On the parametric solution to the second-order Sylvester matrix equation .
On the partitioned matrix and its associated system
On the periodic quotient singular value decomposition.
On the preconditioned biconjugate gradients for solving linear complex equations arising from finite elements
The paper analyses the biconjugate gradient algorithm and its preconditioned version for solving large systems of linear algebraic equations with nonsingular sparse complex matrices. Special emphasis is laid on symmetric matrices arising from discretization of complex partial differential equations by the finite element method.
On the pseudoinverse of a sum of symmetric matrices with applications to estimation
On the Quadratic Convergence of the Special Cyclic Jacobi Method.
On the Rate of Convergence of the Preconditioned Conjugate Gradient Method.
On the reduction of a Hamiltonian matrix to Hamiltonian Schur form.
On the reduction of a random basis
For p ≤ n, let b1(n),...,bp(n) be independent random vectors in with the same distribution invariant by rotation and without mass at the origin. Almost surely these vectors form a basis for the Euclidean lattice they generate. The topic of this paper is the property of reduction of this random basis in the sense of Lenstra-Lenstra-Lovász (LLL). If is the basis obtained from b1(n),...,bp(n) by Gram-Schmidt orthogonalization, the quality of the reduction depends upon the sequence of ratios...
On the relation between the AINV and the FAPINV algorithms.
On the set of weighted least squares solutions of systems of convex inequalities
On the Sharpness of Some Upper Bounds for the Spectral Radii of S.O.R. Iteration Matrices.
On the shifted QR iteration applied to companion matrices.
On the singular two-parameter eigenvalue problem.
On the solution of Cauchy systems of equations.
On the solution of multiparameter problems of algebra. IV: The algorithm and its applications.
On the solution of multiparameter problems of algebra. V: The - factorization algorithm and its applications.
On the Solution of Singular Linear Systems of Algebraic Equations by Semiiterative Methods.
On the Stability of Finite Numerical Procedures.
On the subspace projected approximate matrix method
We provide a comparative study of the Subspace Projected Approximate Matrix method, abbreviated SPAM, which is a fairly recent iterative method of computing a few eigenvalues of a Hermitian matrix . It falls in the category of inner-outer iteration methods and aims to reduce the costs of matrix-vector products with within its inner iteration. This is done by choosing an approximation of , and then, based on both and , to define a sequence of matrices that increasingly better approximate...