An Optimal Order Multigrid Method for Biharmonic, C1 Finite Element Equations.
An optimum iteration for the matrix polar decomposition.
An SVD approach to identifying metastable states of Markov chains.
An unusual way of solving linear systems
Mediante integrali multipli agevoli per il calcolo numerico vengono espressi il valore assoluto di un determinante qualsiasi e le formule di Cramer.
An upper bound on the number of monomials in determinants of sparse matrices with symbolic entries.
Analysis of multilevel decomposition iterative methods for mixed finite element methods
Analysis of some Krylov subspace methods for normal matrices via approximation theory and convex optimization.
Analysis of the Du Fort-Frankel method for linear systems
Analysis of the generalized total least squares problem AX ... B when some columns of A are free of error.
Analysis of the Schwarz algorithm for mixed finite elements methods
Analysis of two-dimensional FETI-DP preconditioners by the standard additive Schwarz framework.
Analysis of two-level domain decomposition preconditioners based on aggregation
In this paper we present two-level overlapping domain decomposition preconditioners for the finite-element discretisation of elliptic problems in two and three dimensions. The computational domain is partitioned into overlapping subdomains, and a coarse space correction is added. We present an algebraic way to define the coarse space, based on the concept of aggregation. This employs a (smoothed) aggregation technique and does not require the introduction of a coarse grid. We consider a set of assumptions...
Analysis of two-level domain decomposition preconditioners based on aggregation
In this paper we present two-level overlapping domain decomposition preconditioners for the finite-element discretisation of elliptic problems in two and three dimensions. The computational domain is partitioned into overlapping subdomains, and a coarse space correction is added. We present an algebraic way to define the coarse space, based on the concept of aggregation. This employs a (smoothed) aggregation technique and does not require the introduction of a coarse grid. We consider a...
Application du théorème de Sylvester à la localisation des valeurs propres de dans le cas symétrique
Application of the infinitely many times repeated BNS update and conjugate directions to limited-memory optimization methods
To improve the performance of the L-BFGS method for large scale unconstrained optimization, repeating of some BFGS updates was proposed e.g. in [1]. Since this can be time consuming, the extra updates need to be selected carefully. We show that groups of these updates can be repeated infinitely many times under some conditions, without a noticeable increase of the computational time; the limit update is a block BFGS update [17]. It can be obtained by solving of some Lyapunov matrix equation whose...
Application of the partitioning method to specific Toeplitz matrices
We propose an adaptation of the partitioning method for determination of the Moore-Penrose inverse of a matrix augmented by a block-column matrix. A simplified implementation of the partitioning method on specific Toeplitz matrices is obtained. The idea for observing this type of Toeplitz matrices lies in the fact that they appear in the linear motion blur models in which blurring matrices (representing the convolution kernels) are known in advance. The advantage of the introduced method is a significant...
Applications of Shortest Path Algorithms to Matrix Scalings.
Applications of the Moore-Penrose inverse in digital image restoration.
Applying approximate LU-factorizations as preconditioners in eight iterative methods for solving systems of linear algebraic equations
Many problems arising in different fields of science and engineering can be reduced, by applying some appropriate discretization, either to a system of linear algebraic equations or to a sequence of such systems. The solution of a system of linear algebraic equations is very often the most time-consuming part of the computational process during the treatment of the original problem, because these systems can be very large (containing up to many millions of equations). It is, therefore, important...
Approximate determination of eigenvalues and eigenvectors of selfadjoint operators