On the singular two-parameter eigenvalue problem.
On the trace characterization of the joint spectral radius.
On the use of larger bulges in the QR algorithm.
Orthogonal polynomials and quadrature.
Parallel, synchronous and asynchronous two-stage multisplitting methods.
Partitioning inverse Monte Carlo iterative algorithm for finding the three smallest eigenpairs of generalized eigenvalue problem.
Perturbation analysis for eigenstructure assignment of linear multi-input systems.
Perturbation d'une matrice hermitienne ou normale.
Perturbation theorems for the matrix eigenvalue problem
Polynomial eigenvalue problems with Hamiltonian structure.
Polynomials of the eigenvalues and powers of matrices
Preconditioning block Toeplitz matrices.
Preconditioning eigensolvers – an Oxymoron?
Presentation geometrique des methodes de calcul des valeurs propres.
QR in two dimensions.
Quadratic convergence bounds of scaled iterates by the serial Jacobi methods for indefinite Hermitian matrices.
Quasi-Monte Carlo Methods for some Linear Algebra Problems. Convergence and Complexity
We present quasi-Monte Carlo analogs of Monte Carlo methods for some linear algebra problems: solving systems of linear equations, computing extreme eigenvalues, and matrix inversion. Reformulating the problems as solving integral equations with a special kernels and domains permits us to analyze the quasi-Monte Carlo methods with bounds from numerical integration. Standard Monte Carlo methods for integration provide a convergence rate of O(N^(−1/2)) using N samples. Quasi-Monte Carlo methods...
Rank-One Modification of the Symmetric Eigenproblem.
Rational Krylov for nonlinear eigenproblems, an iterative projection method
In recent papers Ruhe suggested a rational Krylov method for nonlinear eigenproblems knitting together a secant method for linearizing the nonlinear problem and the Krylov method for the linearized problem. In this note we point out that the method can be understood as an iterative projection method. Similarly to the Arnoldi method the search space is expanded by the direction from residual inverse iteration. Numerical methods demonstrate that the rational Krylov method can be accelerated considerably...
Realistic Error Bounds for a Simple Eigenvalue and its Associated Eigenvector.