Sharp lower bounds for the dimension of linearizations of matrix polynomials.
Simultaneous Iteration for Computing Invariant Subspaces of Non-Hermitian Matrices.
Simultaneous triangularization of commuting matrices for the solution of polynomial equations
We present an extension of the QR method to simultaneously compute the joint eigenvalues of a finite family of commuting matrices. The problem is motivated by the task of finding solutions of a polynomial system. Several examples are included.
Solving large-scale quadratic eigenvalue problems with Hamiltonian eigenstructure using a structure-preserving Krylov subspace method.
Some Computational Aspects of the Consistent Mass Finite Element Method for a (semi-)periodic Eigenvalue Problem
We consider a model eigenvalue problem (EVP) in 1D, with periodic or semi–periodic boundary conditions (BCs). The discretization of this type of EVP by consistent mass finite element methods (FEMs) leads to the generalized matrix EVP Kc = λ M c, where K and M are real, symmetric matrices, with a certain (skew–)circulant structure. In this paper we fix our attention to the use of a quadratic FE–mesh. Explicit expressions for the eigenvalues of the resulting algebraic EVP are established. This leads...
Some Convergent Jacobi-like Procedures for Diagonalising J-Symmetric Matrices.
Some Generalisations of the Theory of Successive Over-Relaxation.
Some parallel procedures for computing the eigenvalues of a real symmetric matrix.
Some results on eigenvalues of nonnegative matrices
Spectral approximation of multiplication operators.
Splitting Certain Eigenvalue Eigenvector Problems.
Spolehlivost numerických výpočtů
Stabilité d'un algorithme de recherche de valeur propre de problème généralisé
Stationary Schrödinger equations governing electronic states of quantum dots in the presence of spin-orbit splitting
In this work we derive a pair of nonlinear eigenvalue problems corresponding to the one-band effective Hamiltonian accounting for the spin-orbit interaction governing the electronic states of a quantum dot. We show that the pair of nonlinear problems allows for the minmax characterization of its eigenvalues under certain conditions which are satisfied for our example of a cylindrical quantum dot and the common InAs/GaAs heterojunction. Exploiting the minmax property we devise an efficient iterative...
Structure preserving algorithms for perplectic eigenproblems.
Structured polynomial eigenproblems related to time-delay systems.
Structured QR algorithms for Hamiltonian symmetric matrices.
Structured tools for structured matrices.
Sturm-Liouville difference equations and banded matrices
Sur la réduction des déterminants des matrices de Jacobi d'un type spécial avec l'application à la recherche de leurs valeurs propres