An Iterative Method for the Matrix Principal n-th Root

In this paper we give an iterative method to compute the principal n-th root and the principal inverse n-th root of a given matrix. As we shall show this method is locally convergent. This method is analyzed and its numerical stability is investigated.

Growing Neural Networks Using Nonconventional Activation Functions

In the paper, an ontogenic artificial neural network (ANNs) is proposed. The network uses orthogonal activation functions that allow significant reducing of computational complexity. Another advantage is numerical stability, because the system of activation functions is linearly independent by definition. A learning procedure for proposed ANN with guaranteed convergence to the global minimum of error function in the parameter space is developed. An algorithm for structure network structure adaptation is proposed. The algorithm allows adding or deleting a node in real-time without retraining of the network. Simulation results confirm the efficiency of the proposed approach.

Viability, Optimality and Stability of Dynamical Systems and Estimation of Convergence of Numerical Schemes

AMS subject classification: 49N35,49N55,65Lxx.

Multibody System Mechanics: Modelling, Stability, Control, and Robustness by V. A. Konoplev and A. Cheremensky

BOOK REVIEWS Multibody System Mechanics: Modelling, Stability, Control, and Ro- bustness, by V. A. Konoplev and A. Cheremensky, Mathematics and its Appli- cations Vol. 1, Union of Bulgarian Mathematicians, Sofia, 2001, XXII + 288 pp., $ 65.00, ISBN 954-8880-09-01

Stability of an Optimal Schedule for a Job-Shop Problem with Two Jobs

The usual assumption that the processing times of the operations are known in advance is the strictest one in scheduling theory. This assumption essentially restricts practical aspects of deterministic scheduling theory since it is not valid for the most processes arising in practice. The paper is devoted to a stability analysis of an optimal schedule, which may help to extend the significance of scheduling theory for decision-making in the real-world applications. The term stability is generally used for the phase of an algorithm, at which an optimal solution of a problem has already been found, and additional calculations are performed in order to study how solution optimality depends on variation of the numerical input data.