Original title unknown
Partition of unity method for Helmholtz equation: -convergence for plane-wave and wave-band local bases
In this paper we study the -version of the Partition of Unity Method for the Helmholtz equation. The method is obtained by employing the standard bilinear finite element basis on a mesh of quadrilaterals discretizing the domain as the Partition of Unity used to paste together local bases of special wave-functions employed at the mesh vertices. The main topic of the paper is the comparison of the performance of the method for two choices of local basis functions, namely a) plane-waves, and b) wave-bands....
Perturbation series and defect correction for the refinement of approximate eigenelements of linear integral operators
Pointwise Rational Approximation and Iterative Methods for Ill-Posed Problems.
Projection methods in the approximate solution of the eigenvalue problem in a Hilbert space
Quasi-iteration methods of Chebyshev type for the approximate solution of operator equations
Regularity Theorems and Optimal Errors Estimates for Linear Parabolic Cauchy Problems.
Resolvent estimates in controllability theory and applications to the discrete wave equation
We briefly present the difficulties arising when dealing with the controllability of the discrete wave equation, which are, roughly speaking, created by high-frequency spurious waves which do not travel. It is by now well-understood that such spurious waves can be dealt with by applying some convenient filtering technique. However, the scale of frequency in which we can guarantee that none of these non-traveling waves appears is still unknown in general. Though, using Hautus tests, which read the...
Semi-Iterative Methods for the Approximate Solution of Ill-Posed Problems.
Sequential regularization of ill-posed problems involving unbounded operators
Single step methods for inhomogeneous linear differential equations in Banach space
Smoothing and interpolation in a convex subset of a Hilbert space : II. The semi-norm case
Some functions of eigenvalues of normal operator
Kellogg's iterations in the eigenvalue problem are discussed with respect to the boundary spectrum of a linear normal operator.
Some insights into the regularization of ill-posed problems.
Some possibilities in solving operator equations using non stationary iterative method
Some remarks on best regularization
Some theorems on the stability of numerical processes
Nell’articolo si dimostrano alcuni teoremi sulla stabilità dei processi numerici di Ritz e della collocazione in rapporto agli errori di «distorsione».
Spectral approximation of positive operators by iteration subspace method
The iteration subspace method for approximating a few points of the spectrum of a positive linear bounded operator is studied. The behaviour of eigenvalues and eigenvectors of the operators arising by this method and their dependence on the initial subspace are described. An application of the Schmidt orthogonalization process for approximate computation of eigenelements of operators is also considered.
Splines and pseudo-inverses
Stabilité et convergence des méthodes spectrales polynômiales. Application à l'équation d'advection