Recovering decay rates from noisy measurements with maximum entropy in the mean.
Recovery of an unknown flux in parabolic problems with nonstandard boundary conditions: Error estimates
In this paper, we consider a 2nd order semilinear parabolic initial boundary value problem (IBVP) on a bounded domain , with nonstandard boundary conditions (BCs). More precisely, at some part of the boundary we impose a Neumann BC containing an unknown additive space-constant , accompanied with a nonlocal (integral) Dirichlet side condition. We design a numerical scheme for the approximation of a weak solution to the IBVP and derive error estimates for the approximation of the solution and...
Rectangular Scott-type permanents.
Recurrent evaluation of integrals of the type , with respect to numerical stability
Recursive algorithms for solving systems of nonlinear equations
A way of generalizing onedimensional root-finding algorithms to the multidimensional case by means of recursion is shown and means to make the algorithms robust are discussed. In the second part, the algorithm is modified so as to exploit sparsity of large systems of equations for reducing the recursion depth and consequently decreasing the computational requirements of the method.
Recursive classification of pseudo-random sequences
Recursive computation of certain integrals of elliptic type.
Recursive linear estimation for discrete-time systems in the presence of different multiplicative observation noises.
Recursive smoothers for hidden discrete-time Markov chains.
Reduced basis method for finite volume approximations of parametrized linear evolution equations
The model order reduction methodology of reduced basis (RB) techniques offers efficient treatment of parametrized partial differential equations (P2DEs) by providing both approximate solution procedures and efficient error estimates. RB-methods have so far mainly been applied to finite element schemes for elliptic and parabolic problems. In the current study we extend the methodology to general linear evolution schemes such as finite volume schemes for parabolic and hyperbolic evolution equations....
Reduced basis solver for stochastic Galerkin formulation of Darcy flow with uncertain material parameters
In this contribution, we present a solution to the stochastic Galerkin (SG) matrix equations coming from the Darcy flow problem with uncertain material coefficients in the separable form. The SG system of equations is kept in the compressed tensor form and its solution is a very challenging task. Here, we present the reduced basis (RB) method as a solver which looks for a low-rank representation of the solution. The construction of the RB consists of iterative expanding of the basis using Monte...
Reduced continuity finite element methods for first order scalar hyperbolic equations
Reduced order controllers for Burgers' equation with a nonlinear observer
A method for reducing controllers for systems described by partial differential equations (PDEs) is applied to Burgers' equation with periodic boundary conditions. This approach differs from the typical approach of reducing the model and then designing the controller, and has developed over the past several years into its current form. In earlier work it was shown that functional gains for the feedback control law served well as a dataset for reduced order basis generation via the proper orthogonal...
Reduced Piecewise Bivariate Hermite Interpolations.
Reducibility and characterization of symplectic Runge-Kutta methods.
Reducing of variance by a combined scheme based on Bernstein polynomials.
Reducing the bandwidth in solving linear algebraic systems arising in the finite element method
The matrix of the system of linear algebraic equations, arising in the application of the finite element method to one-dimensional problems, is a bandmatrix. In approximations of high order, the band is very wide but the elements situated far from the diagonal of the matrix are negligibly small as compared with the diagonal elements. The aim of the paper is to show on a model problem that in practice it is possible to work with a matrix of the system the bandwidth of which is reduced. A simple...
Réduction de la résolution d'un problème de réseau maillé (B) : sur la convergence locale de certaines méthodes
Reduction of huge, sparse matrices over finite fields via created catastrophes.
Reduktionsverfahren für Differenzengleichungen bei Randwertaufgaben II. -Solving Difference Equations for Boundary Value Problems by Reduction Methods II.