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  • 1
    Electronic Resource
    Electronic Resource
    On factoring the polyvariance operator (1981)
    Springer
    Theory of computing systems 14 (1981), S. 67-82 
    Details
    ISSN: 1433-0490
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract The minimum phase factorization of bounded Hermitian operators (covariance operators) is an essential ingredient in linear filtering and stochastic control. In a recent article the author studied an analogous class of polynomic filtering and stochastic control problems. The present study uses the concept of a Hilbert scale to establish a minimum phase factorization procedure for the polynomic setting. The linear theory is carried over in its entirety.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01752390
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Operator factorization on partially ordered Hilbert resolution spaces (1983)
    Springer
    Theory of computing systems 16 (1983), S. 67-77 
    Details
    ISSN: 1433-0490
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract The classical study of factorization of operators along a linearly ordered chain of orthoprojectors is extended to the more general context of partially ordered chains. With this extension the factorization theory becomes relevant to stochastic approximation, filtering and control of multidimensional systems.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01744570
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    A basic optimization problem in linear systems (1971)
    Springer
    Theory of computing systems 5 (1971), S. 20-44 
    Details
    ISSN: 1433-0490
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01691464
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    Paper (German National Licenses)
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  • 4
    Electronic Resource
    Electronic Resource
    Approximation by bernstein systems (1977)
    Springer
    Theory of computing systems 11 (1977), S. 259-274 
    Details
    ISSN: 1433-0490
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract LetK denote an arbitrary compact subset of realL 2. Letf be any causal continuous function onL 2. Then there is a linear differential system:ż(t)=A(t)z(t)+B(t)u(t), and a memoryless polynomic state to output mapw(t)=φ(z(t),t) such that the system, $$\hat f$$ , thereby computed satisfies $$\mathop {\sup }\limits_{u \in K} ||f(u) - \hat f(u)||〈 \varepsilon$$ whereε 〉0 is arbitrary. This and other results are developed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01768480
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    Paper (German National Licenses)
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  • 5
    Electronic Resource
    Electronic Resource
    Recent progress on higher order moment neural arrays (1993)
    Springer
    Circuits, systems and signal processing 12 (1993), S. 309-329 
    Details
    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract Higher order moment computations are generally necessary wherever the recognition task exceeds the confines of linearity. This paper provides an overview of recent progress on a specific neural network design, which explicitly uses higher order moment information. Attention is focused on the training algorithms used in the design and on network performance in prototype applications.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01189879
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  • 6
    Electronic Resource
    Electronic Resource
    Array resolutions of linear maps (1987)
    Springer
    Circuits, systems and signal processing 6 (1987), S. 127-137 
    Details
    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract The identification of concurrency is a critical factor in the high-speed calculation of algorithms. This study considers maps onX, a discrete resolution space. We establish a resolution on the space of linear maps onX which exhibit compatibility with array processing. Our results are extended to the partially ordered resolution space setting. While on-line array processing motivates our study, the results also suggest efficient processing procedures for off-line applications.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01598955
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    Paper (German National Licenses)
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  • 7
    Electronic Resource
    Electronic Resource
    The approximating capability of fast forms (1999)
    Springer
    Circuits, systems and signal processing 18 (1999), S. 365-376 
    Details
    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract In earlier studies the concept of a fast form was generalized to a format that unified such discrete transform examples as the FFT, the FCT, the FST, and the FHT. In this study we consider the approximation of arbitrary linear maps by fast forms. Using simulation we evaluate the approximation capabilities of the generalized fast form.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01200788
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    Paper (German National Licenses)
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  • 8
    Electronic Resource
    Electronic Resource
    Auxilliary computations for perceptron networks (1996)
    Springer
    Circuits, systems and signal processing 15 (1996), S. 51-69 
    Details
    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract In this study we consider a multilayer perceptron network with sigmoidal activation and trained via the backpropagation algorithm. The output of all neurons is collected and a simple linear regression is performed. It is shown that untrained networks with randomly chosen coefficients perform comparably with fully trained networks. This result casts a new light on the role of activation functions, the impact of dimensionality, and the efficacy of training algorithms such as backpropagation.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01187693
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    Paper (German National Licenses)
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  • 9
    Electronic Resource
    Electronic Resource
    An overview of the special issue: Concurrent architectures for signal processing (1988)
    Springer
    Circuits, systems and signal processing 7 (1988), S. 115-118 
    Details
    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01602093
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    Paper (German National Licenses)
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  • 10
    Electronic Resource
    Electronic Resource
    Generalized Schur-Coleski factorization with applications to image processing (1984)
    Springer
    Circuits, systems and signal processing 3 (1984), S. 315-325 
    Details
    ISSN: 1531-5878
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract A special type of factorization for operators defined on partially ordered Hilbert resolution spaces is considered. The main result includes, as a particular case, the classical Schur-Coleski triangular factorization. Connections with stochastic optimization and image-processing problems are established.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01599079
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    Paper (German National Licenses)
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