New explicit fourth- and lower orderRunge-Kutta formulas are presented. These formulas include a stepsize control procedure based on a complete coverage of the leading term of the local truncation error. The formulas ...
详细信息
New explicit fourth- and lower orderRunge-Kutta formulas are presented. These formulas include a stepsize control procedure based on a complete coverage of the leading term of the local truncation error. The formulas have considerably smaller truncation errors than corresponding formulas of other authors. These new formulas are suitable for the numerical integration of heat transfer problems after discretisation of these problems in the space variables, since stability considerations, occurring in such problems, would eliminate the benefits (large permissible stepsize) of high-orderRunge-Kutta formulas. The formulas are appl.ed to an example for a heat transfer problem.
The general convex programming problemf(x)=Min! with constraintsx∈Q, g(x)∈Y in reflexive Banach spaces will be treated as a two step problem which we solve with the aid of the method of regularization. The result of...
详细信息
The general convex programming problemf(x)=Min! with constraintsx∈Q, g(x)∈Y in reflexive Banach spaces will be treated as a two step problem which we solve with the aid of the method of regularization. The result of this is a penalty method for convex programming problems with infinitely many constraints. Fictitious solutions appearing in connection with ill posed problems are identified. In some cases we obtain a representation and a method for the approximate calculation of multipliers.
LetA, M, N be real matrices, letA=M−N and letM andM−N(M−1N)k−1 for some integerk≧1 be non-singular. LetM′ y≧0 imply[N(M−1N)k−1]′ y≧0 (where the prime denotes the transpose). Then[M−N(M−1N)k−1]′ y≧0 implies[N (M...
详细信息
LetA, M, N be real matrices, letA=M−N and letM andM−N(M−1N)k−1 for some integerk≧1 be non-singular. LetM′ y≧0 imply[N(M−1N)k−1]′ y≧0 (where the prime denotes the transpose). Then[M−N(M−1N)k−1]′ y≧0 implies[N (M−1N)k−1]′ y≧0 if and only if the spectral radius ϱ(M−1N) ofM−1N is less than one. The same conclusions are true ifA, M andN are replaced byA′, M′ andN′ respectively.
For one- and multistep methods for numerical integration of ordinary differential equations,y'=f(x, y) (a≤x≤b),y (a)=ya we prove intermediate convergence estimates of the following type:f ε Lip (α, p; Q) ⇋yh=y...
详细信息
For one- and multistep methods for numerical integration of ordinary differential equations,y'=f(x, y) (a≤x≤b),y (a)=ya we prove intermediate convergence estimates of the following type:f ε Lip (α, p; Q) ⇋yh=y+0 (hα) (0<α≤p) whereyh denotes the approximate solution. The results extend classical ones.
A computer programming algorithm is presented which is based on Yen's principle [1] for finding the K loopless paths that have the shortest lengths from one fixed node to another in a network. Several modification...
详细信息
A computer programming algorithm is presented which is based on Yen's principle [1] for finding the K loopless paths that have the shortest lengths from one fixed node to another in a network. Several modifications and extensions permitted to construct an extremely efficient algorithm, with regard to the number of necessary memory addresses as well as to the need of operations. The computer time increases linearly with K and is mostly less than the time of Hoffman-Pavley's algorithm [2], moreover, each of the generated paths is loopless. The algorithm published in this paper may be one of the best methods available till now for the solution of the K-shortest paths problem.
In this paper we investigateTschebyscheff-Approximations for realvalued continuous functions by asymptotic convex familiesV of functions, which depend on a finite-dimensional set of real parameters. To obtain a charac...
详细信息
In this paper we investigateTschebyscheff-Approximations for realvalued continuous functions by asymptotic convex familiesV of functions, which depend on a finite-dimensional set of real parameters. To obtain a characterization of best approximation extremal signatures are defined. We derive necessary and sufficient conditions for a subset ofV to be a set of best approximations for a given continuous functionf and for the dimension of the set of all best approximations forf to be bounded by a constant independent off. Finally we consider approximations by familiesV, which are differentiable in the parameters.
In this paper we develop kind of a gradient procedure for the solution of the discrete linearChebyshev approximation problem based on a criterion for best approximants due toKolmogoroff. Compared with the usual simple...
详细信息
In this paper we develop kind of a gradient procedure for the solution of the discrete linearChebyshev approximation problem based on a criterion for best approximants due toKolmogoroff. Compared with the usual simplex methods it has the advantage of less numerical work and need of storage in a computer.
Assuming the existence of an isolated solution of the given boundary value problem, we show the convergence of the shooting method combined with iteration methods of regula-falsi-type. Nonlinear, Fréchet-differen...
详细信息
Assuming the existence of an isolated solution of the given boundary value problem, we show the convergence of the shooting method combined with iteration methods of regula-falsi-type. Nonlinear, Fréchet-differentiable boundary conditions are admissable. The efficiency of the method is demonstrated by several numerical examples.
This paper is concerned with some basic notions of intervall arithmetic, particularly with the definitionsindependent intervals, dependent intervals, interdependent intervals, and with ideas of the extended interval a...
详细信息
This paper is concerned with some basic notions of intervall arithmetic, particularly with the definitionsindependent intervals, dependent intervals, interdependent intervals, and with ideas of the extended interval arithmetic, *** andKulisch, [1] and [2]. These notions will be investigated from a formal point of view and put into a logically satisfactory frame. We shall also demonstrate that the set of all intervals which aredependent on A and whose generating function is apoint function does not form a field, contrary to a theorem in [1]. Furthermore we shall consider two formal ambiguities resulting from a certainidentification as well as from aspecial form of representing rational interval functions. In this connection we shall also formulate several requirements that thederivative of an interval function should satisfy. In the appendix to the paper we shall propose a more precise and logically correct form of the simple and the extended interval arithmetic.
In Part I is shown, how to decompose a connected graph into triply connected components in a canonical manner and how to compute a standard form of an arbitrary graph from standard forms of triply connected ***, in pa...
详细信息
In Part I is shown, how to decompose a connected graph into triply connected components in a canonical manner and how to compute a standard form of an arbitrary graph from standard forms of triply connected ***, in part II a method is given, which allows to construct a standard form of triply connected planar graphs. Besides that, an ALGOL-program is presented which realizes both this method and a planarity criterium.
暂无评论