It is a common belief that Tikhonov scheme with ‖ · ‖L2 -penalty fails to reconstruct a sparse structure with respect to a given system {φi}. However, in this paper we present a procedure for sparsity reconstruction, which is totally based on the standard Tikhonov method. This procedure consists of two steps. At first Tikhonov scheme is used as a sieve to find the coefficients near φi, which ar...

Lanczos-hybrid regularization methods have been proposed as effective approaches for solving largescale ill-posed inverse problems. Lanczos methods restrict the solution to lie in a Krylov subspace, but they are hindered by semi-convergence behavior, in that the quality of the solution first increases and then decreases. Hybrid methods apply a standard regularization technique, such as Tikhonov...

We develop numerically stable and accurate stochastic simulation approaches for solving dynamic economic models. First, instead of standard least-squares approximation methods, we examine a variety of alternatives, including leastsquares methods using singular value decomposition and Tikhonov regularization, least-absolute deviations methods, and principal component regression method, all of wh...

This paper describes a minimax state estimation approach for linear Differential-Algebraic Equations (DAE) with uncertain parameters. The approach addresses continuous-time DAE with non-stationary rectangular matrices and uncertain bounded deterministic input. An observation’s noise is supposed to be random with zero mean and unknown bounded correlation function. Main results are a Generalized ...

rational functions are of great interest to engineers and geoscientists. the rational polynomial coefficient (rpc) model as a generalized sensor model has been introduced as an alternative for the rigorous sensor model of the satellite imaging. numerical instability of normal equations is the only single obstacle to the implementation of these functions. practically, estimating rational functio...

the methods applied to regularization of the ill-posed problems can be classified under “direct” and “indirect” methods. practice has shown that the effects of different regularization techniques on an ill-posed problem are not the same, and as such each ill-posed problem requires its own investigation in order to identify its most suitable regularization method. in the geoid computations witho...

We develop a hybrid iterative approach for computing solutions to large-scale illposed inverse problems via Tikhonov regularization. We consider a hybrid LSMR algorithm, where Tikhonov regularization is applied to the LSMR subproblem rather than the original problem. We show that, contrary to standard hybrid methods, hybrid LSMR iterates are not equivalent to LSMR iterates on the directly regul...

For a parameter-dependent system of ordinary differential equations we present a systematic approach to the determination of parameter values near which singular perturbation scenarios (in the sense of Tikhonov and Fenichel) arise. We call these special values Tikhonov parameter values. The principal application we intend is to equations that describe chemical reactions, in the context of quasi...

Magnetic resonance images are affected by motion artefacts due to breathing and cardiac beating that occur during the acquisition. Methods for joint reconstruction of image and motion have been proposed recently. Such optimization problems are ill-conditioned, therefore regularization methods are required such as motion smoothness constraints using the Tikhonov method. However with Tikhonov met...

It is well known that Tikhonov regularization in standard form may determine approximate solutions that are too smooth, i.e., the approximate solution may lack many details that the desired exact solution might possess. Two different approaches, both referred to as fractional Tikhonov methods have been introduced to remedy this shortcoming. This paper investigates the convergence properties of ...