The intelligent behavior of a highschool student, who constructs triangles from three given pieces shows that he generates auxiliary points of a tree-like structure by means of geometric loci. The formalization of thi...
详细信息
The intelligent behavior of a highschool student, who constructs triangles from three given pieces shows that he generates auxiliary points of a tree-like structure by means of geometric loci. The formalization of this leads to a system of points, geometric loci and rules. In each case the mechine is able to decide whether and how the triangle can be contructed and this leads to the decision-procedure we called the „Dreiecksalgorithmus”.
The first derivatives of a solution of the Poisson Equation on a polygonal domain may be unbounded. Using the usual method of finite differences on an equidistant mesh (meshsizeh) we observe an error, which behaves li...
详细信息
The first derivatives of a solution of the Poisson Equation on a polygonal domain may be unbounded. Using the usual method of finite differences on an equidistant mesh (meshsizeh) we observe an error, which behaves likehα−ε (ε>0 arbitrary), at a corner with interior angle π/α. With local mesh refinement it is possible to obtain uniformly (almost) quadratic convergence and to suppress the observed pollution effect.
The imbedding of a nonlinear problem into a family of nonlinear problems is studied. We will discuss in detail the projection of a family of nonlinear problems into a finite-dimensional subspace. Then we will present ...
详细信息
The imbedding of a nonlinear problem into a family of nonlinear problems is studied. We will discuss in detail the projection of a family of nonlinear problems into a finite-dimensional subspace. Then we will present some numerical methods for the solution of the finite-dimensional family of problems.
The minimization of functions that are not necessarily convex is studied for those iterations, where in every step the problem is reduced to a minimum problem with a convex quadratic function. A facilitation important...
详细信息
The minimization of functions that are not necessarily convex is studied for those iterations, where in every step the problem is reduced to a minimum problem with a convex quadratic function. A facilitation important for numerical appl.cation is derived and is discussed by means of the gradient method [1, 2] and the so called standard method [3]. Moreover it is proved that for problems arising from least-squares-fits the standard method is superior than the gradient method. The results may be easily extended to problems with linear constraints.
For the numerical solution of improperly posed problems a regularization by linear inqualities is proposed. In order to avoid difficulties with ill-conditioned matrices, the problem is solved by computing certain corr...
详细信息
For the numerical solution of improperly posed problems a regularization by linear inqualities is proposed. In order to avoid difficulties with ill-conditioned matrices, the problem is solved by computing certain correct functionals and by singular value decomposition of the matrices.
The present paper is concerned with the numerical solution of quasilinear elliptic differential equations of the fourth order by the method of finite differences. A discrete analogue of the corresponding variational p...
详细信息
The present paper is concerned with the numerical solution of quasilinear elliptic differential equations of the fourth order by the method of finite differences. A discrete analogue of the corresponding variational problem is constructed. Existence and uniqueness of the solution of the discrete problem and, in connection with the convergence to the exact solution, consistence and stability are treated.
作者：
PERL, JTECH UNIV BERLIN
FACHBEREICH KYBERNETIK 20OTTO SUHR ALLEE 18-20D-1000 BERLIN 10WEST GERMANY
Graph algorithms for shortest paths form a class of very efficient algorithms which are of versatile appl.cability (i.e. see [1], [2], [3], [4]). This class corresponds with a rather general class of problems which ar...
详细信息
Graph algorithms for shortest paths form a class of very efficient algorithms which are of versatile appl.cability (i.e. see [1], [2], [3], [4]). This class corresponds with a rather general class of problems which are solvable by these algorithms (see [4], [5]).It is shown that the general covering problem does not belong to this problem class.
A method to construct test matrices with free parameters is given. As an example of appl.cation a new test matrix of even order which is also appropriate to the eigenproblem is derived. Moreover some known test matric...
详细信息
A method to construct test matrices with free parameters is given. As an example of appl.cation a new test matrix of even order which is also appropriate to the eigenproblem is derived. Moreover some known test matrices with constant elements are generalized in such a way that they can be supplied with condition numbers of arbitrary order.
In a partially ordered ring we give a method for the two-sided approximation of the inverse of an element which needs the same number of multiplications as known methods of convergence order two. The new method has th...
详细信息
In a partially ordered ring we give a method for the two-sided approximation of the inverse of an element which needs the same number of multiplications as known methods of convergence order two. The new method has the convergence order three.
Nonlinear Equations with known localisation of the solution are solved by the fixed point method of Kuhn-MacKinnon. A small sample of typical computational experience is given.
Nonlinear Equations with known localisation of the solution are solved by the fixed point method of Kuhn-MacKinnon. A small sample of typical computational experience is given.
暂无评论