Spectrum of a matrix

About: Spectrum of a matrix is a research topic. Over the lifetime, 1064 publications have been published within this topic receiving 19841 citations. The topic is also known as: matrix spectrum.

Eigenvalue assignment in an upper Hessenberg matrix

Abstract: A simple algorithm is described for the determination of the elements in the first row of a real unreduced upper Hessenberg matrix so that this matrix has a specified set of eigenvalues. The method is extended for application to descriptor systems.

Calculating Derivatives of Repeated and Nonrepeated Eigenvalues Without Explicit Use of Eigenvectors

Abstract: The analysis of inverse problems in parametric model updating often require the sensitivities of eigenvalues. The calculation of these sensitivities is mathematically related to the derivatives of the eigenvalues with respect to the model parameters. A common method to calculate these derivatives is the Nelson method, which requires the eigenvectors. The method introduced in this paper is derived from the characteristic equation of the underlying general eigenvalue problem and allows the derivatives of eigenvalues with respect to the model parameters to be calculated without explicit use of the eigenvectors. The method is extended for the case of repeated eigenvalues, which leads to restrictions on the parameterization. For repeated eigenvalues of multiplicity two, these restrictions are formulated expicitly. Applications and limitations of the method are demonstrated by examples.

On an iterative method for finding lovver eigenvalues

Abstract: We present the analysis of the errors involved in approximate orthogonalization with respect to previously found eigenvectors in preconditioned iterations of a subspace for simultaneous determination of a cluster of eigenvalues and the corresponding eigenvectors of a large sparse symmetrical eigenvalue problem.