We describe a method for finding errorbounds for eigenvalues and eigenvectors. Results from an earlier paper by the author (see [6]) are used to find a fast algorithm that produces good errorbounds.
We describe a method for finding errorbounds for eigenvalues and eigenvectors. Results from an earlier paper by the author (see [6]) are used to find a fast algorithm that produces good errorbounds.
In linear programming often it is important whether a given linear programming problem is equivalent to a transportation problem. In this case, the stepping-stone method could be taken for solving the problem, instead...
详细信息
In linear programming often it is important whether a given linear programming problem is equivalent to a transportation problem. In this case, the stepping-stone method could be taken for solving the problem, instead of the simplex method, which requires more storage capacity and computing time.—To decide this question a so-called simplex matrix is used, which results from the given linear programming problem treated by the simplex method. By help of two necessary conditions as well as a necessary and sufficient condition it can be concluded whether the linear programming problem belonging to that simplex matrix is equivalent to a transportation problem or not.—The practical handling of the developed algorithm is shown by an example.
Two ALGOL-60 algorithms are presented to solve systems of linear equations whose coefficients are known to vary in given intervals. So it is possible to handle with such systems on an arbitrary computer possessing an ...
详细信息
Two ALGOL-60 algorithms are presented to solve systems of linear equations whose coefficients are known to vary in given intervals. So it is possible to handle with such systems on an arbitrary computer possessing an ALGOL-60 compiler. Simultaneously all rounding errors are included. For understanding the programs a brief introduction is given.
作者：
NUDING, ERechenzentrum
Universität Heidelberg Im Neuenheimer Feld 293 D-6900 Heidelberg Bundesrepublik Deutschland
An algorithm is proposed for computation of the exponential of a matrixX which uses the well known continued fraction expansion of tanhX. ForX essentially-nonnegative the following is proved: In interval arithmetic th...
详细信息
An algorithm is proposed for computation of the exponential of a matrixX which uses the well known continued fraction expansion of tanhX. ForX essentially-nonnegative the following is proved: In interval arithmetic the algorithm is feasible, numerically convergent and bound conserving; after possibly a few initial steps it gives alternatively lower and upper bounds to the exact result.
Accurate computer methods are evaluated which transform uniformly distributed random numbers into quantities that follow gamma, beta, Poisson, binomial and negative-binomial distributions. All algorithms are designed ...
详细信息
Accurate computer methods are evaluated which transform uniformly distributed random numbers into quantities that follow gamma, beta, Poisson, binomial and negative-binomial distributions. All algorithms are designed for variable parameters. The known convenient methods are slow when the parameters are large. Therefore new procedures are introduced which can cope efficiently with parameters of all sizes. Some algorithms require sampling from the normal distribution as an intermediate step. In the reported computer experiments the normal deviates were obtained from a recent method which is also described.
In this paper some definitions and properties of interval-norms and spans are treated. Then severalNewton-algorithms for finding roots of functions with one variable are given. The algorithms use interval-arithmetics ...
详细信息
In this paper some definitions and properties of interval-norms and spans are treated. Then severalNewton-algorithms for finding roots of functions with one variable are given. The algorithms use interval-arithmetics and yield an interval-result containing the exact root. The algorithms then are generalized to solve systems of equations.
In this paper we prove the convergence of the Davidon-Fletcher-Powell-method for strictly convex minimization problems in Hilbert space. Furthermore it is shown, that this method yields an admissible sequence of direc...
详细信息
In this paper we prove the convergence of the Davidon-Fletcher-Powell-method for strictly convex minimization problems in Hilbert space. Furthermore it is shown, that this method yields an admissible sequence of directions in case of a quadratic minimization problem in Hilbert space.
An iterative method for the solution of a system of linear inequalities is given. The rate of convergence of the method is estimated under various assumptions.
An iterative method for the solution of a system of linear inequalities is given. The rate of convergence of the method is estimated under various assumptions.
A theory of hybrid finite element approximation is developed for a class of shell problems. Though it is appl.ed only to the special case of clamped shallow shells with regular triangularization the results may be of ...
详细信息
A theory of hybrid finite element approximation is developed for a class of shell problems. Though it is appl.ed only to the special case of clamped shallow shells with regular triangularization the results may be of larger interest comparing the predicted convergence rate with the numerical outcome of some appl.cations of the hybrid finite element method. The convergence speed can only be increased by higher degrees of the approximation and the stresses at the edges correspondingly. The use of a so-called rank condition plays a fundamental role in the study. Weak coerciveness of the under lyigg bilinear form for the derivation of hybrid elements is proved by showing the existence of a stationary point.
暂无评论