A complete characterization of the convergence factor can be very useful when analyzing the asymptotic convergence of an iterative method. We will here establish a formula for the convergence factor of the method called residual inverse iteration, which is a method for nonlinear eigenvalue problems and a generalization of the well known inverse iteration. The formula for the convergence factor ...

where A1, . . . , Am are given n × n matrices and the functions p1, . . . , pm are assumed to be entire. This does not only include polynomial eigenvalue problems but also eigenvalue problems arising from systems of delay differential equations. Our aim is to compute the -pseudospectral abscissa, i.e. the real part of the rightmost point in the -pseudospectrum, which is the complex set obtained...

Gradient iterations for the Rayleigh quotient are simple and robust solvers to determine a few of the smallest eigenvalues together with the associated eigenvectors of (generalized) matrix eigenvalue problems for symmetric matrices. Sharp convergence estimates for the Ritz values and Ritz vectors are derived for various steepest descent/ascent gradient iterations. The analysis shows that poores...

In this paper, we present several verifiable conditions for eigenvalue intervals of real symmetric interval matrices overlapping or not overlapping. To above cases, two new methods with algorithms for computing eigenvalue bounds of real symmetric matrices are developed. We can estimate eigenvalue bounds moving away the assumption that two intervals containing two eigenvalues of real symmetric i...

An inverse eigenvalue problem concerns the reconstruction of a structured matrix from prescribed spectral data. Such an inverse problem arises in many applications where parameters of a certain physical system are to be determined from the knowledge or expectation of its dynamical behavior. Spectral information is entailed because the dynamical behavior often is governed by the underlying natur...

In this paper a noniterative algorithm to be used for the analytical determination of the sorted eigenvalues and corresponding orthonormalized eigenvectors obtained by diffusion tensor magnetic resonance imaging (DT-MRI) is described. The algorithm uses the three invariants of the raw water spin self-diffusion tensor represented by a 3 x 3 positive definite matrix and certain math functions tha...

In this work, we define the joint normal eigenvalue, joint reducing approximate eigenvalue and we obtain some important and new results about the boundary of joint numerical range of n-tuple operators on a complex Hilbert space.

Martin COSTABEL & Monique DAUGE Abstract. The 2 2 system of integral equations corresponding to the biharmonic single layer potential in R2 is known to be strongly elliptic. It is also known to be positive definite on a space of functions orthogonal to polynomials of degree one. We study the question of its unique solvability without this orthogonality condition. To each curve , we associate a ...

Two generalizations of the notion of principal eigenvalue for elliptic operators in RN are examined in this paper. We prove several results comparing these two eigenvalues in various settings: general operators in dimension one; self-adjoint operators; and “limit periodic” operators. These results apply to questions of existence and uniqueness for some semi-linear problems in all of space. We a...