For Chebyshev's method and the method of tangential hyperbolas we prove convergence if appl.ed to equationsF(x)=0, for whichF andF′ are both orderconvex.
For Chebyshev's method and the method of tangential hyperbolas we prove convergence if appl.ed to equationsF(x)=0, for whichF andF′ are both orderconvex.
作者：
VOGL, FTH VIENNA
INST MATH 1GUSSHAUS STR 27-29A-1040 VIENNAAUSTRIA
By means of the theory of distributions the possibilities to obtain qualitative statements concerning solutions of systems of linear differential equations with discontinuous right hand sides are investigated. A numbe...
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By means of the theory of distributions the possibilities to obtain qualitative statements concerning solutions of systems of linear differential equations with discontinuous right hand sides are investigated. A number of existence and uniqueness theorems is proved for a suitable defined initial value problem. Moreover the structure of solutions (continuity, periodicity etc.) is investigated more closely. It is shown that a number of theorems known from the classical theory of periodical solutions is appl.cable to differential equations in the space of distributions with only slight modifications.
A class of optimal assignment problems is defined. These problems often occur in practice and are essentially more general than the classical assignment problem. The problems may be reduced to the task of finding feas...
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A class of optimal assignment problems is defined. These problems often occur in practice and are essentially more general than the classical assignment problem. The problems may be reduced to the task of finding feasible network flows with given sets of values. The described algorithm is based on a decomposition procedure.
On spaces of analytic functions withL p -norms, 1≤p≤∞, the norm of the quadrature error functional of rules with special fixed nodes is minimized with respect to the weights. These unique determined optimal weights...
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On spaces of analytic functions withL p -norms, 1≤p≤∞, the norm of the quadrature error functional of rules with special fixed nodes is minimized with respect to the weights. These unique determined optimal weights and the corresponding error norm are evaluated.
Let beX the set of all inverse matricesA−1, whereA is contained in a given M-matrixinterval. Then using some properties of M-matrices it will be proved, that an interval version of the Schulz-method produces universal...
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Let beX the set of all inverse matricesA−1, whereA is contained in a given M-matrixinterval. Then using some properties of M-matrices it will be proved, that an interval version of the Schulz-method produces universally — i. e. without any restrictive condition for convergence — the best possible interval inclusion of the setX.
To generate pseudo random numbers with piecemeal continuous probability distribution, which may have a finite number of discontinuities and which may be represented by linear functions in any interval of continuity we...
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To generate pseudo random numbers with piecemeal continuous probability distribution, which may have a finite number of discontinuities and which may be represented by linear functions in any interval of continuity we deduce a new algorithm by a transformation method, using a random generator with uniform distribution. This algorithm has some practical appl.cations.
An algorithm (M) for the determination of minimal paths and spanning trees in graphs with weighted edges is described. (M) produces a connection between some known constructions.
An algorithm (M) for the determination of minimal paths and spanning trees in graphs with weighted edges is described. (M) produces a connection between some known constructions.
Using generating functions we obtain in the case ofn+1 equidistant data points a method for the calculation of the interpolating spline functions(x) of degree 2k+1 with boundary conditionss(κ) (x0)=y (κ)0 ,s(κ) (x ...
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Using generating functions we obtain in the case ofn+1 equidistant data points a method for the calculation of the interpolating spline functions(x) of degree 2k+1 with boundary conditionss(κ) (x0)=y (κ)0 ,s(κ) (x n )=y (κ) n , κ=1(1)k, which only needs the inversion of a matrix of orderk. The appl.cability of our method in the case of general boundary conditions is also mentioned.
The main subject of this paper is the scaling of a given set of differential equations in such a way that the output voltages of the integrators of the associated analogue computer set-up do not exceed certain upper a...
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The main subject of this paper is the scaling of a given set of differential equations in such a way that the output voltages of the integrators of the associated analogue computer set-up do not exceed certain upper and lower bounds imposed by the reference voltage and the limited power of resolution of the elements of the analogue computer. The paper gives a priori bounds on the solution of the differential set. Some of these bounds work with norms, others ***'s stability theorem mentioned in the title of this paper results by inserting special norms and neglecting lower bounds. A difficulty arises by the relative weakness of the condition “‖x‖≤a implies ‖f(x,t)‖≤v(t)‖x‖” on the right hand side of the setdx/dt=f(x,t), where ‖...‖ is any norm anda is a positive real constant. As a consequence of this, it seems no longer possible to use the usual techniques known from the literature on existence theorems and bounds for the solution of differential equations. To cope with this situation, a conditional version of the well-known theorem ofGronwall (also known by the name of “Lemma ofBellman”) will be derived.
The tedious proof ofPontrjagin's maximum principle, based on geometric considerations, can be fully replaced by methods of functional analysis: instead of complete differentiation of the process and the objective ...
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The tedious proof ofPontrjagin's maximum principle, based on geometric considerations, can be fully replaced by methods of functional analysis: instead of complete differentiation of the process and the objective functional in the direct method, only partial derivation in direction of state variables are used, while the difference in direction of the control is not linearized. The costate variables furnish a means to transform an innerproduct. (They are the solution of a linear equation whose operator is the adjoint of the partial derivative of the process operator and whose right side is formed by the partial linearized objective functional.) As result we obtain the wellknown unequality of the Hamiltonians, whose domain of validity is globalized in a proof by *** proof by methods of functional analysis is more concise, constructive and more general: appl.cation of the maximal principle to ergodic Marcovprocesses with rewards results inHoward's method of policy iteration.
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