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1
Content available Optimization Method Based on Minimization M-Order Central Moments Used In Surveying Engineering Problems
Cellmer Sławomir, Bobojć Andrzej
Technical Sciences / University of Warmia and Mazury in Olsztyn
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2021
|
nr 24(1)
39--49
EN
A new optimization method presented in this work – the Least m-Order Central Moments method, is a generalization of the Least Squares method. It allows fitting a geometric object into a set of points in such a way that the maximum shift between the object and the points after fitting is smaller than in the Least Squares method. This property can be very useful in some engineering tasks, e.g. in the realignment of a railway track or gantry rails. The theoretical properties of the proposed optimization method are analyzed. The computational problems are discussed. The appropriate computational techniques are proposed to overcome these problems. The detailed computational algorithm and formulas of iterative processes have been derived. The numerical tests are presented, in order to illustrate the operation of proposed techniques. The results have been analyzed, and the conclusions were then formulated.
2
Content available On rational functions related to algorithms for a computation of roots. II
Baran Mirosław
Science, Technology and Innovation
|
2019
|
Vol. 7, no. 4
26--29
EN
We discuss a nice composition properties related to algorithms for computation of N-roots. Our approach gives direct proof that a version of Newton's iterative algorithm is of order 2. A basic tool used in this note are properties of rational function Φ(w; z) = z-w/(z+w), which was used earlier in [1] in the case of algorithms for computations of square roots.
3
Content available Inexact Newton’s method for generalized operator equations in Banach spaces
Singh V. K.
Journal of Applied Mathematics and Computational Mechanics
|
2018
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Vol. 17, nr 4
85--97
EN
In the present paper, we introduce a new inexact Newton-like algorithm for solving the generalized operator equations containing non differentiable operators in Banach space setting and discuss its semilocal convergence analysis under the weak Lipschitz condition with larger convergence domain and tighter error bounds. The main result of this paper is the significant improvement over the Newton’s method as well as the inexact Newton method.
4
Content available Metoda pozycjonowania powierzchni stawowych w modelowaniu MES
Klekiel T.
Aktualne Problemy Biomechaniki
|
2017
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z. 12
41--50
PL
Praca dotyczy opracowania metody przeznaczonej do pozycjonowania modeli geometrycznych kości na podstawie przyjętego obiektywnego kryterium. Zagadnienie zdefiniowano jako problem optymalizacyjny. Zastosowano metodę Newtona do pozycjonowania elementów kostnych stawu kolanowego dla dowolnego kąta zgięcia. Zaproponowano rozwiązanie umożliwiające ustalenie wzajemnego położenia powierzchni stawowych stawu kolanowego dla modeli geometrycznych kości udowej oraz piszczelowej pozyskanej z tomografii komputerowej dla wyprostowanej kończyny. Zastosowanie proponowanej metody umożliwia dokładne pozycjonowanie elementów bryłowych, dzięki czemu uzyskano wymagany kontakt powierzchni stawowych. Przedstawiona metoda umożliwia uzyskanie dokładnych modeli stawu dla dowolnych położeń.
EN
This paper presents the method to preparation geometrical models in which the suitable position is required. The author applied the Newton algorithm to finding solution for nonlinear set of equations. These equations are prepared from general relations between independent coordinates. Application was realized in VBA language based on data received from model generated in ANSYS Inc. Software. The proposed method was examined for finding position problem for the fibula and tibia bones in knee joint for different angles during bending of knee. The error of solutions was determined as a mean distance between selected spaces. The results were compared on the space selected to represented the cartilage contact in the joint.
5
Content available An algorithm of a freeform surfaces measurement adjustment using a specification of the workpiece coordinate system location
Buša J., Buša J. Jr., Dovica M., Fabian M., Ižol P., Honus S.
Advances in Science and Technology. Research Journal
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2017
|
Vol. 11, no 3
223--232
EN
A difficulty of freeform surfaces evaluations lies in a setup of a coordinate measuring system in general, when it is not possible to use the standard system of alignment by a point, a line, and a surface. An algorithm for the measurement adjustment using a small workpiece coordinate system movement and rotation to achieve a smaller least square error of the produced surface for a given freeform surface defined by the function of two variables is considered. The algorithm uses the Newton method for calculation of the orthogonal distance of a measured point to a given surface and also for minimization of the sum of the distance squares. Numerical results for an example are given.
6
Content available Implicit solution of 1d nonlinear porous medium equation using the four-point Newton- EGMSOR iterative method
Chew J. V. L., Sulaiman J.
Journal of Applied Mathematics and Computational Mechanics
|
2016
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Vol. 15, nr 2
11--21
EN
The numerical method can be a good choice in solving nonlinear partial differential equations (PDEs) due to the difficulty in finding the analytical solution. Porous medium equation (PME) is one of the nonlinear PDEs which exists in many realistic problems. This paper proposes a four-point Newton-EGMSOR (4-Newton-EGMSOR) iterative method in solving 1D nonlinear PMEs. The reliability of the 4-Newton-EGMSOR iterative method in computing approximate solutions for several selected PME problems is shown with comparison to 4-Newton-EGSOR, 4-Newton-EG and Newton-Gauss-Seidel methods. Numerical results showed that the proposed method is superior in terms of the number of iterations and computational time compared to the other three tested iterative methods.
7
Content available An analytical and numerical approach to a bilateral contact problem with nonmonotone friction
Barboteu M., Bartosz K., Kalita P.
International Journal of Applied Mathematics and Computer Science
|
2013
|
Vol. 23, no. 2
263--276
EN
We consider a mathematical model which describes the contact between a linearly elastic body and an obstacle, the so-called foundation. The process is static and the contact is bilateral, i.e., there is no loss of contact. The friction is modeled with a nonmotonone law. The purpose of this work is to provide an error estimate for the Galerkin method as well as to present and compare two numerical methods for solving the resulting nonsmooth and nonconvex frictional contact problem. The first approach is based on the nonconvex proximal bundle method, whereas the second one deals with the approximation of a nonconvex problem by a sequence of nonsmooth convex programming problems. Some numerical experiments are realized to compare the two numerical approaches.
8
Content available The inverse determination of volume fraction of fibres in reinforced composite with imperfect thermal contact between constituents
Mierzwiczak M., Kołodziej J. A.
Journal of Theoretical and Applied Mechanics
|
2011
|
Vol. 49 nr 4
987-1001
EN
The paper considers the problem of determination of the volume fraction of fibres in an unidirectionally reinforced composite in order to provide the appropriate effective thermal conductivity. The problem formulated in such a way should be treated as an inverse heat transfer problem. The thermal conductivities of constituents (fibres and matrix) and fibres arrangement are known. The calculations are carried out for an imperfect thermal contact between the fibres and matrix.
PL
W pracy rozważa się problem określenia objętościowego udziału włókien w jednokierunkowo wzmocnionym kompozycie w celu uzyskania odpowiedniego efektywnego współczynnika przewodzenia ciepła. Problem sformułowany w ten sposób jest traktowany jako odwrotny problem przewodzenia ciepła. Współczynniki przewodzenia ciepła składników (włókien i matrycy) oraz sposób ułożenia włókien są znane. Obliczenia są wykonane dla niedoskonałego kontaktu termicznego pomiędzy włóknami i matrycą.
9
Content available remote Metric regularity under approximations
Dontchev A. L., Veliov V. M.
Control and Cybernetics
|
2009
|
Vol. 38, no 4B
1283-1303
EN
In this paper we show that metric regularity and strong metric regularity of a set-valued mapping imply convergence of inexact iterative methods for solving a generalized equation associated with this mapping. To accomplish this, we first focus on the question how these properties are preserved under changes of the mapping and the reference point. As an application, we consider discrete approximations in optimal control.
10
Content available On the Chaplyghin method for first order partial differential equations
Puźniakowska E.
Opuscula Mathematica
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2008
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Vol. 28, no. 2
163-178
EN
Classical solutions of initial problems for nonlinear first order partial differential equations are considered. It is shown that under natural assumptions on given functions, there exist Chaplyghin sequences and they are convergent. Error estimates for approximate solutions are given. The method of characteristics is used for the construction of approximate solutions.
11
Content available remote On the Chaplygin method for the Darboux problem
Jaruszewska-Walczak D.
Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae
|
2007
|
Vol. 47, [Z] 1
11-21
EN
In the paper we deal with the Darboux problem for hyperbolic functional differntial equations. We give the sufficient conditions for the existence of the sequence {z^(m)} such that if z is a classical solution of the original problem then {z^(m)} is uniformly convergent to z. The convergence that we get is of the Newton type.
12
Content available remote Fast level set based algorithms using shape and topological sensitivity information
Hintermuller M.
Control and Cybernetics
|
2005
|
Vol. 34, no 1
305-324
EN
A framework for descent algorithms using shape as well as topological sensitivity information is introduced. The concept of gradient-related descent velocities in shape optimization is defined, a corresponding algorithmic approach is developed, and a convergence analysis is provided. It is shown that for a particular choice of the bilinear form involved in the definition of gradient-related directions a shape Newton method can be obtain. The level set methodology is used for representing and updating the geometry during the iterations. In order to include topological changes in addition to merging and splitting of existing geometries, a descent algorithm based on topological sensitivity is proposed. The overall method utilizes the shape sensitivity and topological sensitivity based methods in a serial fashion. Finally, numerical results are presented.
13
Content available remote A logarithmic barrier function method for solving nonlinear multiobjective programming problems
Tlas M., Abdul Ghani B.
Control and Cybernetics
|
2005
|
Vol. 34, no 2
487-504
EN
An interior point method for solving nonlinear multiobjective programming problems, over a convex set contained in the real space R^n, has been developed in this paper. In this method a new strictly concave logarithmic barrier function has been suggested in order to transform the orginal problem into a sequence of unconstrained subproblems. These subproblems can be solved using Newton method for determining Newton's directions along which line searches are performed. It also has been proved that the number of iterations required by the suggested algorithm to converge to an [epsilon]-optimal solution is 0(m|ln[epsilon]|), depending on predetermined error tolerance [epsilon] and the number of constraints m.
14
Multi-loop linear control systems design
Goncharov V., Barkovsky A., Blinova N., Datsko O.
Systems Science
|
2002
|
Vol. 28, nr 4
5-16
EN
A numerical synthesis method of continuous control systems having few internal loops is proposed. Every loop may contain the correcting devices both in the direct channel and in the feedback circuit. The basis of the method is a real integral transform allowing writing the synthesis equation in the image domain in such a way that it contains the functions of real argument only. The interpolation approach provides the development of synthesis equations for the unknown coefficients of correcting device transfer functions. The system solution by Newton's method is found.
15
Wyznaczanie płaskich przepływów cieczy lepkiej metodą kolejnych przybliżeń Newtona
Kosma Z.
Zeszyty Naukowe Katedry Mechaniki Stosowanej / Politechnika Śląska
|
1999
|
z. 9
123-128
PL
Przedstawiono algorytmy obliczeniowe przeznaczone do wyzna­czania płaskich, laminarnych przepływów cieczy lepkiej, które zostały oparte na linearyzacji równania czwartego rzędu dla funkcji prądu. Po aproksymacji kolej­nych przybliżeń funkcji prądu dwusześcienną funkcją sklejaną otrzymano układy równań liniowych dla współczynników występujących w przedstawieniu funkcji sklejanej przez B-funkcje. Obliczenia testowe wykonano dla przepływu cieczy lepkiej w kwadratowym zagłębieniu z jedną poruszającą się ścianką dla liczb Reynoldsa Re < 1000.
EN
The calculation of plane viscous motion consits in integration of quasi-linear equation for the stream function, which is linearised by means of the Newton's method. The linearised fourth order equations for the stream function are ap­proximated by bicubic spline functions and by the use of the collocation method systems of linear equations for unknown coefficients of the spline functions are derived. The proposed algorithms have been applied to the driven cavity flow problem for Reynolds numbers Re < 1000.
16
Przedziałowe metody rozwiązywania algebraicznych równań nieliniowych mechaniki konstrukcji
Pownuk A.
Zeszyty Naukowe Katedry Mechaniki Stosowanej / Politechnika Śląska
|
1999
|
z. 9
231-236
PL
W pracy przedstawiono przedziałowe metody znajdowania wszystkich pierwiastków algebraicznych równań nieliniowych oraz relacji oparte na matematyce przedziałowej. Przedstawione algorytmy zastosowano do rozwiązywania nieliniowych równań równowagi, problemów stateczności oraz drgań własnych układów prętowych.
EN
In this paper the methods for system of nonlinear algebraic equations and relations based on interval mathematics are presented. Presented algorithms were applied to solve systems of nonlinear equilibrium equations, stability problems and free vibrations of bars.
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