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1
Content available Sensor location for travel time estimation based on the user equilibrium principle: Application of linear equations
Cao Shuhan, Shao Hu, Shao Feng
International Journal of Applied Mathematics and Computer Science
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2022
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Vol. 32, no. 1
23--33
EN
Travel time is a fundamental measure in any transportation system. With the development of technology, travel time can be automatically collected by a variety of advanced sensors. However, limited by objective conditions, it is difficult for any sensor system to cover the whole transportation network in real time. In order to estimate the travel time of the whole transportation network, this paper gives a system of linear equations which is constructed by the user equilibrium (UE) principle and observed data. The travel time of a link which is not covered by a sensor can be calculated by using the observed data collected by sensors. In a typical transportation network, the minimum number and location of sensors to estimate the travel time of the whole network are given based on the properties of the solution of a systems of linear equations. The results show that, in a typical network, the number and location of sensors follow a certain law. The results of this study can provide reference for the development of transportation and provide a scientific basis for transportation planning.
2
Content available remote Solving system of linear equations via bicomplex valued metric space
Gnanaprakasam Arul Joseph, Boulaaras Salah Mahmoud, Mani Gunaseelan, Cherif Bahri, Idris Sahar Ahmed
Demonstratio Mathematica
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2021
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Vol. 54, nr 1
474--487
EN
In this paper, we prove some common fixed point theorems on bicomplex metric space. Our results generalize and expand some of the literature’s well-known results. We also explore some of the applications of our key results.
3
Content available remote Column-Row Factorization Method for Unordered Sparse Matrices
Saukh S. Y.
Journal of Applied Computer Science
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2009
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Vol. 17, nr 1
85-93
EN
The column-row (CR-) factorization method is offered. The CRfactorization method differs from the LU- factorization method by property of adaptive to the placement of pivoting entries. Suggested method allows to give up implementation of actions by transposition of columns and rows in the process of matrix factorization and therefore to accelerate the solving of the large-scale systems of linear algebraic equalizations.
4
Content available remote Influence of preconditioning and blocking on accuracy in solving Markovian models
Bylina B., Bylina J.
International Journal of Applied Mathematics and Computer Science
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2009
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Vol. 19, no 2
207-217
EN
The article considers the effectiveness of various methods used to solve systems of linear equations (which emerge while modeling computer networks and systems with Markov chains) and the practical influence of the methods applied on accuracy. The paper considers some hybrids of both direct and iterative methods. Two varieties of the Gauss elimination will be considered as an example of direct methods: the LU factorization method and the WZ factorization method. The Gauss-Seidel iterative method will be discussed. The paper also shows preconditioning (with the use of incomplete Gauss elimination) and dividing the matrix into blocks where blocks are solved applying direct methods. The motivation for such hybrids is a very high condition number (which is bad) for coefficient matrices occuring in Markov chains and, thus, slow convergence of traditional iterative methods. Also, the blocking, preconditioning and merging of both are analysed. The paper presents the impact of linked methods on both the time and accuracy of finding vector probability. The results of an experiment are given for two groups of matrices: those derived from some very abstract Markovian models, and those from a general 2D Markov chain.
5
Wybrane procedury estymacji wektora parametrów modeli liniowych za pomocą sieci neuronowych
Gil J.
Prace Naukowe Instytutu Górnictwa Politechniki Wrocławskiej. Konferencje
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2005
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Vol. 114, nr 45
143-150
PL
W pracy rozważano zagadnienie wykorzystania sieci neuronowych do rozwiązywania układów równań liniowych o określonej redundancji (sieć geodezyjna pionowa) z uwzględnieniem zdefiniowanej funkcji energetycznej oraz funkcji aktywacji. Sieci tego rodzaju należą do sieci optymalizujących, których zastosowanie do rozwiązywania tego typu zadań jest ściśle związane z odpowiednią strukturą obwodową. Estymację parametrów układu obserwacyjnego zrealizowano klasyczną procedurą najmniejszych kwadratów oraz jako alternatywę zastosowano zasadę estymacji mocnych w aspekcie identyfikacji obserwacji odstających.
EN
The paper discusses the problem of using neural networks for solving systems of linear equations with a determined redundancy (a vertical geodetic network) including a defined energy function and an activation function. Networks of this kind belong to optimizing networks, whose use for solving tasks of this kind is closely connected to a suitable circuit structure. The estimation of parameters of the observation system was realised through the classical least squares procedure, and the method of robust estimations in the aspect of identifying outlaying observations was used as an alternative.
6
Content available remote Preconditioning GMRES for discontinuous Galerkin approximations
Banaś K., Wheeler M. F.
Computer Assisted Mechanics and Engineering Sciences
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2004
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Vol. 11, No. 1
47-62
EN
The paper presents an implementation and the performance of several preconditioners for the discontinuous Galerkin approximation of diffusion dominated and pure diffusion problems. The preconditioners are applied for the restarted GMRES method and test problems are taken mainly from subsurface flow modeling. Discontinuous Galerkin approximation is implemented within an hp-adaptive finite element code that uses hierarchical 3D meshes. The hierarchy of meshes is utilized for multi-level (multigrid) preconditioning. The results of numerical computations show the necessity of using multi-level preconditioning and insufficiency of simple stationary preconditioners, like Jacobi or Gauss-Seidel. Successful preconditioners comprise a multi-level block ILU algorithm and a special multi-level block Gauss-Seidel method.
7
Content available remote Methods for solving systems of linear equations of structure mechanics with interval parameters
Skalna I.
Computer Assisted Mechanics and Engineering Sciences
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2003
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Vol. 10, No. 3
281-293
EN
Interval analysis permits to calculate guaranteed a posteriori bounds for the solutions of problems with uncertain (interval) input data. Most of the methods of interval analysis assume that all input data vary independently within the given lower and upper bounds. In many practical applications it need not be a case, and the assumption of independence may lead to large overestimation of the set of solutions. The subject of this work is the problem of solving systems of linear interval equations with coefficients linearly dependent on a set of interval parameters called coefficient dependence problem. The purpose of this work is to present methods producing sharp bounds for the set of solutions of systems with dependent input data. The paper starts with an introduction to systems of linear interval equations and the problem of data dependencies in such systems. A parametric formulation of the coefficient dependence problem follows next. Finally, three algorithms to calculate tighter bounds for problems with linearly dependent coefficients, namely the Rump's method, its improved version developed by the author, and the IPM method based on the results from Neumaier [8] are presented and discussed. The algorithms are evaluated and compared using some examples of truss structure analysis.
8
Content available remote Sztuczna inteligencja modeluje powierzchnię Ziemi
Olszewski R.
Geodeta : magazyn geoinformacyjny
|
2002
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nr 5
28--31
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