摘要:

AbstractAn approximation method is given for calculating the periodic solutions of non‐linear oscillators based upon the well‐known method of collocation, which belongs to the class of projection methods. Unlike available techniques, the method leads to a simple and efficient algorithmic procedure which consists of solving a system of non‐linear equations given in a simple explicit form.To demonstrate the effectiveness of the proposed algorithm, the results of some typical oscillator circuits are pro

ISSN:0098-9886    

DOI:10.1002/cta.4490200202

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1992

数据来源: WILEY

摘要:

AbstractA general method for analysing asynchronous high‐order two‐frequency oscillators is presented. the oscillator model is made up of aGCnon‐linear parallel group embedded in a linear lumped time‐invariant network of any order. the approach devised rests on the identification of a pair of narrow‐band impedance operators which permit one to derive first‐approximation steady state and dynamic equations in the phasor domain—as well as stability criteria—in a simple and expressive manner. Previous results from averaging and perturbation treatments on fourth‐order asynchronous oscillators are shown to be obtainable from this theory as particular cases. the sixth‐order oscillator chosen as an application example shows that computational efficiency and accuracy are among the fea

ISSN:0098-9886    

DOI:10.1002/cta.4490200203

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1992

数据来源: WILEY

摘要:

AbstractTo perform a mixed mode analysis with the electrical and gate levels in the waveform relaxation context, an initial steady state of the analysed circuit must be computed prior to transient analysis. By using Boolean algebra and discrete relaxation, we propose various algorithms to compute a stable state or a stable total state of a logic synchronous sequential system with master‐slave flip‐flops. Furthermore, a dynamic ordering of the logic gates which improves the convergence of the computation of a stable total state is presented. We show that a stable state can be calculated within only two iterati

ISSN:0098-9886    

DOI:10.1002/cta.4490200204

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1992

数据来源: WILEY

摘要:

AbstractIn this paper we present in a unified framework the gradient algorithms employed in the adaptation of linear time filters (TF) and the supervised training of (non‐linear) neural networks (NN). the optimality criteria used to optimize the parametersHof the filter or network are the least squares (LS) and least mean squares (LMS) in both contexts. They respectively minimize the total or the mean squares of the errore(k)between an (output) reference sequenced(k)and the actual system outputy(k)corresponding to the inputX(k). Minimization is performed iteratively by a gradient algorithm. the indexkin (TF) is time and it runs indefinitely. Thus iterations start as soon as reception ofX(k)begins. the recursive algorithm for the adaptationH(k– 1) →H(k)of the parameters is implemented each time a new inputX(k)is observed. When training a (NN) with a finite number of examples, the indexkdenotes the example and it is upper‐bounded. Iterative (block) algorithms wait until allKexamples are received to begin the network updating. However,Kbeing frequently very large, recursive algorithms are also often preferred in (NN) training, but they raise the question of ordering the examplesX(k).Except in the specific case of a transversal filter, there is no general recursive technique for optimizing the LS criterion. However,X(k)is normally a random stationary sequence; thus LS and LMS are equivalent whenkbecomes large. Moreover, the LMS criterion can always be minimized recursively with the help of the stochastic LMS gradient algorithm, which has low computational complexity.In (TF),X(k)is a sliding window of (time) samples, whereas in the supervised training of (NN) with arbitrarily ordered examples,X(k– 1) andX(k)have nothing to do with each other. When this (major) difference is rubbed out by plugging a time signal at the network input, the recursive algorithms recently developed for (NN) training become similar to those of adaptive filtering. In this context the present paper displays the similarities between adaptive cascaded linear filters and trained multilayer networks. It is also shown that there is a close similarity between adaptive recursive filters and neural networks including feedback loops.The classical filtering approach is to evaluate the gradient by ‘forward propagation’, whereas the most popular (NN) training method uses a gradient backward propagation method. We show that when a linear (TF) problem is implemented by an (NN), the two approaches are equivalent. However, the backward method can be used for more general (non‐linear) filtering problems. Conversely, new insights can be drawn in the (NN) context by the use of a gradient forward computation.The advantage of the (NN) framework, and in particular of the gradient backward propagation approach, is evidently to have a much larger spectrum of applications than (TF), since (i) the inputs are arbitrary and (ii) the (NN) can perform

ISSN:0098-9886    

DOI:10.1002/cta.4490200205

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1992

数据来源: WILEY

摘要:

AbstractWe introduce the concept ofperfect pairsof trees of a graph as a natural generalization of so‐called maximally distant pairs of trees. Several propositions and remarks are presented to display the properties of this new notion. Lemma 1, which plays a central role, gives five equivalent statements characterizing the relation ‘to be maximally distant from’ between pairs of trees. Symmetrization of this relation leads to our concept of a perfect pair of trees, the properties of which are given in Theorem 1. Remark 4 shows how naturally our new concept arises. Additionally, certain examples are provided to illustrate perfect pair structures in a

ISSN:0098-9886    

DOI:10.1002/cta.4490200206

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1992

数据来源: WILEY

ISSN:0098-9886    

DOI:10.1002/cta.4490200207

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1992

数据来源: WILEY

ISSN:0098-9886    

DOI:10.1002/cta.4490200201

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1992

数据来源: WILEY