optical fibres. The method is applied to index-guiding fibres as well as air-core photonic bandgap fibres, and in both cases qualitatively correct results are found. The strength of this approach lies in ...

We study the global structure of the set of radial solutions of a nonlinear Dirichlet eigenvalue problem involving the p-Laplacian with p > 2, in the unit ball of RN , N > 1. We show that all non-trivial radial solutions lie on smooth curves of respectively positive and negative solutions, bifurcating from the first eigenvalue of a weighted p-linear problem. Our approach involves a local bifurc...

Two methods for model behavioural analysis are implemented on a simple 2 order nonlinear model. The results of applying Ford’s behavioral approach are compared with those obtained using both system-wide and variable-specific loop eigenvalue elasticity analysis. Differences in the division of the time span into analysis intervals are identified as are discrepancies in the outcomes. The effort re...

The QR algorithm is the crux of the serial nonsymmetric eigenvalue problem. Recent eeorts to parallelize this algorithm have made signiicant advances towards solving the parallel nonsym-metric eigenvalue problem. Most methods to date suuer a scalability problem. In this talk we discuss an approach for parallelizing QR which overcomes many of the disadvantages to date. We also give insights into...

We consider the solution of large-scale symmetric eigenvalue problems for which it is known that the eigenvectors admit a low-rank tensor approximation. Such problems arise, for example, from the discretization of high-dimensional elliptic PDE eigenvalue problems or in strongly correlated spin systems. Our methods are built on imposing low-rank (block) TT structure on the trace minimization cha...

We introduce a semistochastic implementation of the power method to compute, for very large matrices, the dominant eigenvalue and expectation values involving the corresponding eigenvector. The method is semistochastic in that the matrix multiplication is partially implemented numerically exactly and partially stochastically with respect to expectation values only. Compared to a fully stochasti...

Given four complex matrices $A$‎, ‎$B$‎, ‎$C$ and $D$ where $Ainmathbb{C}^{ntimes n}$‎ ‎and $Dinmathbb{C}^{mtimes m}$ and let the matrix $left(begin{array}{cc}‎ A & B ‎ C & D‎ end{array} right)$ be a normal matrix and‎ assume that $lambda$ is a given complex number‎ ‎that is not eigenvalue of matrix $A$‎. ‎We present a method to calculate the distance norm (with respect to 2-norm) from $D$‎ to ...