There are well known methods to investigate the mappings-properties of Analytic Functions on Analog computers. In the present paper these methoextended to a more general Function Theory and illustrated by examples.
There are well known methods to investigate the mappings-properties of Analytic Functions on Analog computers. In the present paper these methoextended to a more general Function Theory and illustrated by examples.
A new model of a Turing Machine, called “Tabulator Turing Machine”, is defined. It can shift its head over several squares of the tape and is therefore more similar to a real computer than a normal Turing Machine. T...
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A new model of a Turing Machine, called “Tabulator Turing Machine”, is defined. It can shift its head over several squares of the tape and is therefore more similar to a real computer than a normal Turing Machine. The complexity classes defined by this machine are different from those defined by a normal multitape Turing Machine. This device is appl.ed to measure the complexity of several recognition procedures for context free languages.
In this paper we investigate the expected complexityE(C) of distributive (“bucket”) sorting algorithms on a sampleX1, ...,X n drawn from a densityf onR1. Assuming constant time bucket membership determination and as...
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In this paper we investigate the expected complexityE(C) of distributive (“bucket”) sorting algorithms on a sampleX1, ...,X n drawn from a densityf onR1. Assuming constant time bucket membership determination and assuming the use of an average timeg(n) algorithm for subsequent sorting within each bucket (whereg is convex,g(n)/n↑∞,g(n)/n2 is nonincreasing andg is independent off), the following is shown: 1) Iff has compact support, then ∫g(f(x))dx<∞ if and only ifE(C)=0(n). 2) Iff does not have compact support, then\(E(C)/n\xrightarrow{n}\infty \). No additional restrictions are put onf.
For systems of linear equations whose coefficients are intervals we consider the symmetric single-step-method. Sufficient and necessary conditions for convergence are given. For a modification of this method we show t...
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For systems of linear equations whose coefficients are intervals we consider the symmetric single-step-method. Sufficient and necessary conditions for convergence are given. For a modification of this method we show that in each step the fixed point of a linear system with intervals as coefficients can be included at least as good as by all other known methods. This is demonstrated by some numerical examples.
The result of this paper is the economizing of cpu-time by identical guaranteed precision of the approximate solution. This is possible by an optimal selection ofn j in every iteration stepj, wheren j is the number of...
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The result of this paper is the economizing of cpu-time by identical guaranteed precision of the approximate solution. This is possible by an optimal selection ofn j in every iteration stepj, wheren j is the number of subintervals for the numerical integration. The determination ofn1,n2, ... is reduced to the solution of a solvable convex optimization job.
We consider a system carrying a number of in the worst case periodically activated tasks with fixed priorities. We show that the strategy of giving higher priority to tasks with shorter guaranteed response times is op...
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We consider a system carrying a number of in the worst case periodically activated tasks with fixed priorities. We show that the strategy of giving higher priority to tasks with shorter guaranteed response times is optimal in the sense that, if this strategy fails, all others will fail too. Furthermore, we give an algorithm for choosing a subset of tasks of which response times can be guaranteed.
A theorem is proved by means of Brouwer's theorem which allows to decide whether a given interval matrix [S] has the inclusion property relative to the unknown inverseA−1 of a known matrixA. It is demonstrated in ...
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A theorem is proved by means of Brouwer's theorem which allows to decide whether a given interval matrix [S] has the inclusion property relative to the unknown inverseA−1 of a known matrixA. It is demonstrated in which cases the theorem may be used and how to choose [S] in these cases.
The dispatcher is a main component of an operating system. It serves to establish the transfer mechanisms between cooperating processes using the principle of coroutines. Depending on the technical facts, the number o...
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The dispatcher is a main component of an operating system. It serves to establish the transfer mechanisms between cooperating processes using the principle of coroutines. Depending on the technical facts, the number of processors, or the desired behaviour, the details of a dispatcher can be designed differently. This paper discusses possible versions and seeks to arrange them within a general structure.
Several kinds of differentiability are defined, which are adapted to the study of a large class of optimization problems. A theory is constructed with special respect to problems with nonsmooth target-functions and si...
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Several kinds of differentiability are defined, which are adapted to the study of a large class of optimization problems. A theory is constructed with special respect to problems with nonsmooth target-functions and side conditions.
From the argument principle of the theory of functions of a complex variable follows that for any given regionG of the complexz-plane, the number of zeros of a polynomialf (z) inG can be expressed by an integral formu...
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From the argument principle of the theory of functions of a complex variable follows that for any given regionG of the complexz-plane, the number of zeros of a polynomialf (z) inG can be expressed by an integral formula, providedf (z) ≠ 0 on the boundary ofG, and multiple zeros are counted according to their multiplicity. The aim of this paper is to show how to determine the number of these zeros by evaluating a finite number of values of the functionf (z), ifG is a polygonial region. Furthermore, a method will be given, by means of which it becomes possible to associate with any polynomial of degreen, a set of at mostn rectangular regions such that all zeros of the polynomial are contained in the union of these regions. The method will work with any positive upper bound imposed on the diameters of the rectangular regions. Thus a method results for the evaluation of zeros of a polynomial.
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