Search

The purpose of this paper is to describe a new gradient method for maximizing general functions. After a brief discussion of various known gradient methods the mathematical foundation is laid for the new algorithm which rests on maximizing a quadratic approximation to the function on a suitably chosen spherical region. The method requires no assumptions about the concavity of the function to be maximized and automatically modifies the step size in the light of the success of the quadratic approximation to the function. The paper further discusses some practical problems of implementing the algorithm and presents recent computational experience with it. [ABSTRACT FROM AUTHOR]

This paper presents mathematical evaluation measures to characterize the effect of known erroneous performance by stemming routines, and generalizes these procedures to other types of nonstatistical clustering algorithms. When clusters, or groups of intrinsically related elements, are split into smaller groups (by under-matching the elements), there is a loss in recall in information retrieval; larger groups (caused by over- matching) induce a loss in precision or relevance. The magnitude of error is taken to be a function of frequencies of cluster elements. When these ore words in a subject-term index generated by a stemming algorithm, retrieval capability is also affected by the strength of the algorithm, the size and content of the stemmed index, and the number of words in a query. The present Project Intrex stemming algorithm has estimated stemming-error losses of 4% in recall and 1% in relevance on one-word queries; the former could be reduced to almost zero by straightforward corrections of known errors in the algorithm. An expanded probabilistic model is introduced to handle a more general case in which any element need not belong unambiguously to a single cluster. Error evaluation in document classification and thesauri also is discussed in broad terms. [ABSTRACT FROM AUTHOR]

Geometric programming is a mathematical programming technique that is designed to determine the constrained minimum value of a generalized polynomial objective function. To date, most applications of the technique have been restricted to certain classes of engineering problems. This paper presents a brief summary of geometric programming and then illustrates its application to managerial problems by applying it to three well-known inventory models. [ABSTRACT FROM AUTHOR]

The article comments on the paper "Syminv: An Algorithm for the Inversion of a Positive Definite Matrix by the Cholesky Decomposition," by Terry Seaks, published in volume 40 of "Econometrica." In his article Seaks describes an algorithm for the Cholesky decomposition of a positive symmetric matrix, citing J.H. Wilkinson's work. The author explains that the relevant conclusions in Wilkinson's paper are those for floating point calculation and that the numerical advantage of the Cholesky procedure depends on being able to accumulate inner products accurately.