On the trace characterization of the joint spectral radius.
On the use of larger bulges in the QR algorithm.
On the worst-case convergence of MR and CG for symmetric positive definite tridiagonal Toeplitz matrices.
On theoretical and practical acceleration of randomized computation of the determinant of an integer matrix.
On Transformations of Graded Matrices, with Applications to Stiff ODE's.
On Updating Triangular Products of Householder Reflections.
On worst-case GMRES, ideal GMRES, and the polynomial numerical hull of a Jordan block.
One-sided simultaneous inequalities and sandwich theorems for diagonal similarity and diagonal equivalence of nonnegative matrices.
Operator preconditioning with efficient applications for nonlinear elliptic problems
This paper is devoted to the numerical solution of nonlinear elliptic partial differential equations. Such problems describe various phenomena in science. An approach that exploits Hilbert space theory in the numerical study of elliptic PDEs is the idea of preconditioning operators. In this survey paper we briefly summarize the main lines of this theory with various applications.
Optimal interpolatory splines using -spline representation
Optimal quadratic interpolatory splines on general knotset
Optimal Successive Overrelaxation Iterative Methods fo P-Cyclic Matrices.
Optimality Relationships for p-Cyclic SOR.
Optimally Conditioned Vandermonde Matrices.
Optimally rotated vectors.
Optimally Scaled Matrices, Necessary and Sufficient Conditions.
Optimizing tensor product computations in stochastic automata networks
Optimum Stationary and Nonstationary Iterative Methods for the Solution of Singular Linear Systems.
Orthogonal polynomials and quadrature.
Orthogonal polynomials and the Lanczos method
Lanczos method for solving a system of linear equations is well known. It is derived from a generalization of the method of moments and one of its main interests is that it provides the exact answer in at most n steps where n is the dimension of the system. Lanczos method can be implemented via several recursive algorithms known as Orthodir, Orthomin, Orthores, Biconjugate gradient,... In this paper, we show that all these procedures can be explained within the framework of formal orthogonal polynomials....