Using new special functions the solution of linear second-order differential equations with constant coefficients is transformed in such a way so that it no longer contains numerical singularities. A numerical algorit...
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Using new special functions the solution of linear second-order differential equations with constant coefficients is transformed in such a way so that it no longer contains numerical singularities. A numerical algorithm for the computation of an approach for this solution and an ALGOL 60-program are given.
The theorems, known for systems of linear equations, on the convergence of “Successive overrelaxation methods (SOR)” and “Alternating direction methods (ADI)” are transferred to analogous methods for systems of no...
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The theorems, known for systems of linear equations, on the convergence of “Successive overrelaxation methods (SOR)” and “Alternating direction methods (ADI)” are transferred to analogous methods for systems of nonlinear equations. In doing so, only so-called “local” convergence theorems can be proved, however, as it is the case with other iteration procedures for nonlinear problems. Furthermore, it is examined under what conditions there exist difference approximations for nonlinear elliptic differential equations, such as to the functional matrix of the resulting system of nonlinear equations being symmetric and positive definite. SOR for 0<ω<2 and ADI are then converging. Such approximations can be derived at least for more general semilinear equations if the differential equation is theEuler equation of a variational problem. Finally, an example is given.
Exact computation of sums with a large number of terms is often very time-consuming. Unfortunately, for many term functions the usual method of approximating such sums by integrals leads to a very large error. Moreove...
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Exact computation of sums with a large number of terms is often very time-consuming. Unfortunately, for many term functions the usual method of approximating such sums by integrals leads to a very large error. Moreover, the most efficient methods of integration demand that the term function is available not only at integers but also at real points contrary to its nature. In consideration of such difficulties a, method of controllable accuracy is presented requiring no integrations. The method detects the regions in the interval of summation requiring improvements of the approximation and carries out these improvements. Bounds for the error and for the number of required terms are deduced and an Algol-60-procedure for the method is stated.
We give an iterative method for determining nested bounds for the Frobenius-rootr(A) of a nonnegative matrixA. This method still works when there are several eigenvalues with modulusr(A).
We give an iterative method for determining nested bounds for the Frobenius-rootr(A) of a nonnegative matrixA. This method still works when there are several eigenvalues with modulusr(A).
In the present paper we discuss several steplength procedures from a general point of view. We consider their influence on the convergence of algorithms for the numerical treatment of optimization problems without con...
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In the present paper we discuss several steplength procedures from a general point of view. We consider their influence on the convergence of algorithms for the numerical treatment of optimization problems without constraints. We define efficient step-size functions and show that well known steplength procedures are efficient. Necessary and sufficient conditions for convergence of descent methods with efficient step-size functions and appl.cations to conjugate gradient methods are given.
Processes execute in critical sections, if they acces a common data base (list). Many solutions of the necessary mutual exclusion so far lock the total list (total list locking) by the processP*, which is authorized t...
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Processes execute in critical sections, if they acces a common data base (list). Many solutions of the necessary mutual exclusion so far lock the total list (total list locking) by the processP*, which is authorized to access, whereas all other processesPi demanding access have to wait untilP* has left the critical section. However, in the following proposal only certain subsets of the list are locked for a single accessing process (partial list locking), whereas the rest of the list remains accessable for further processes. The organization of this solution is presented on the basis of typical list operations and known list types; finally simulation results to the behaviour of partial list locking in comparison with total list locking are presented.
In this paper we investigate the approximation by sums of exponentials in the sense ofChebyshev. The best approximation is shown to be unique apart from exceptions not previously recognized. However, there is always u...
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In this paper we investigate the approximation by sums of exponentials in the sense ofChebyshev. The best approximation is shown to be unique apart from exceptions not previously recognized. However, there is always uniqueness, when only sums of positive exponentials are considered. This family has a structure which is different from that of other generalizations of linear families of functions. This feature is reflected in the criterion on the alternations of the error curve.
The algorithm for the traversal of an undirected, connected graph is based on the principle of the thread of Ariadne. Starting with a node the algorithm handels the graph systematically until all nodes are reached at ...
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The algorithm for the traversal of an undirected, connected graph is based on the principle of the thread of Ariadne. Starting with a node the algorithm handels the graph systematically until all nodes are reached at least once and all arcs traversed exactly twice. The complexity isO (m), m=number of edges.
In the present paper we give an interval arithmetic, which is an extension of that given in [1]. It is one of the essential features of this new interval arithmetic, that in the case of interval functions we get the e...
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In the present paper we give an interval arithmetic, which is an extension of that given in [1]. It is one of the essential features of this new interval arithmetic, that in the case of interval functions we get the exact range of interval values. Further on we give a machine interval arithmetic corresponding to the new interval arithmetic and study properties of these arithmetics.
In this paper a universal recurrence formular is given for the calculation of theLegendre-Polynomials an their derivates. The first values for the beginning of the recurrence are calculated. Then there are given some ...
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In this paper a universal recurrence formular is given for the calculation of theLegendre-Polynomials an their derivates. The first values for the beginning of the recurrence are calculated. Then there are given some simple formulas for the values of functions with the arguments 0 and 1 at the ends of the considered interval. At last the functional equations are generalized.
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