Fast method to compute the scalar product of gradient and given vector

The paper deals with a special problem in Automatic Differentiation. Letf be a rational function ofn variables, let #(f) denote the number of operations to evaluatef(x), letg denote the gradient off. Many algorithms for minimizingf(x) require the scalar productg(u) ^tv. In the standard method for computingg(u) ^tv the amount of work grows withn·#(f). In this note a new method for computingg(u) ^tv is presented. The new method is considerably faster, its amount of work only grows with #(f).     

The possibility of evolving a theory for predicting the service life of reinforced concrete structures

The development in recent years with increasing air pollution, increasing need of energy saving and last not least the growing number of damage in old structures leads to a raising demand to calculate the durability of structures, too. The paper has been prepared by request of the RILEM Technical Committee 45-LTO to show that, in principle, it is possible to evolve a theory for predicting the service life of r.c. structures and to sketch a way how that could be achieved. A lot of necessary basic data can be found scattered in the literature. To collect these data will be the first step to take.     

Embedding universal computer arithmetic in higher programming languages

In numerical computations mainly real and complex numbers, intervals as well as matrices and vectors with such components occur. It is well known that the arithmetic operations with real numbers, complex numbers etc. can be carried over to real floating-point numbers, complex floating-point numbers etc. using roundings. This proceeding results in agreeable arithmetic-, order- and compatibility-properties for an abundance of numerical data types and the accompanying arithmetic operations. Most programming languages however only provide real floating-point numbers; all the other data types and operations have to be simulated, e. g. in the form of arrays and procedure calls, which often causes loss of accuracy and arithmetic properties. Furthermore the complicate notation makes programs difficult to read. Therefore in this article an extension of PASCAL is presented which serves as an example for the way these numerical data types can be embedded into the syntax of a programming language.     

How to avoid logarithms in comparisons with uniform random variables

In many algorithms for sampling from non-uniform distributions the logarithm of a uniform deviate must be compared with some test quantity. It is shown that all these comparisons can be done efficiently without calling a logarithm subprogram: two procedures for this task are presented and compared.     

On plastic potentials for anisotropic metals and their derivation from the texture function

Summary Plastic yielding of anisotropic metals can be either described by a macroscopic constitutive relation or assessed by means of a model which correlates single and polycrystal behaviors. The mathematical identification of the plastic work rate derived from the two approaches, for all strain rate tensors, leads to a fit of the polycrystal yield surface by an analytical function. When a quadratic from is assumed, the macroscopic anisotropy parameters become explicit functions of the texture coefficients. This identification method is applied to calculate yield surfaces andR-values of rolled and annealed steel sheets: theR-values and in general the flow rule, are more significantly modified by the fitting than the yield surface. Thus, it is worth extending the method to more general constitutive relations which may be given by the form of their work function: alternative forms of the work function for plastic materials are explored, especially in the bearing of convexity and homogeneity where quadratic forms have a distinct advantage. Finally, it is shown that the identification of the work function allows to express the phenomenological coefficients as analytical functions of the texture parameters for many forms of the work function; in the other cases, these coefficients may be obtained by linear or non-linear regression.     

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