Although the regularization increased the popularity of parameter identi)cation due to its capability of deriving a stable solution, the signi)cant problem is that the solution depends upon the regularization parameters chosen. This paper presents a technique for deriving solutions without the use of the parameters and, further, an optimization method, which can work e=ciently for problems of c...

We introduce three spectral regularization methods for solving a backward heat conduction problem (BHCP). For the three spectral regularization methods, we give the stability error estimates with optimal order under an a-priori and an a-posteriori regularization parameter choice rule. Numerical results show that our theoretical results are effective.

We describe two regularization techniques based on optimal control for solving two types of ill-posed problems. We include convergence proofs of the regularization method and error estimates. We illustrate our method through problems in signal processing and parameter identification using an efficient Riccati solver. Our numerical results are compared to the same examples solved using Tikhonov ...

In this paper, we set forth a new family of regularizing filters based on the magnitude response function of Chebyshev-I lowpass filter. The corresponding regularization strategies for inverse problem are constructed. The optimum asymptotic order of the regularized solution is obtained by a priori choice of the regularization parameter. Finally, numerical results are given to demonstrate the ef...

Solodkiı̆ (1998) applied the modified projection scheme of Pereverzev (1995) for obtaining error estimates for a class of regularization methods for solving ill-posed operator equations. But, no a posteriori procedure for choosing the regularization parameter is discussed. In this paper, we consider Arcangeli’s type discrepancy principles for such a general class of regularization methods with m...

In this paper we present a new scheme of a kernel adaptive regularization algorithm, where the kernel and the regularization parameter are adaptively chosen within regularization procedure. The construction of such fully adaptive regularization algorithm is motivated by the problem of reading the blood glucose concentration of diabetic patients. We describe how proposed scheme can be used for t...

The generalization ability of a neural network can sometimes be improved dramatically by regularization. To analyze the improvement one needs more refined results than the asymptotic distribution of the weight vector. Here we study the simple case of one-dimensional linear regression under quadratic regularization, i.e., ridge regression. We study the random design, misspecified case, where we ...

The widespread applicability of the multi-penalty regularization is limited by the fact that theoretically optimal rate of reconstruction for a given problem can be realized by a oneparameter counterpart, provided that relevant information on the problem is available and taken into account in the regularization. In this paper, we explore the situation, where no such information is given, but st...

The regularization of a convex program is exact if all solutions of the regularized problem are also solutions of the original problem for all values of the regularization parameter below some positive threshold. For a general convex program, we show that the regularization is exact if and only if a certain selection problem has a Lagrange multiplier. Moreover, the regularization parameter thre...

Tikhonov regularization with the regularization parameter determined by the discrepancy principle requires the computation of a zero of a rational function. We describe a cubically convergent zero-finder for this purpose. AMS subject classification: 65F22, 65H05, 65R32.