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EN
We discuss simple functional transductions defined by invertible Mealy automata under iteration and in particular the question when the orbit relation defined by iteration is rational. We identify a class of these automata that has relatively complicated orbits, yet some of them are still orbit rational and discuss a number of decision problems associated with these devices.
2
Content available remote A Note on the Singh Six-order Variant of Newton’s Method
EN
In 2009 in this journal it was published the paper of M. K. Singh [1], in which the author presented a six-order variant of Newton’s method. Unfortunately, in this paper there were a number of printer errors and a serious error in the proof of theorem on the order of the method proposed. Therefore, we have opted for presenting the correct proof of this theorem.
EN
The problem of transformation between Cartesian and geodetic (ellipsoidal) coordinates occurs often in day-to-day geodetic practice. Thus, from years it attracts interest of many scientists and practitioners. Despite the fact that many algorithms of the conversion exist to this day one may still observe new methods and approaches to the problem. In this work a comparison as to the efficiency of iterative methods of the cubic rate convergence to the solution of "latitude equation" in three representations has been presented. Two of them are polynomial representations (quartic equations) and one is in the form of an irrational equation. A comparison has been performed on two ellipsoidal height intervals: from -10 km to 10 km, from 10 km to 36 000 km and from 0° to 90° for the latitude.
PL
Problem transformacji między współrzędnymi kartezjańskim i współrzędnymi geodezyjnymi (elipsoidalnymi) pojawia się często w praktyce geodezyjnej, dlatego od lat stanowi przedmiot zainteresowania wielu naukowców oraz praktyków. Mimo że znanych jest wiele algorytmów przeliczania współrzędnych, ciągle pojawiają się nowe metody i sposoby. W artykule przedstawiono porównanie efektywności metod iteracyjnych o zbieżności sześciennej oraz „równania szerokości" w trzech reprezentacjach. Dwie z nich to reprezentacje wielomianowe (równania czwartego stopnia), a jedna to reprezentacja w formie równania niewymiernego. Porównanie przeprowadzono dla dwóch przedziałów wysokości elipsoidalnej: od -10 km do 10 km oraz od 10 km do 36 000 km, a także dla przedziału szerokości geodezyjnej od 0° do 90°.
EN
We present structural properties of languages constructed with catenation and shuffle, comprising iteration lemmata and closure properties of the language classes, as well as decidability results that follow.
EN
The paper considers performance issues of a class of iterative minimization methods of unconstrained single variable problems. Problem structures that assure superior performance of a specific method have been stipulated with appropriate conclusions drawn.
PL
W artykule poruszono zagadnienie szybkości działania metod minimalizacji funkcji jednej zmiennej dla zadań programowania nieliniowego bez ograniczeń. Wskazano przypadki, dla których konkretna metoda działa szybciej niż pozostałe oraz wyciągnięto wnioski odnośnie takiego stanu rzeczy.
EN
The interest in efficient root-finding iterations is nowadays growing and influenced by the widespread use of high-speed computers. On the other hand, the calculation of derivatives is often hard, when the problems are formulated in terms of nonlinear equations and as a result, the importance of derivative-free methods emerges. For these reasons, some efficient three-step families of iterations for solving nonlinear equations are suggested, where the analytical proofs show their seventh-order error equations consuming only four function evaluations per iteration. We employ hard numerical test problems to illustrate the accuracy of the new methods from the families.
EN
Several methods have been proposed in the literature to address the problem of automatic mapping by a robot using range scan data, under localization uncertainty. Most scan matching methods rely on the minimization of the matching error among individual range scans. However, uncertainty in sensor data often leads to erroneous matching, hard to cope with in a purely automatic approach. This paper proposes a semi-automatic approach, denoted interactive mapping, involving a human operator in the process of detecting and correcting erroneous matches. Instead of allowing the operator complete freedom in correcting the matching in a frame by frame basis, the proposed method facilitates the adjustment along the directions with more ambiguity, while constraining the others. Experimental results using LIDAR data are presented to validate empirically the approach, together with a preliminary user study to evaluate the benefits of the approach.
EN
We present basic structures, definitions, normal forms, and a hierarchy of languages based on catenation, shuffle and their iterations, defined by algebraic closures or least fixed point solutions to systems of equations.
9
Content available remote Solving RFIC Simulation Tasks Using GPU Computations
EN
New generation of General Purpose Graphic Processing Unit (GPGPU) cards with their large computation power allow to approach difficult tasks from Radio Frequency Integrated Circuits (RFICs) modeling area. Using different electromagnetic modeling methods, the Finite Element Method (FEM) and the Finite Integration Technique (FIT), to model Radio Frequency Integrated Circuit (RFIC) devices, large linear equations systems have to be solved. This paper presents the benefits of using Graphic Processing Unit (GPU) computations for solving such systems which are characterized by sparse complex matrices. CUSP is a GPU generic parallel algorithms library for sparse linear algebra and graph computations based on Compute Unified Device Architecture (CUDA). The code is calling iterative methods available in CUSP in order to solve those complex linear equation systems. The tests were performed on various Central Processing Units (CPU) and GPU hardware configurations. The results of these tests show that using GPU computations for solving the linear equations systems, the electromagnetic modeling process of RFIC devices can be accelerated and at the same time a high level of computation accuracy is maintained. Tests were carried out on matrices obtained for an integrated inductor designed for RFICs, and for Micro Stripe (MS) designed for Photonics Integrated Circuit (PIC).
EN
Efficient iterative solution of large linear systems on grid computers is a complex problem. The induced heterogeneity and volatile nature of the aggregated computational resources present numerous algorithmic challenges. This paper describes a case study regarding iterative solution of large sparse linear systems on grid computers within the software constraints of the grid middleware GridSolve and within the algorithmic constraints of preconditioned Conjugate Gradient (CG) type methods. We identify the various bottlenecks induced by the middleware and the iterative algorithm. We consider the standard CG algorithm of Hestenes and Stiefel, and as an alternative the Chronopoulos/Gear variant, a formulation that is potentially better suited for grid computing since it requires only one synchronisation point per iteration, instead of two for standard CG. In addition, we improve the computation-to-communication ratio by maximising the work in the preconditioner. In addition to these algorithmic improvements, we also try to minimise the communication overhead within the communication model currently used by the GridSolve middleware. We present numerical experiments on 3D bubbly flow problems using heterogeneous computing hardware that show lower computing times and better speed-up for the Chronopoulos/Gear variant of conjugate gradients. Finally, we suggest extensions to both the iterative algorithm and the middleware for improving granularity.
EN
In this paper we consider an iterative method of finding a regularized solution of a general linear system Ax = b. For a given scalar α and an initial vector g it produces a sequence that converges to the least squares solution of this system. The limiting point minimizes the distance between g and the set of all least squares solutions of the problem. An estimate of the rate of convergence is also provided.
EN
In this paper, we consider approximation methods for operator equations of the form Au + Bu = ƒ, where A is a discrete Wiener-Hopf operator on lp (1≤ p < ∞) which symbol has roots on the unit circle with arbitrary multiplicities (not necessary integers). Conditions on perturbation B and ƒ are given in order to guarantee the applicability of projection-iterative methods. Effective error estimates, and simultaneously, decaying properties for solutions are obtained in terms of some smooth spaces.
13
Content available remote Iteracyjne strojenie nastaw regulatora PID
PL
W artykule przedstawiono metodę iteracyjnego strojenia nastaw regulatora PID o strukturze równoległej. Symulacje przeprowadzono dla modelu drugiego rzędu z opóźnieniem. Przedstawioną metodę porównano z metodą projektowania odpornego regulatora PID zaproponowaną w [4].
EN
Iterative feedback tuning (IFT) method for a parallel structure of PID controller is derived and simulated. The performance of PID controller tuned with IFT is compared with robust PID controller proposed in [4]. To this end a plant model of second-order with time delay is considered.
14
Content available remote Numerical stability of the Richardson second order method
EN
In this paper we study numerical properties of the Richardson second order method (RS) for solving a linear system Ax = b, where A € Rnxn is infinitysymmetric and positive definite. We consider the standard model of floating point arithmetic (cf. [6], [7], [11]). We prove that the RS-algorithm is numerically stable. This means that the algorithm computes approximations xk to the exact solution x* = A-1b such that the error limfk||xk - x*ll2 ls of order eMcond(A), where eM is the machine precision and cond(A) = ||A || 2 ||A-1|| denotes the condition number of the matrix A.
EN
This paper deals with the problem of robustness of P-type iterative learning control for uncertain nonlinear system. Besides the vector field, the control matrix and output matrix of the control system considered in this paper all have uncertainties. Iterative learning laws for initial states and for inputs are presented. A new technique has been developed to estimate the tracking errors of iterative control systems, which have an initial state error. Based on the estimation, upper bounds of the norms of the uncertainties of the control matrix and the output matrix are obtained, which guarantee that the iterative learning laws for initial states and for inputs are convergent. The results in this paper show that the P-type iterative learning control has robustness with respect to the uncertainties of the control matrix and the output matrix.
EN
The paper concerns the application of advanced evolutionary algorithms for solving a complex scheduling problem of manufacturing tasks. The case of scheduling of independent, non-preemptive tasks on unrelated moving executors, to minimize the makespan is considered. New heuristic solution algorithms based on an evolutionary computation are proposed. They use three different ways of multiple crossovers. The computer simulation experiments have been performed to investigate the dependence of results of the tasks scheduling on parameters of evolutionary algorithms as well as the quality of the solution algorithms in terms of the makespan and the time of computation. The evolutionary algorithms have been compared with a traditional solution algorithm that has been determined using the functional decomposition of the problem. A numerical example together with conclusions completes the paper.
17
Content available remote Parallel computing applied to solving large Markov chains. A feasibility study.
EN
The article is concerned with parallel computation issues arising in numerical solution of systems of linear eąuations which describe stationary pro-babilitifis of stat.es in largc Markov chairis. Upon introduction to the .subject of Markov chains and their solution, several adeąuate solution methods arę surreyed, froni the cla.ssical through projection to decompositional ones. Each algoriUiin is accoinpaniocl by a study of its suitability to parallel computing (rnulti- and vector procfissing). Additional opinions on aspects of the potential for parallelization in the discussed methods arę contained in the conclusion.
PL
Artykuł jest poświęcony zagadnieniom obliczeń równoległych, występującym w trakcie numerycznego rozwiązywania układów równań liniowych, opisujących stacjonarne prawdopodobieństwa stanów w dużych łańcuchach Markowa. Po wprowadzeniu do tematyki łańcuchów Markowa, dokonano przeglądu wybranych metod rozwiązywania, począwszy od klasycznych, poprzez projekcyjne, do metod dekompozycyjnych. Dla każdego algorytmu została dokonana analiza, na ile nadaje się on do wykonania w trybie równoległym (wieloprocesorowyrn lub wektorowym). Dodatkowe uwagi dotyczące możliwości zrównoleglania dla omawianych metod zawarto w części końcowej.
EN
Sensitivity analysis determines the dependence of global or local electromagnetic quantities on geometrical or physical parameters expressed in the form of an objective function. The final aim of the field calculation methods is generally the design of an electromagnetic device. Solution of inverse problem on the basis of the finite elements method (FEM) makes the optimal shape design possible, as well as the identification of material cracks and flaws inside the conducting materials with the help of the eddy-current method. These tasks can be defined similarly for recognition of the spatial distribution of material parameters. The recognition takes place in iterative manner, basing on gradient information derived from the sensitivity analysis. The work deals with sensitivity evaluation in conjunction with finite element algorithms. It will be shown that the sensitivity analysis necessary to solve an inverse problem, requires only a low additional calculation cost.
PL
Przedstawiono teoretyczną metodę wyznaczania charakterystyk podnośników hydraulicznych stosowanych w ciągnikach rolniczych. Zbadano zbieżność wyników uzyskiwanych za pomocą tej metody z charakterystyką wykreśloną na postawie pomiarów podnośnika ciągnika John Deer 6210. Stwierdzono konieczność zaopatrzenia modelu matematycznego we współczynniki zależne od konstrukcji podnośnika.
EN
Theoretical method of appointing characterization of hydraulic lift applied in agricultural tractors. Convergence of results obtained with this method with characterization drafted on the base of measurements of a pick-up tractor John Deer 6210 was examined. It was stated that it is necessary to equip a mathematical model with coefficients dependent on construction of a pick-up.
20
Content available remote Inequality-Based Approximation of Matrix Eigenvectors
EN
A novel procedure is given here for constructing non-negative functions with zero-valued global minima coinciding with eigenvectors of a general real matrix A. Some of these functions are distinct because all their local minima are also global, offering a new way of determining eigenpairs by local optimization. Apart from describing the framework of the method, the error bounds given separately for the approximation of eigenvectors and eigenvalues provide a deeper insight into the fundamentally different nature of their approximations.
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