Related papers: A GCV based Arnoldi-Tikhonov regularization method
This paper introduces and analyzes an original class of Krylov subspace methods that provide an efficient alternative to many well-known conjugate-gradient-like (CG-like) Krylov solvers for square nonsymmetric linear systems arising from…
Various problems in computer vision and medical imaging can be cast as inverse problems. A frequent method for solving inverse problems is the variational approach, which amounts to minimizing an energy composed of a data fidelity term and…
The Inverse Problem for the estimation of a point-wise approximation error occurring at the discretization and solving of the system of partial differential equations is addressed. The set of the differences between the numerical solutions…
For large-scale discrete ill-posed problems, LSQR, a Lanczos bidiagonalization process based Krylov method, is most often used. It is well known that LSQR has natural regularizing properties, where the number of iterations plays the role of…
This paper explores the incorporation of Tikhonov regularization into the least squares approximation scheme using trigonometric polynomials on the unit circle. This approach encompasses interpolation and hyperinterpolation as specific…
In this work, we consider the linear inverse problem $y=Ax+\epsilon$, where $A\colon X\to Y$ is a known linear operator between the separable Hilbert spaces $X$ and $Y$, $x$ is a random variable in $X$ and $\epsilon$ is a zero-mean random…
Although regularization methods based on derivatives are favored for their robustness and computational simplicity, research exploring higher-order derivatives remains limited. This scarcity can possibly be attributed to the appearance of…
This paper is concerned with recovering the solution of a final value problem associated with a parabolic equation involving a non linear source and a non-local term, which to the best of our knowledge has not been studied earlier. It is…
We define an a posteriori verification procedure that enables to control and certify PGD-based model reduction techniques applied to parametrized linear elliptic or parabolic problems. Using the concept of constitutive relation error, it…
LSQR, a Lanczos bidiagonalization based Krylov subspace iterative method, and its mathematically equivalent CGLS applied to normal equations system, are commonly used for large-scale discrete ill-posed problems. It is well known that LSQR…
Generalized cross-validation (GCV) is a widely-used method for estimating the squared out-of-sample prediction risk that employs a scalar degrees of freedom adjustment (in a multiplicative sense) to the squared training error. In this…
Vector tomography methods intend to reconstruct and visualize vector fields in restricted domains by measuring line integrals of projections of these vector fields. Here, we deal with the reconstruction of irrotational vector functions from…
The aim of this paper is to investigate the use of an entropic projection method for the iterative regularization of linear ill-posed problems. We derive a closed form solution for the iterates and analyze their convergence behaviour both…
In this work we propose and analyze a numerical method for electrical impedance tomography of recovering a piecewise constant conductivity from boundary voltage measurements. It is based on standard Tikhonov regularization with a…
For solving linear ill-posed problems regularization methods are required when the right hand side is with some noise. In the present paper regularized solutions are obtained by implicit iteration methods in Hilbert scales. % By exploiting…
This paper investigates the properties of the solutions of the generalised discrete algebraic Riccati equation arising from the solution of the classic infinite-horizon linear quadratic control problem. In particular, a geometric analysis…
Optimization on Riemannian manifolds widely arises in eigenvalue computation, density functional theory, Bose-Einstein condensates, low rank nearest correlation, image registration, and signal processing, etc. We propose an adaptive…
A numerical algorithm for regularization of the solution of the source problem for the diffusion-logistic model based on information about the process at fixed moments of time of integral type has been developed. The peculiarity of the…
We systematically investigated the limited inverse discrete Fourier transform of the quasi distributions from the perspective of inverse problem theory. This transformation satisfies two of Hadamard's well-posedness criteria, existence and…
We study multi-parameter Tikhonov regularization, i.e., with multiple penalties. Such models are useful when the sought-for solution exhibits several distinct features simultaneously. Two choice rules, i.e., discrepancy principle and…