Finding approximations to the eigenvalues of nonlinear eigenvalue problems is a common problem which arises from many complex applications. In this paper, iterative algorithms for finding approximations to the eigenvalues of nonlinear eigenvalue problems are verified. These algorithms use an efficient numerical approach for calculating the first and second derivatives of the determinant of the ...

We explore singularly perturbed convection-diffusion equations in a circular domain. Considering boundary layer analysis of the singularly perturbed equations and we show convergence results. In view of numerical analysis, We discuss approximation schemes, error estimates and numerical computations. To resolve the oscillations of classical numerical solutions due to the stiffness of our problem...

Abstract. In this paper, we consider a basic N-dimensional competition model in the unstirred chemostat with Beddington-DeAngelis functional response. The bifurcation solutions from a simple eigenvalue and a double eigenvalue are obtained respectively. In particular, for the double eigenvalue, we establish the existence and stability of coexistence solutions by the techniques of space decomposi...

This paper describes an algorithm for robust time-delay estimation (TDE) in situations where a large amount of additive noise and reverberation is present. In [1] an adaptive eigenvalue decomposition algorithm has been developed for TDE between two microphones in highly reverberant acoustic environments. In this paper we extend this algorithm to highly noisy and reverberant environments, by usi...

Some new properties of the eigenvalues of the subdirect sums are presented for the particular case of 1-subdirect sums. In particular, it is shown that if an eigenvalue λ is associated with certain blocks of matrix A or matrix B then λ is also an eigenvalue associated with the 1-subdirect sum A ⊕1 B. Some results concerning eigenvectors of the k-subdirect sum A⊕k B for an arbitrary positive int...