Calculation of Gauss Quadratures with Multiple Free and Fixed Knots
Calculation of the Weights of Interpolarory Quadratures
Checking nonsingularity of tridiagonal matrices.
Cholesky-like factorizations of skew-symmetric matrices.
Complexity issues for the symmetric interval eigenvalue problem
We study the problem of computing the maximal and minimal possible eigenvalues of a symmetric matrix when the matrix entries vary within compact intervals. In particular, we focus on computational complexity of determining these extremal eigenvalues with some approximation error. Besides the classical absolute and relative approximation errors, which turn out not to be suitable for this problem, we adapt a less known one related to the relative error, and also propose a novel approximation error....
Componentwise Inclusion and Exclusion Sets for Solutions of Quadratic Equations in Finite Dimensional Spaces.
Computation of eigenvalue and eigenvector derivatives for a general complex-valued eigensystem.
Computation of the Smallest Positive Eigenvalue of a Quadratic ..-matrix.
Computing codimensions and generic canonical forms for generalized matrix products.
Computing the CS and the Generalized Singular Value Decompositions.
Convergence analysis of an inexact truncated RQ-iteration.
Convergence of approximation methods for eigenvalue problem for two forms
The paper concerns an approximation of an eigenvalue problem for two forms on a Hilbert space . We investigate some approximation methods generated by sequences of forms and defined on a dense subspace of . The proof of convergence of the methods is based on the theory of the external approximation of eigenvalue problems. The general results are applied to Aronszajn’s method.
Convergence of -norms of a matrix
a recurrence relation for computing the -norms of an Hermitian matrix is derived and an expression giving approximately the number of eigenvalues which in absolute value are equal to the spectral radius is determined. Using the -norms for the approximation of the spectral radius of an Hermitian matrix an a priori and a posteriori bounds for the error are obtained. Some properties of the a posteriori bound are discussed.
Convergence of the shifted QR algorithm on 3 x 3 normal matrices.
Convergence theory for inexact inverse iteration applied to the generalised nonsymmetric eigenproblem.
Convergence theory for the exact interpolation scheme with approximation vector as the first column of the prolongator and Rayleigh quotient iteration nonlinear smoother
We extend the analysis of the recently proposed nonlinear EIS scheme applied to the partial eigenvalue problem. We address the case where the Rayleigh quotient iteration is used as the smoother on the fine-level. Unlike in our previous theoretical results, where the smoother given by the linear inverse power method is assumed, we prove nonlinear speed-up when the approximation becomes close to the exact solution. The speed-up is cubic. Unlike existent convergence estimates for the Rayleigh quotient...