Bounds including round off errors are given for real simple eigenvalues and corresponding eigenvectors of a square matrix by using interval-arithmetics. For this error estimate approximate values are needed for an eig...
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Bounds including round off errors are given for real simple eigenvalues and corresponding eigenvectors of a square matrix by using interval-arithmetics. For this error estimate approximate values are needed for an eigenvalue and the corresponding eigenvector which can be gained by an arbitrary numerical method. The result is an interval and an intervalvector containing the exact eigenvalue and eigenvector respectively. Also the existence of a real eigenvalue is verified.
作者：
STREHMEL, KPEPER, CSektion Mathematik
Martin-Luther-Universität Halle-Wittenberg Weinbergweg 17 DDR-402 Halle a. d. Saale Deutsche Demokratische Republik
In the present paper a new exponentially fitted one-step method is given for the numerical treatment of the initial value problemy(n)=f(x, y, y′, ..., y(n−1)),y(j) (x0)=y (j)0 j=0, 1, ...n−1. The method is given by a...
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In the present paper a new exponentially fitted one-step method is given for the numerical treatment of the initial value problemy(n)=f(x, y, y′, ..., y(n−1)),y(j) (x0)=y (j)0 j=0, 1, ...n−1. The method is given by a local linearisation off(x, y, y′, ..., y(n−1)). Using new functions the solution of a special linear differential equation of then-th order with constant coefficients is transformed in such a way so that it no longer contains numerical singularities. The efficiency of the method is demonstrated by several numerical stiff-examples.
Three methods (iteration, projection (P) and projection-iteration (PI) methods) with the corresponding error estimations are given to compute the forced oscillations of nonlinear periodic systems. It is proved, that t...
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Three methods (iteration, projection (P) and projection-iteration (PI) methods) with the corresponding error estimations are given to compute the forced oscillations of nonlinear periodic systems. It is proved, that the convergence conditions for the P-method are also sufficient for the convergence of the PI-method. The PI-method has the following advantages: 1. The coefficients of the approximation of orderm can be calculated immidiately from the coefficients of the foregoing approximation. 2. It is no longer necessary to solve nonlinear equations.
The following method of multiplication is based upon computations with simultaneous congruences. The translations needed between the binary form of numbers and their representation by residues can be performed suffici...
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The following method of multiplication is based upon computations with simultaneous congruences. The translations needed between the binary form of numbers and their representation by residues can be performed sufficiently fast by use of a modul of the form Π (2q i–1). A recursive iteration of this principle and additional numbertheoretical arguments lead to the estimateO\((n^1 + (\sqrt 2 + \varepsilon )/\sqrt {^2 lg{\text{ }}n} )\) for the work involved in the multiplication of numbers withn bits. In this context the amount of work is measured by the number of elementary steps of a multitape Turing machine representing this method. This result however is mainly of theoretical importance, for a practical improvement of the trivial boundO (n2) becomes possible only forn>=no with a very largeno.
In the following paper we treat the numerical solution of quasilinear elliptic differential equations of fourth and higher order which are Euler-equations of certain variational problems We reduce the differential equ...
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In the following paper we treat the numerical solution of quasilinear elliptic differential equations of fourth and higher order which are Euler-equations of certain variational problems We reduce the differential equation to a system of equations of the second order and solve this system by the method of finite differences. Existence and uniqueness of a minimal solution of the discrete problem and convergence to the solution of the variational problem under the assumptions of consistency and stability are established as the mesh size and the Penalty-parameter tend to zero.
LetE={e1, ...,e m } be a set of random eventsei occuring with probabilitiesP i . An evente i is followed by an event ŗ of another set of events Ξ with a probability conditional one i . To ŗ is assigned a random vecto...
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LetE={e1, ...,e m } be a set of random eventsei occuring with probabilitiesP i . An evente i is followed by an event ŗ of another set of events Ξ with a probability conditional one i . To ŗ is assigned a random vector x. It is assumed that estimates are obtainable forP i , the mean, and the central second order moments with respect to the conditional probability. Further, the hypothesis is made that the conditional probability can be described by a density functionf i (d i ) which depends only on a positive definite quadratic formd 2 i (x). Then it is shown that for arbitraryf i the quadratic form is determined by the mean and the central second order moments. Let an estimate for the one-dimensional density functionf i (d) be known. Then, if any x is presented it can be decided in probability whiche i preceded x.
Effective procedures for the decision whether two finite graphs are isomorphic or not make use of some information about the automorphism groups of these graphs. The paper deals with a systematic representation of thi...
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Effective procedures for the decision whether two finite graphs are isomorphic or not make use of some information about the automorphism groups of these graphs. The paper deals with a systematic representation of this information and proposes an algorithm scheme for the determination of the automorphisms of a graph.
作者：
FEHLBERG, ENASA
MARSHALL SPACE FLISHT CTRCOMP LABHUNTSVILLEAL 35812
New explicit Runge-Kutta-Nyström formulas for differential equations of the type\(\ddot x = f(t, x)\) are presented. These formulas include a stepsize control procedure based on a complete coverage of the leading...
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New explicit Runge-Kutta-Nyström formulas for differential equations of the type\(\ddot x = f(t, x)\) are presented. These formulas include a stepsize control procedure based on a complete coverage of the leading term of the local truncation error inx. The formulas require fewer evaluations per step than our Runge-Kutta formulas for first-order differential equations. A numerical example is presented. For results of the same accuracy, the computer time for the new formulas is only about 25% to 50% of the time for the corresponding Runge-Kutta formulas.
The idea of regula falsi to use only function-values is extended to the computing of extreme-values by differentiable functions of several variables. Iterative methods of this kind will be found by approximating the f...
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The idea of regula falsi to use only function-values is extended to the computing of extreme-values by differentiable functions of several variables. Iterative methods of this kind will be found by approximating the function by an interpolation polynomial and by taking its extreme-value. The interpolation polynomial being appropriately chosen, the methods converge if the initial values approximate the solution sufficiently well. The speed of convergence is better than linear.
A general theoretical basis for the design of exponentially fitted numerical integration methods will be derived for obtaining methods which, from accuracy and stability, allow large discretization intervals even for ...
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A general theoretical basis for the design of exponentially fitted numerical integration methods will be derived for obtaining methods which, from accuracy and stability, allow large discretization intervals even for systems with large eigenvalues. The technique of transforming existing numerical methods to an exponentially fitted version will be exemplified and the influence of exponential fitting on discretization error and stability for one-step methods will be discussed.
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