In this letter we present a new way for computing generalized eigenvalue problems in engineering applications. To transform a generalized eigenvalue problem into an associated problem for solving nonlinear dynamic equations by using optimization techniques, we can determine all eigenvalues and their eigenvectors for general complex matrices. Numerical examples are given to verify the formula of dynamic equations.

Conventional approaches to neural network training do not consider possibility of selecting training samples dynamically during the learning phase. Neural network is simply presented with the complete training set at each iteration of the learning. The learning can then become very costly for large data sets. Huge redundancy of data samples may lead to the ill-conditioned training problem. Ill-conditioning during the training causes rank-deficiencies of error and Jacobean matrices, which results in slower convergence speed, or in the worst case, the failure of the algorithm to progress. Rank-deficiencies of essential matrices can be avoided by an appropriate selection of training exemplars at each iteration of training. This article presents underlying theoretical grounds for dynamic sample selection (DSS), that is mechanism enabling to select a subset of training set at each iteration. Theoretical material is first presented for general objective functions, and then for the objective functions satisfying the Lipschitz continuity condition. Furthermore, implementation specifics of DSS to first order line search techniques are theoretically described.

Computational expensiveness of the training techniques, due to the extensiveness of the data set, is among the most important factors in machine learning and neural networks. Oversized data set may cause rank-deficiencies of Jacobean matrix which plays essential role in training techniques. Then the training becomes not only computationally expensive but also ineffective. In [1] the authors introduced the theoretical grounds for dynamic sample selection having a potential of eliminating rank-deficiencies. This study addresses the implementation issues of the dynamic sample selection based on the theoretical material presented in [1]. The authors propose a sample selection algorithm implementable into an arbitrary optimization technique. An ability of the algorithm to select a proper set of samples at each iteration of the training has been observed to be very beneficial as indicated by several experiments. Recently proposed approaches to sample selection work reasonably well if pattern-weight ratio is close to 1. Small improvements can be detected also at the values of the pattern-weight ratio equal to 2 or 3. The dynamic sample selection approach, presented in this article, can increase the convergence speed of first order optimization techniques, used for training MLP networks, even at the value of the pattern-weight ratio (E-FP) as high as 15 and possibly even more.

This paper condiders a problem of logecal configuration in reconfigurable VCDN (Virtual Circuit Data Networks) which is analyzed through a mimimax approach, and its objective is to minimize the largest delay on any logical link, measured in both queueing delay and propagation delay. The problem is formulated as a 0/1 mixed integer programming and analyzed by decomposing it into two subproblems, called routing and dimensioning problems, for which an efficient hauristic algorithm is proposed in an iterating process made beween the two subproblems for solution improvement. The algorithm is tested for its performance eveluation.

A new design method for 2-D IIR digital filters, having a separable denominator,in the spatial domain is presented. The modified Gauss Method is applied in the iterating calculation of the filter coefficients. Also, the 1-D state space representation of the denominator is utilized in determining the impulse response of the designed IIR transfer function and its partial derivatives systematically while the numerator is expressed by a nonseparable polynomial. The error criterion function, which also includes the response outside the given region of support, is minimized in the least square sense. Convergence, together with the stability of the resulting filttr, are guaranteed.

In most of the methods proposed so far to design approximately linear phase IIR digital filters (IIR DFs), the design takes place only in the time or in the frequency domain. However, when both magnitude and phase responses are considered, IIR DFs with better frequency responses can be obtained if their characteristics in both domains are taken into account. This paper proposes a design method for approximately linear phase IIR DFs, which is based on parameter estimation techniques in the time domain followed by a nonlinear optimization algorithm in the frequency domain. Several examples are presented, illustrating the proposed method.

General estimation technique using covariance information is proposed for white Gaussian and white Gaussian plus coloured observation noises in linear stationary stochastic systems. Namely, autocovariance data of signal and coloured noise appear in a semi-degenerate kernel, which represents functional expression of the autocovariance data, in the current technique. Then the signal is estimated by directly using autocovariance data of signal and coloured noise. On the other hand, in the previous technique, the covariance information is expressed in the form of a semi-degenerate kernel, but its elements do not include any autocovariance data.