For a finite connected graph let be the spectral radius of its universal cover. We prove that for any graph of average degree and derive from it the following generalization of the Alon Boppana bound. If the average degree of the graph after deleting any radius ball is at least , then its second largest eigenvalue in absolute value is at least for some absolute constant . This result is tight i...

I present a new differential equation system for dynamic raytracing in inhomogeneous anisotropic media. This new system is computationally much more efficient than the traditional elastic-parameter based system as the right-hand-side functions of this new system are simple. Evaluation of these functions involves only differentiation of phase velocities. Evaluation of the right-hand-side functio...

‎Based on an eigenvalue analysis‎, ‎a new proof for the sufficient‎ ‎descent property of the modified Polak-Ribière-Polyak conjugate‎ ‎gradient method proposed by Yu et al‎. ‎is presented‎.

In this paper we study a nonlinear eigenvalue problem driven by the p-Laplacian. Assuming for the right-hand side nonlinearity only unilateral and sign conditions near zero, we prove the existence of three nontrivial solutions, two of which have constant sign (one is strictly positive and the other is strictly negative), while the third one belongs to the order interval formed by the two opposi...

we are concerned with the discrete right-focal boundary value problem A3z(t) = f(t, z(t + l)), z(ti) = Az(tz) = A2z(ts) = 0, and the eigenvalue problem A3z(t) = Xa(t)f(z(t + 1)) with the same boundary conditions, where tl < t2 < t3. Under various assumptions on f, a, and X, we prove the existence of positive solutions of both problems by applying a fixed-point theorem. @ 2003 Elsevier Science L...

Eigenvalue problems arise in many application areas ranging from computational fluid dynamics to information retrieval. In these fields we are often interested in only a few eigenvalues and corresponding eigenvectors of a sparse matrix. In this paper, we comment on the modifications of the eigenvalue problem that can simplify the computation of those eigenpairs. These transformations allow us t...

In linear stability analysis of a large-scale dynamical system, we need to compute the rightmost eigenvalue(s) for a series of large generalized eigenvalue problems. Existing iterative eigenvalue solvers are not robust when no estimate of the rightmost eigenvalue(s) is available. In this study, we show that such an estimate can be obtained from Lyapunov inverse iteration applied to a special ei...