«multiple eigenvalues»
۲۸۹۱ نتیجهA Global Arnoldi Method for Large non-Hermitian Eigenproblems with Special Applications to Multiple Eigenproblems∗
Global projection methods have been used for solving numerous large matrix equations, but nothing has been known on if and how a global projection method can be proposed for solving large eigenproblems. In this paper, based on the global Arnoldi process that generates an Forthono
A Harmonic Restarted Arnoldi Algorithm for Calculating Eigenvalues and Determining Multiplicity
A restarted Arnoldi algorithm is given that computes eigenvalues and eigenvectors. It is related to implicitly restarted Arnoldi, but has a simpler restarting approach. Harmonic and regular RayleighRitz versions are possible. For multiple eigenvalues, an approach is proposed that
The Formulation and Analysis of Numerical Methods for Inverse Eigenvalue Problems *
We consider the formulation and local analysis of various quadratically convergent methods for solving the symmetric matrix inverse eigenvalue problem. One of these methods is new. We study the case where multiple eigenvalues are given: we show how to state the problem so that it
Eigenvalue-eigenfunction Problem for Steklov’s Smoothing Operator and Differential-difference Equations of Mixed Type
It is shown that any μ ∈ C is an infinite multiplicity eigenvalue of the Steklov smoothing operator Sh acting on the space Lloc(R). For μ 6= 0 the eigenvalue-eigenfunction problem leads to studying a differential-difference equation of mixed type. An existence and uniqueness theo
A numerical method for solving inverse eigenvalue problems
Based on QR~\ike décomposition with column pivoting, a new and efficient numerical method for solving symmetrie matrix inverse eigenvalue problems is proposed, which is suitable for both the distinct and multiple eigenvalue cases. A locally quadratic convergence analysis is given
Perturbation of multiparameter non-self-adjoint boundary eigenvalue problems for operator matrices
We consider two-point non-self-adjoint boundary eigenvalue problems for linear matrix differential operators. The coefficient matrices in the differential expressions and the matrix boundary conditions are assumed to depend analytically on the complex spectral parameter λ and on
Finite Element-Galerkin Approximation of the Eigenvalues and Eigenvectors of Selfao\joint Problems
Refined estimates for finite element or, more generally, Galerkin approximations of the eigenvalues and eigenvectors of selfadjoint eigenvalue problems are presented. More specifically, refined results on the asymptotic behavior of the eigenvalue and eigenvector errors are proved
Gershgorin Theory for the Generalized Eigenvalue Problem Ax — \ Bx
A generalization of Gershgorin's theorem is developed for the eigenvalue problem Ax = XBx and is applied to obtain perturbation bounds for multiple eigenvalues. The results are interpreted in terms of the chordal metric on the Riemann sphere, which is especially convenient for tr
Perturbation of Partitioned Hermitian Generalized Eigenvalue Problem
We are concerned with the perturbation of a multiple eigenvalue μ of the Hermitian matrix A = diag(μI,A22) when it undergoes an off-diagonal perturbation E whose columns have widely varying magnitudes. When some of E’s columns are much smaller than the others, some copies of μ ar
Convergence of adaptive finite element methods for eigenvalue problems
In this article we prove convergence of adaptive finite element methods for second order elliptic eigenvalue problems. We consider Lagrange finite elements of any degree and prove convergence for simple as well as multiple eigenvalues under a minimal refinement of marked elements