In this paper we develop a novel criterion for choosing regularization parameters for nonsmooth Tikhonov functionals. The proposed criterion is solely based on the value function, and thus applicable to a broad range of functionals. It is analytically compared with the local minimum criterion, and a posteriori error estimates are derived. An efficient numerical algorithm for computing the minim...

This paper presents a method for choosing the regularization parameter (α) appearing in Tikhonov regularization based on the L-curve. The point of intersection between the L-curve and a straight line of arbitrary slope tangent to the L-curve is used as the criterion for identifying the corner of the L-curve and the corresponding value of α. This condition is shown to result in a new scalar alge...

In this work, we compare two extensions of two different topic models for the same problem of recommending full-text items: previously developed SVD-LDA and its counterpart SVD-ARTM based on additive regularization. We show that ARTM naturally leads to the inference algorithm that has to be painstakingly developed for LDA.

We consider least-squares problems where the coef-cient matrices A; b are unknown-but-bounded. We minimize the worst-case residual error using (convex) second-order cone programming (SOCP), yielding an algorithm with complexity similar to one singular value decomposition of A. The method can be interpreted as a Tikhonov regularization procedure, with the advantage that it provides an exact boun...

This paper presents a method for choosing the regularization parameter (α) appearing in Tikhonov regularization based on the L-curve. The point of intersection between the L-curve and a straight line of arbitrary slope tangent to the L-curve is used as the criterion for identifying the corner of the L-curve and the corresponding value of α. This condition is shown to result in a new scalar alge...

Abstract. In this paper we deal with linear inverse problems and convergence rates for Tikhonov regularization. We consider regularization in a scale of Banach spaces, namely the scale of Besov spaces. We show that regularization in Banach scales differs from regularization in Hilbert scales in the sense that it is possible that stronger source conditions may lead to weaker convergence rates an...

Empirical data collected in practice usually are not exact. For various reasons it is often suggested in many applications to replace the original data matrix by some lower dimensional representation obtained via subspace approximation or truncation. The truncated singular value decomposition, for example, is one of the most commonly used representations. This note attempts to shed some light o...

Tikhonov regularization is one of the most popular approaches to solving linear discrete ill-posed problems. The choice of regularization matrix may significantly affect the quality of the computed solution. When the regularization matrix is the identity, iterated Tikhonov regularization can yield computed approximate solutions of higher quality than (standard) Tikhonov regularization. This pap...

An H∞ control problem for linear systems with point-wise and distributed state delays is considered. The case, where the output equation does not contain the control variable, is treated. In this case, the problem is singular, i.e., the gametheoretic Riccati equation approach is not applicable to its solution. A method of solution of this problem, based on its regularization and asymptotic solu...