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The paper deals with the theoretical background of the higher order singular value decomposition (HOSVD) based canonical form of functions. Furthermore in special case it describes the relation between the canonical form and the Hilbert-Schmidt type integral operators. The described techniques have a variety of applications, e.g. image processing, system identification, data compression, filtering, etc. As an example of application from the field of intelligent systems, a tensor-product based concept is introduced useful for approximating the behavior of a strongly non-linear system by locally tuned neural network models. The proposed approach may be a useful tool for solving many kind of black-box like identification problems. The weights in the corresponding layers of the input local models are jointly expressed in tensor-product form such a way ensuring the efficient approximation. Similar concept has been used by the authors for approximating the system matrix of linear parameter varying systems in state space representation. We hope that the proposed concept could be an efficient compromised modeling view using both the analytical and heuristic approaches.

Process chains are a common modeling paradigm for analysis and optimization of logistic processes, and are intensively used in many practical applications. The ProC/B toolset is a collection of software tools for modeling, analysis, validation and optimization of process chains. The ProC/B models can be translated into queueing networks or Petri nets, which can be solved by effective techniques and algorithms to evaluate performance metrics. The base queueing model with Mean-Value Analysis evaluation algorithm, and their adaptations for modeling thread pool and queue limit have been verified and validated for multi-tier software systems. The goal of our work is to adapt these models and algorithms for process chains to model parallel processes and queue limit.

This paper addresses the issues to establish performance models and evaluation methodologies applying the identified queue limit performance factors. The computational complexity of the novel algorithms is provided. It is demonstrated that the proposed models and algorithms can be used for performance prediction of web-based software systems in ASP.NET environment. The validity of the novel models and algorithms as well as the correctness of the performance prediction is proven with performance measurements. It is shown that the error of the suggested models and algorithms is less than the error of the original model and algorithm. These methods facilitate more efficient performance prediction of web-based software systems.

The main aim of the paper is to introduce a new representation domain advantageously usable also in the field of image processing. In this case the image is represented by polylinear functions on HOSVD basis. The paper gives an overview, how these functions can be reconstructed and how they can be applied in case of image processing. Comparing to other domains, using the proposed domain the image can be expressed by a reduced number of components (polylinear functions) by maintaining its quality. The efficiency of this representation form is demonstrated by performing an image resolution enhancement trough this new domain by maintaining its quality significantly.