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1

Matrix black box algorithms - a survey

Respondek Jerzy

Bulletin of the Polish Academy of Sciences. Technical Sciences

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2022

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Vol. 70, nr 2

art. no. e140535

EN

The implementations of matrix multiplication on contemporary, vector-oriented, and multicore-oriented computer hardware are very carefully designed and optimized with respect to their efficiency, due to the essential significance of that operation in other science and engineering domains. Consequently, the available implementations are very fast and it is a natural desire to take advantage of the efficiency of those implementations in other problems, both matrix and nonmatrix. Such an approach is often called a black box matrix computation paradigm in the literature on the subject. In this article, we gathered a broad series of algorithms taking advantage of the efficiency of fast matrix multiplication algorithms in other mathematical and computer science operations.

2

Matrix profile for DDoS attacks detection

Alotaibi Faisal, Lisitsa Alexei

Annals of Computer Science and Information Systems

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2021

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Vol. 25

357--361

EN

Previous studies have focused on DDoS, which are a crucial problem in network security. This study explore a time series method MP, which has shown effective results in a number of applications. The MP is potentially well suited to use for DDoS as a rapid method of detection,a factor that is vital for the successful identification and cessation of DDoS.The study examined how the MP performed in diverse situations related to DDoS, as well as identifying those features that are most applicable in various scenarios.Results show the efficiency of MP against all types of DDoS with the exception of NTP.

3

Interval-Valued Intuitionistic Fuzzy Decision-Making Method using Index Matrices and Application in Outsourcing

Traneva Velichka, Tranev Stoyan, Mavrov Deyan

Annals of Computer Science and Information Systems

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2021

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Vol. 25

251--254

EN

Selecting a suitable outsourcing service provider is a challenging problem that requires discussion among a group of experts. The problems of this type belongs to the area of multicriteria decision-making. Interval-valued intuitionistic fuzzy sets, which are an extension of intuitionistic fuzzy sets, are a capable tool in modeling uncertain problems. In this paper we will formulate an optimal interval-valued intuitionistic fuzzy multicriteria decision-making problem in outsourcing and propose a new approach for the selection of the most appropriate candidates; as well as a software program for its automated solution, based on our previous libraries. As an example of a case study, an application of the algorithm on real data from a refinery is demonstrated.

4

Effect of Criteria Range on the Similarity of Results in the COMET Method

Shekhovtsov Andrii, Więckowski Jakub, Kizielewicz Bartłomiej, Sałabun Wojciech

Annals of Computer Science and Information Systems

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2021

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Vol. 25

453--457

EN

Defining input values in the decision-making process can be done with appropriate methods or based on expert knowledge. It is essential to ensure that the values are adequate for the problem to be solved in both cases. There may be situations where values are overestimated, and it should be checked whether this affects the final results. In this paper, the Characteristic Objects Method (COMET) was used to investigate the overestimation effect on the final rankings. The decision matrixes with a different number of alternatives and criteria were assessed The obtained results were compared using the WS similarity coefficient and Spearman's weighted correlation coefficient. The study showed that overestimation has a significant effect on the rankings. A larger number of criteria has a positive effect on the correlation strength of the compared rankings. In contrast, a large overestimation of characteristic values has a negative effect on the similarity of the results.

5

Intuitionistic Fuzzy Transportation Problem by Zero Point Method

Traneva Velichka, Tranev Stoyan

Annals of Computer Science and Information Systems

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2020

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Vol. 21

349--358

EN

The transportation problems (TPs) support the optimal management of the transport deliveries. In classical TPs the decision maker has information about the crisp values of the transportation costs, availability and demand of the products. Sometimes in the parameters of TPs in real life there is ambiguity and vagueness caused by uncontrollable market factors. Uncertain values can be represented by fuzzy sets (FSs) of Zadeh. The FSs have the degrees of membership and nonmembership. The concept of intuitionistic fuzzy sets (IFSs) originated in 1983 as an extension of FSs. Atanasov’s IFSs also have a degree of hesitansy to representing the obscure environment. In this paper we formulate the TP, in which the transportation costs, supply and demand values are intuitionistic fuzzy pairs (IFPs), depending on the diesel prices, road condition, weather and other factors. Additional constraints are included in the problem: limits for the transportation costs. Its main objective is to determine the quantities of delivery from producers to buyers to maintain the supply and demand requirements at the cheapest transportation costs. The aim of the paper is to extend the fuzzy zero point method (FZPM [35]) to the intuitionistic FZPM (IFZPM) to find an optimal solution of the intuitionistic fuzzy TP (IFTP) using the IFSs and index matrix (IM) concepts, proposed by Atanassov. The solution algorithm is demonstrated by a numerical example. Its optimal solution is compared with that obtained by the intuitionistic fuzzy zero suffix method (IFZSM).

6

Intuitionistic Fuzzy Hamiltonian Cycle by Index Matrices

Traneva Velichka, Tranev Stoyan

Annals of Computer Science and Information Systems

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2020

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Vol. 21

345--348

EN

In this paper, the algorithm for finding a Hamiltonian cycle in an intuitionistic fuzzy graph (IFG) is proposed, based on the theories of intuitionistic fuzzy sets (IFSs) and of index matrices (IMs). The aim of the paper is to extend the algorithm to find a fuzzy Hamiltonian cycle (FHC) in an IFG to the intuitionistic fuzzy (IFHC) using the IFSs and IMs concepts. An intuitionistic fuzzy graph example about network of Wizz air airlines is modeled by the extended IM to illustrate the proposed algorithm. In the paper also are introduced for the first time three index-type operations over IMs.

7

On some properties and special identities in the second order matrix algebra over Grassmann algebras

Rashkova T.

Demonstratio Mathematica

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2013

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Vol. 46, nr 1

29--36

EN

The paper considers the anticommutative multiplication property for the matrix algebra M2(G) over the infinite Grassmann algebra G. We define as well some classes of ∗-symmetric and ∗ skew-symmetric matrices in (M2(G),∗) for ∗ being the transpose or the symplectic involution. As a consequence we give some ∗-identities for M2(G) of degree < 8. Examples of the application of finite-dimensional Grassmann algebras in quantum field theory are mentioned and some properties of the algebras G4 and M2(G4) are given as well.

8

Banach algebra homomorphisms via orthogonal projections

Herzog G., Schmoeger C.

Demonstratio Mathematica

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2006

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Vol. 39, nr 1

137-148

EN

Let A be a unital complex Banach algebra with unit e, and p1,... ,pn a collection of orthogonal projections with sum e. The aim of this note is to investigate the close connections of properties of a is an element of A and of (piapj) ia an element of Mn(A), where Mn(A) denotes the matrix algebra of all n x n matrices with entries in A.

9

Pole assignment for higher order linear systems: an algorithmic method

Kalogeropoulos G. I., Papachristopoulos D. P.

Systems Science

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2005

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Vol. 31, no 4

5-20

EN

In this paper, we propose an algorithmic method for a solution of the pole assignment problem which is associated with a higher order linear system, in the case it is completely controllable. The above problem is proved to be equivalent to two subproblems, one linear and the other multilinear. Solutions of the linear problem must be decomposable vectors, that is, they lie in an appropriate Grassmann variety. The method proposed computes a reduced set of quadratic Plucker relations with only three terms each, which describe completely the specific Grassmann variety. Using these relations one can solve the multilinear problem and consequently calculate the feedback matrices which give a solution to the pole assignment problem. Finally, an illustrative example of the algorithmic procedure proposed is given.

10

Using place invariants to isolate faults in concurrent systems

Tabakow I.

Systems Science

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2003

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Vol. 29, nr 4

99-112

EN

A method of fault isolation in a given concurrent system is presented. First, the system considered is modelled by a live and bounded place-transition Petri net. Then the corresponding net place invariants are computed. The system k-distinguishability measure is obtained in an unique way from the place-invariant matrix. For a large value of k, the system model is extended by using some set of additional places called test points. This is in accordance with the practical requirements introduced. To obtain an 1-distinguishable net the notion of a marked graph component is used. Next, two different diagnosis test strategies are discussed, i.e., combinational and sequential fault diagnosis (assuming MTBF -> infinity and MTTR -> 0, respectively). The approach proposed can be extended for higher level Petri nets, e.g., such as coloured nets or also to design self-diagnosable circuit realisations of Boolean interpreted Petri nets. Several examples are given.

11

Robust sliding mode control of multivariable time-delay systems

Jafarov E.M.

Systems Science

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2003

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Vol. 29, nr 3

17-36

EN

In this paper, robust stabilization of multivariable single state-delayed systems with mismatching parameter uncertainties and matching/mismatching external disturbances is considered. To achieve this goal two types of robust sliding mode controller design techniques are advanced. The first one is an integral sliding mode controller design modification to Shyu and Yan type controller design. By using the Lyapunov-Razumikhin-Hale method the mismatching sliding conditions are parametrically obtained and formulated in terms of matrix norm inequalities. In the second contribution, a new combined sliding mode controller design technique for the stabilization of multivariable single state-delayed systems with mismatching parameter perturbations are advanced by using Lyapunov-Krasovskii V-functional method. The sliding, global stability and β-stability conditions are parametrically obtained and formulated in terms of matrix inequalities. Numerical examples with simulation results show the effectiveness of design procedures.

12

PD-sliding mode controller for robot manipulators: A comparison analysis

Parlakci M.N.A., Jafarov E.M., Istefanopulos Y.

Systems Science

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2003

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Vol. 29, nr 2

145-155

EN

This paper introduces a new robust position variable structure controller design method for robot position systems with parameter perturbations. In most situations, the exact knowledge of the robot dynamics does not exist. For this reason a robust variable structure PD-control scheme is proposed for the set-point regulation problem of robot systems. The controller compensates for the inexact information about the robot system. It uses only some robot bound parameters and measurable joint variables. The sufficient conditions are derived for the existence of a sliding mode in the robot system. The techniques of matrix norm inequalities are often addressed for robustness analysis of the controller. In addition, the stability conditions are also investigated in a global sense. Effective parameter-independent conditions are developed by using a full quadratic form of Lyapunov function. Comparative simulation results with classical PD-controller have been presented indicating that the sliding mode PD-like controller yields faster and smoother performance.

13

On the reconstruction of the current state of the linear difference-differential system with commensurable delays

Khartouski V.

Systems Science

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2003

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Vol. 29, nr 4

55-67

EN

In the present paper, we consider the problem of reconstruction of the current state of the difference-differential system with commensurable delays. The results obtained are used for the reconstruction of the current states of linear retarded partial parabolic differential equation.

14

On the performance of high-gain residuals for detecting faults in a pipeline system

Shields D.N.

Systems Science

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2003

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Vol. 29, nr 2

5-16

EN

A theoretical class of nonlinear systems is considered. An n-dimensional pipeline system is examined, as an example system, for investigating the effectiveness of a high-gain observer-based residual for detecting faults. Detailed conditions are given for the investigation of residual effectiveness, such as selection of operating points, control inputs, sensor faults, component faults, fault positions and observer eigenvalues. Then, for various values of n, defined fault types and defined fault positions, the observer-residual performance is noted and characteristics are derived and compared. Qualitative and quantitative evidence in graphical and table form shows, in several ways, how the performance and effectiveness of observer-based residuals change as n, and system complexity, increases.

15

Invariant zeros in singular systems - Algebraic criterions of nondegeneracy

Tokarzewski J.

Systems Science

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2003

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Vol. 29, nr 1

61-78

EN

The question of how the classical concept of the Smith zeros of a LTI continuous-time singular control system S(E,A,B,C,D) can be generalized and related to state-space methods is discussed. The zeros are defined as those complex numbers for which there exists a zero direction with nonzero state-zero direction. Such a definition admits an infinite number of zeros (then the system is called degenerate). Algebraic criterions of degeneracy/nondegeneracy based on Weierstrass-Kronecker canonical form of the system and on the first nonzero Markov parameter are analyzed.

16

Controlled balanced growth of positive linear discrete-time systems

Rumchev V.G., James D.J.G.

Systems Science

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2003

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Vol. 29, nr 1

5-14

EN

In this paper properties of M-matrices are used to develop procedures to ensure that a positive discrete-time linear system achieves a specified desired balanced growth rate. Both closed-loop and open-loop control procedures are considered, with state feedback being adopted for implementing the closed-loop control. Procedures developed are illustrated by simple examples.

17

Computation of minimal realizations for compartmental linear systems

Kaczorek T.

Systems Science

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2003

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Vol. 29, nr 1

15-29

EN

A new method for computation of minimal compartmental realizations of a proper transfer function is proposed. The method is based on a suitable transformation of an asymptotically stable positive realization to the desired compartmental realization. The transformation is characterized by a generalized permutation matrix. Sufficient conditions for the existence of minimal compartmental realizations are established. Two-step procedures for computation of minimal compartmental realizations for both continuous-time and discrete-time linear systems are derived and illustrated by a numerical example.

18

An LMI approach to H infinity control of networked control systems

Zhong M., Jia L., Wang J.

Systems Science

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2003

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Vol. 29, nr 1

45-60

EN

Networked control systems (NCSs) are of major interest nowadays with the development and applications of computer and information technology in industry. The main problem encountered in the application of NCSs to real-time system control is lack of the approaches in system modelling and analysis. Time delays are inevitable and unpredictable due to the transmission delay of communication network. When the time delays are taken into account, the traditional methods in both system characteristic analysis and design may not be validated. Based on a brief introduction of NCSs with network-induced time delays, this paper proposes to investigate the Hinfinity control problem of NCSs with stochastic time delays by using a combined method of sampled-data system technique and time delay system Hinfinity control theory. Applying a linear matrix inequality (LMI) approach, the sufficient conditions for the existence and further solution of state feedback controller are derived in terms of LMIs. It is shown that the Hinfinity controller can be constructed by using LMI solutions.

19

Feedback holdability of singular discrete-time linear systems

Kaczorek T.

Systems Science

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2000

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Vol. 26, nr 4

25-37

EN

The feedback holdability problem for singular discrete-time linear systems is considered. Conditions are established for the existence of solutions to the following three problems for singular system (1) with regular pencil (E, A). Problem 1: find a gain matrix K such that the closed-loop trajectory is inside the nonnegative orthant R+n. Problem 2: find a gain matrix K such that the state vector xi of the closed-loop system xi = 0 for i greater than or equal k - 1, k = 1,...,n. Problem 3: find a gain matrix K such that ui = Kxi ∈ R+m and the trajectory of closed-loop system is inside R+n

20

Remarks on stability of positive linear systems

Mitkowski W.

Control and Cybernetics

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2000

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Vol. 29, no 1

295-304

EN

Spectral properties of nonegative matrices are considered. Asymptotic stability and stabilisation problems of positive discrete-time and continous-time linear systems by feedbacks are discussed. The electric RC-networks are presented as examples of positive systems. Numerical calculations were made using the MATLAB program.