In a network the lengths of the shortest paths from a set of vertices to all other vertices are given. If any part of the network is altered the lengths of some shortest paths are altered consequently. An algorithm fo...
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In a network the lengths of the shortest paths from a set of vertices to all other vertices are given. If any part of the network is altered the lengths of some shortest paths are altered consequently. An algorithm for correcting these lengths is explained.
All those totally real algebraic number fieldsK of degreen=4 will be studied which have a quadratic subfield Ω. The paragraphs 1.–3. contain the computation of a basis, independant units, and the class number ofK, ...
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All those totally real algebraic number fieldsK of degreen=4 will be studied which have a quadratic subfield Ω. The paragraphs 1.–3. contain the computation of a basis, independant units, and the class number ofK, if Ω has class number one. They are followed by a short examination about the modifications which are necessary, if Ω has a class number greater than one. The last paragraph illustrates the numerical utilization.
We establish two linear lower bounds on the minimal number of 2-ary Boolean operations that are necessary to compute certain Boolean functions. The first bound depends on the structure of primimplicants of the Boolean...
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We establish two linear lower bounds on the minimal number of 2-ary Boolean operations that are necessary to compute certain Boolean functions. The first bound depends on the structure of primimplicants of the Boolean function. The second bound depends on the structure of the set of subfunctions. Both lower bounds yield the exact cost of an optimal computation in certain cases.
We consider five notions of decompositions of Semi-Thue-Systems. These are interesting in view of the theory of Semi-Thue-Systems as well as in regard to practical appl.cations (simplification of the analysisproblem)....
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We consider five notions of decompositions of Semi-Thue-Systems. These are interesting in view of the theory of Semi-Thue-Systems as well as in regard to practical appl.cations (simplification of the analysisproblem). The decompositions form a simple hierarchy. We proof a necessary and sufficient condition for each of the decompositions. Three of the notions are shown to be determinable in general, the other two notions are determinable only for contextfree Semi-Thue-Systems.
This paper deals with numerical evaluation of complex Fourier coefficients of the nonperiodic and real-valued functionf(x)(x∈[a, b], −∞<a<b∞). Our method consists in approximatingf(x) by the natural spline fu...
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This paper deals with numerical evaluation of complex Fourier coefficients of the nonperiodic and real-valued functionf(x)(x∈[a, b], −∞
This paper is an approach in using multistep-methods for integrating “stiff”-systems of ordinary differential equations. New classes of explicit, implicit and PECE-algorithms are developed. The PECE-algorithms are c...
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This paper is an approach in using multistep-methods for integrating “stiff”-systems of ordinary differential equations. New classes of explicit, implicit and PECE-algorithms are developed. The PECE-algorithms are characterized by an absolute stability domain, which, concerning values of some parameters, can decay into two parts, one of which can be placed free along the negative real axis in the complex plane. Beside this, some timeconstant will be integrated exactly. Technical problems show the appl.cation of the algorithms.
In ALGOL-like programming languages with procedures there are several properties of programs concerning procedures that may be used to improve resp. optimise the performance of the runtime system. In these considerati...
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In ALGOL-like programming languages with procedures there are several properties of programs concerning procedures that may be used to improve resp. optimise the performance of the runtime system. In these considerations problems very soon arise, because in general one has to discuss programs with an arbitrary nesting of procedure declarations. This paper shows that an arbitrary ALGOL 60-program can be transformed into an ALGOL 60-program which has a maximal procedure nesting 2, and both programs define the same input-output function. In order to prove this property a new notion for equivalence of ALGOL-like programs with procedures is introduced.
Several orthogonal-invariant fixpoint theorems for the convergence of the Gauss-Newton Method are given which reduce to well-known Newton-Attraction theorems in case of a system of nonlinear equations. Subsequently th...
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Several orthogonal-invariant fixpoint theorems for the convergence of the Gauss-Newton Method are given which reduce to well-known Newton-Attraction theorems in case of a system of nonlinear equations. Subsequently this result is extended to the Levenberg-Morrison-Marquardt Algorithm.
We introduce the concept of a (numerical) algorithm and the following properties: consistency, local and global stability, numerical convergence. We exhibit classes of such algorithms with the following property: cons...
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We introduce the concept of a (numerical) algorithm and the following properties: consistency, local and global stability, numerical convergence. We exhibit classes of such algorithms with the following property: consistency and local stability together with a suitable termination criterion imply numerical convergence. It is shown that all known results in the literature may be deduced from two theorems on monotone algorithms.
An ordinary differential equation system is given, of which the right side depends on constant parameters. They should be determined together with the initial value of the system, in a way that the curves of the solut...
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An ordinary differential equation system is given, of which the right side depends on constant parameters. They should be determined together with the initial value of the system, in a way that the curves of the solution approximate pointwise given curves. We can explain the problem as an overdetermined boundary value *** numerical solving method is based on the principle of maximum of the control theory. It is appl.cable to normal and overdetermined problems and needs less expense than theNewton method. It is given a comparison with theNewton method.
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