QR factorizations using a restricted set of rotations.
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...
Rehabilitation of the Gauss-Jordan Algorithm.
Řešení soustav lineárních algebraických rovnic s komplexními koeficienty
Résolution systolique de systèmes linéaires denses
Solution of a system of linear equations with given error sets for coefficients
In the paper, a method is given for finding all solutions of a system of linear equations with interval coefficients and with additional supposition that these coefficients fulfil a given system of homogeneous linear equations.
Solution of Linear Equations with Hankel and Toeplitz Matrices.
Solving Confluent Vandermonde Systems of Hermite Type.
Solving linear systems with a Levinson-like solver.
Some characterizations of totally nonpositive (totally negative) matrices.
Special Similarity Transformations in Connection with the Quadrant Interlocking Factorisation Techniques
Stabilité numérique de l'algorithme de Levinson
Stochastic Arithmetic Theory and Experiments
Stochastic arithmetic has been developed as a model for exact computing with imprecise data. Stochastic arithmetic provides confidence intervals for the numerical results and can be implemented in any existing numerical software by redefining types of the variables and overloading the operators on them. Here some properties of stochastic arithmetic are further investigated and applied to the computation of inner products and the solution to linear systems. Several numerical experiments are performed showing...
Strong rank revealing Cholesky factorization.
Sur l'inversion de matrice
System of linear equations
The Analysis of a Nested Dissection Algorithm.
The Coordinex Problem and Its Relation to the Conjecture of Wilkinson.
The General Neville-Aitken-Algorithm and Some Applications.
The inversion of cyclic tridiagonal matrices