Finite element least-squares methods for a compressible Stokes system.
Finite element methods on non-conforming grids by penalizing the matching constraint
The present paper deals with a finite element approximation of partial differential equations when the domain is decomposed into sub-domains which are meshed independently. The method we obtain is never conforming because the continuity constraints on the boundary of the sub-domains are not imposed strongly but only penalized. We derive a selection rule for the penalty parameter which ensures a quasi-optimal convergence.
Finite element methods on non-conforming grids by penalizing the matching constraint
The present paper deals with a finite element approximation of partial differential equations when the domain is decomposed into sub-domains which are meshed independently. The method we obtain is never conforming because the continuity constraints on the boundary of the sub-domains are not imposed strongly but only penalized. We derive a selection rule for the penalty parameter which ensures a quasi-optimal convergence.
Finite-difference preconditioners for superconsistent pseudospectral approximations
The superconsistent collocation method, which is based on a collocation grid different from the one used to represent the solution, has proven to be very accurate in the resolution of various functional equations. Excellent results can be also obtained for what concerns preconditioning. Some analysis and numerous experiments, regarding the use of finite-differences preconditioners, for matrices arising from pseudospectral approximations of advection-diffusion boundary value problems, are presented...
Forward Error Analysis of Gaussian Elimination. Part I: Error and Residual Estimates.
Forward Error Analysis of Gaussian Elimination. Part II: Stability Theorems.
Fourier analysis of iterative aggregation-disaggregation methods for nearly circulant stochastic matrices
We introduce a new way of the analysis of iterative aggregation-disaggregation methods for computing stationary probability distribution vectors of stochastic matrices. This new approach is based on the Fourier transform of the error propagation matrix. Exact formula for its spectrum can be obtained if the stochastic matrix is circulant. Some examples are presented.
Frequency analysis of preconditioned waveform relaxation iterations
The error analysis of preconditioned waveform relaxation iterations for differential systems is presented. This analysis extends and refines previous results by Burrage, Jackiewicz, Nørsett and Renaut by incorporating all terms in the expansion of the error of waveform relaxation iterations in the Laplace transform domain. Lower bounds for the size of the window of rapid convergence are also obtained. The theory is illustrated for waveform relaxation methods applied to differential systems resulting...
Full rank factorization and the Flanders theorem.
Gaussian Elimination is not Optimal.
General highly accurate algebraic coarsening.
General theory of direct methods for solving systems of equations with band matrices
A unified approach to the theory and construction of direct methods is presented. The approach is based on the idea of the transfer of conditions. In examples it is shown how to obtain a particular method from the general algorithm.
Generalization of the Bauer-Fike Theorem.
Generalizations of harmonic and refined Rayleigh-Ritz.
Generalizations of Nekrasov matrices and applications
In this paper we present a nonsingularity result which is a generalization of Nekrasov property by using two different permutations of the index set. The main motivation comes from the following observation: matrices that are Nekrasov matrices up to the same permutations of rows and columns, are nonsingular. But, testing all the permutations of the index set for the given matrix is too expensive. So, in some cases, our new nonsingularity criterion allows us to use the results already calculated...
Generalizations of the Projection Method with Applications to SOR Theory for Hermitian Positive Semidefinite Linear Systems.
Generalized combined field integral equations for the iterative solution of the three-dimensional Helmholtz equation
This paper addresses the derivation of new second-kind Fredholm combined field integral equations for the Krylov iterative solution of tridimensional acoustic scattering problems by a smooth closed surface. These integral equations need the introduction of suitable tangential square-root operators to regularize the formulations. Existence and uniqueness occur for these formulations. They can be interpreted as generalizations of the well-known Brakhage-Werner [A. Brakhage and P. Werner, Arch....
Generalized Kronrod Patterson type imbedded quadratures
We present algorithms for the determination of polynomials orthogonal with respect to a positive weight function multiplied by a polynomial with simple roots inside the interval of integration. We apply these algorithms to search for and calculate all possible sequences of imbedded quadratures of maximal polynomials order of precision for the generalized Laguerre and Hermite weight functions.
Generalized Pascal -eliminated functional matrix with variables.
Geometric convergence of iterative methods for variational inequalities with -matrices and diagonal monotone operators