Improving the convergence of iterative methods
The author considers the operator equation . Methods for acceleration of convergence of the iterative process are investigated.
Inverse problems in spaces of measures
The ill-posed problem of solving linear equations in the space of vector-valued finite Radon measures with Hilbert space data is considered. Approximate solutions are obtained by minimizing the Tikhonov functional with a total variation penalty. The well-posedness of this regularization method and further regularization properties are mentioned. Furthermore, a flexible numerical minimization algorithm is proposed which converges subsequentially in the weak* sense and with rate 𝒪(n-1)...
Iterative refinement for approximate eigenelements of compact operators
Iterative solution of eigenvalue problems for normal operators
We will discuss Kellogg's iterations in eigenvalue problems for normal operators. A certain generalisation of the convergence theorem is shown.
Linear problems (with extended range) have linear optimal algorithms.
Moving Dirichlet boundary conditions
This paper develops a framework to include Dirichlet boundary conditions on a subset of the boundary which depends on time. In this model, the boundary conditions are weakly enforced with the help of a Lagrange multiplier method. In order to avoid that the ansatz space of the Lagrange multiplier depends on time, a bi-Lipschitz transformation, which maps a fixed interval onto the Dirichlet boundary, is introduced. An inf-sup condition as well as existence results are presented for a class of second...
On a certain algorithm of eigenvalue localization for normal operators
On determination of eigenvalues and eigenvectors of selfadjoint operators
Two simple methods for approximate determination of eigenvalues and eigenvectors of linear self-adjoint operators are considered in the following two cases: (i) lower-upper bound of the spectrum of is an isolated point of ; (ii) (not necessarily an isolated point of with finite multiplicity) is an eigenvalue of .
On Morozov's method for Tikhonov regularization as an optimal order yielding algorithm.
On spectral approximation. Part 1. The problem of convergence
On spectral approximation. Part 2. Error estimates for the Galerkin method
On strongly stable approximations.
In this paper we prove that the convergence of (T - Tn)Tn-k to zero in operator norm (plus some technical conditions) is a sufficient condition for Tn to be a strongly stable approximation to T, thus extending some previous results existing in the literature.
On the convergence of eigenvalues for mixed formulations
On the convergence of semiiterative methods to the Drazin inverse solution of linear equations in Banach spaces.
On the Fast Convergence of a Galerkin-Like Method for Equations of the Second Kind.
On the Operational Solution of a System of Fractional Differential Equations
MSC 2010: 26A33, 44A45, 44A40, 65J10We consider a linear system of differential equations with fractional derivatives, and its corresponding system in the field of Mikusiński operators, written in a matrix form, by using the connection between the fractional and the Mikusiński calculus. The exact and the approximate operational solution of the corresponding matrix equations, with operator entries are determined, and their characters are analyzed. By using the packages Scientific Work place and...
On the Regularization of Projection Methods for Solving Ill-Posed Problems.
On the relationship between difference and projection-difference methods
On the Steps of Convergence of Approximate Eigenvectors in the Rayleigh-Schrödinger Series.
Optimal order yielding discrepancy principle for simplified regularization in Hilbert scales: finite-dimensional realizations.