QR Factorization of Toeplitz Matrices.
QR factorizations using a restricted set of rotations.
QR in two dimensions.
Quadratic convergence bounds of scaled iterates by the serial Jacobi methods for indefinite Hermitian matrices.
Quadratically constrained least squares and quadratic problems.
Quantum dynamical entropy and an algorithm by Gene Golub.
Quasi-boundary value method for non-well posed problem for a parabolic equation with integral boundary condition.
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...
Quasi-Newton preconditioners for the inexact Newton method.
Raffinement de la borne spectrale d'un faisceau de matrices
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...
Real and complex pseudozero sets for polynomials with applications
Pseudozeros are useful to describe how perturbations of polynomial coefficients affect its zeros. We compare two types of pseudozero sets: the complex and the real pseudozero sets. These sets differ with respect to the type of perturbations. The first set – complex perturbations of a complex polynomial – has been intensively studied while the second one – real perturbations of a real polynomial – seems to have received little attention. We present a computable formula for the real pseudozero...
Realistic Error Bounds for a Simple Eigenvalue and its Associated Eigenvector.
Rectangular Scott-type permanents.
Reducing the bandwidth in solving linear algebraic systems arising in the finite element method
The matrix of the system of linear algebraic equations, arising in the application of the finite element method to one-dimensional problems, is a bandmatrix. In approximations of high order, the band is very wide but the elements situated far from the diagonal of the matrix are negligibly small as compared with the diagonal elements. The aim of the paper is to show on a model problem that in practice it is possible to work with a matrix of the system the bandwidth of which is reduced. A simple...
Reduction of huge, sparse matrices over finite fields via created catastrophes.
Regular Splittings and the Discrete Neumann Problem.
Reguläre Zerlegungen und Berechnung des Spektralradius nichtnegativer Matrizen.
Regularization and stabilization of discrete saddle-point variational problems.