In this paper, we study statistical inverse problems. We are interested in the case where the operator is not exactly known. Using the penalized blockwise Stein’s rule, we construct an estimator that produces sharp asymptotic oracle inequalities in different settings. In particular, we consider the case, where the set of bases is not associated with the singular value decomposition. The represe...

‎in this paper‎, ‎we consider an inverse boundary value problem for two-dimensional heat equation in an annular domain‎. ‎this problem consists of determining the temperature on the interior boundary curve from the cauchy data (boundary temperature and heat flux) on the exterior boundary curve‎. ‎to this end‎, ‎the boundary integral equation method is used‎. ‎since the resulting system of linea...

In this paper, the regularized solutions of an ill{conditioned system of linear equations are computed for several values of the regularization parameter. Then, these solutions are extrapolated at = 0 by various vector rational extrapolations techniques built for that purpose. These techniques are justiied by an analysis of the regularized solutions based on the singular value decomposition and...

Abstract. Tikhonov regularization is one of the most popular approaches to solve discrete ill-posed problems with error-contaminated data. A regularization operator and a suitable value of a regularization parameter have to be chosen. This paper describes an iterative method, based on Golub-Kahan bidiagonalization, for solving large-scale Tikhonov minimization problems with a linear regularizat...

The solution of the linear system of equations Ax ≈ b arising from the discretization of an ill-posed integral equation with a square integrable kernel H(s, t) is considered. The Tikhonov regularized solution x is found as the minimizer of J(x) = {‖Ax − b‖2 + λ‖Lx‖2} and depends on regularization parameter λ which trades off the fidelity of the solution data fit and its smoothing norm, determin...

Inference of model parameters is one step in an engineering process often ending in predictions that support decision in the form of design or control. Incorporation of end goals into the inference process leads to more efficient goal-oriented algorithms that automatically target the most relevant parameters for prediction. In the linear setting the control-theoretic concepts underlying balance...

1. Introduction and historical remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160 2. Spectral estimators, parameter estimators and nonlinear problems . . . . . . . . . . . . . . . . . . . . . . . . . . . 164 3. Non-Hermitian quantum mechanics: connection to the harmonic inversion problem (HIP) . . . . . . . . . 167 4. HIP can be solve...

Following the results of cite{Med}, regarding the Aluthge transform of polynomial matrices, the symbolic computation of the Duggal transform of a polynomial matrix $A$ is developed in this paper, using the polar decomposition and the singular value decomposition of $A$. Thereat, the polynomial singular value decomposition method is utilized, which is an iterative algorithm with numerical charac...

A deconvolution approach for dynamic contrast enhanced magnetic resonance imaging using an approximation basis of exponential functions constrained to be non-negative and non-increasing is developed and compared with widely used methods. Monotonicity in an exponential basis is implemented in terms of a newly derived condition which is a considerable generalization over a previous condition that...