By Mac Leod there was presented an improved algorithm for the computation of cubic natural Splines with equi-spaced knots. In this paper his algorithm is extended to the case of type I and II L-Splines corresponding t...
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By Mac Leod there was presented an improved algorithm for the computation of cubic natural Splines with equi-spaced knots. In this paper his algorithm is extended to the case of type I and II L-Splines corresponding to operators of second order with constant coefficients and appl.ed to a problem concerning the static deflection of beams.
In this paper an algorithm for the inclusion of the solution set of a linear least squares problem with interval coefficients is given. It is based on a combination of Björck's iterative procedure for the sol...
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In this paper an algorithm for the inclusion of the solution set of a linear least squares problem with interval coefficients is given. It is based on a combination of Björck's iterative procedure for the solution of the linear least squares problem [5] and a well known algorithm for the solution of linear equations with interval coefficients.
This note presents a matrix representation of iterative methods which is a generalization of those given by Miranker [6] and Rice [8]. It is based on an elementary theorem which show that the order of convergence of s...
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This note presents a matrix representation of iterative methods which is a generalization of those given by Miranker [6] and Rice [8]. It is based on an elementary theorem which show that the order of convergence of some nonlinear single-step and total-step methods is the spectral radius of a certain matrix. Thus a large class of iterative methods are easy to analyze especially such as: Hermiteinterpolatory methods, composite Hermite-interpolatory methods, several parallel methods and even special methods for systems of equations.
The conditional iterationx n+1 =sup (x n ,x n +x n (e−ax n )),y n−1 =inf (y n ,x n +y n (e−ax n )) generating sequences (x n ) and (y n ) is considered in partially ordered spaces. Under certain conditions it is shown...
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The conditional iterationx n+1 =sup (x n ,x n +x n (e−ax n )),y n−1 =inf (y n ,x n +y n (e−ax n )) generating sequences (x n ) and (y n ) is considered in partially ordered spaces. Under certain conditions it is shown, that the inversea−1 of a positive elementa≧0 is monotonously enclosed in the sensex n ≦x n+1 ≦a−1≦y n+1 ≦y n and that (x n ) and (y n ) converge toa−1 quadratically.
作者：
WEBER, HAbteilung Mathematik
Universität Dortmund Postfach 500 500 D-4600 Dortmund 50 Bundesrepublik Deutschland
We present a method for the numerical solution of perturbed bifurcation problems of boundary-value problems for ordinary differential equations by standard techniques. This is achieved by reparametrisation by perturba...
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We present a method for the numerical solution of perturbed bifurcation problems of boundary-value problems for ordinary differential equations by standard techniques. This is achieved by reparametrisation by perturbation parameters and definition of appropriate boundary-value problems which have isolated solutions. The efficiency of the method is demonstrated by a numerical example —a special rod buckling problem.
In optimization theory an essential assumption for the existence of solutions as well as the convergence of algorithms is the compactness of the so-called level sets. Here some general tools for the proof of this prop...
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In optimization theory an essential assumption for the existence of solutions as well as the convergence of algorithms is the compactness of the so-called level sets. Here some general tools for the proof of this property in the case of minimum norm problems are provided. Finally for an approximation problem suggested in [3] for the numerical solution of a class of free boundary problems, compactness of the corresponding sets is shown. Therewith for this approximation problem, existence of a solution and in addition global convergence of the family of algorithms presented in [4] is guaranteed.
Error bounds for the Galerkin procedure are given for a class of non linear problems. In Sectin 3, these results are appl.ed to non linear boundary value problems and to polynomials as coordinate functions. In this ca...
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Error bounds for the Galerkin procedure are given for a class of non linear problems. In Sectin 3, these results are appl.ed to non linear boundary value problems and to polynomials as coordinate functions. In this case, known results are improved.
In this paper the behavior of sorting methods in a paging environment is studied. We give an algorithm which has a page fault rate always independant of the numbern of records in the file to be sorted and depending on...
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In this paper the behavior of sorting methods in a paging environment is studied. We give an algorithm which has a page fault rate always independant of the numbern of records in the file to be sorted and depending only on the number of pages required for the file. The expected number of page exceptions has with 0(p logp) the same order of magnitude as with the classic quicksort procedure but is by the factor 2 lower and we avoid the dependance onn in cases, when the sequence is in partial order.
Several iterative methods for determining the spectral radius ϱ of a nonnegative matrixA are given. Convergence is proved under the assumption of irreducibility. Contrary to the power method, these methods are insensi...
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Several iterative methods for determining the spectral radius ϱ of a nonnegative matrixA are given. Convergence is proved under the assumption of irreducibility. Contrary to the power method, these methods are insensitive to the presence of other eigenvalues with modulus ϱ.
A method is presented for the evaluation of the best rationalChebyshev-approximation for the square root function. The basis of the method is a modification ofHeron's algorithm and a generalisation of the alternat...
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A method is presented for the evaluation of the best rationalChebyshev-approximation for the square root function. The basis of the method is a modification ofHeron's algorithm and a generalisation of the alternating properties. Errorbounds are also given.
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