The problem is to calculate a simple zero of a non-linear function f n-1 by iteration. We exhibit a family of iterations of order 2 which use n evaluations of f and no derivative evaluations, as well as a second family of iterations of order 2 n ^ based on n-1 evaluations of f and one of f f . In particular, with four evaluations we construct an iteration of eighth order.The best previous result for four evaluations was fifth order.We prove that the optimal order of one general class of multipoint n 1 iterations is 2 and that an upper bound on the order of a multipoint iteration based on n evaluations of f (no derivatives) is 2 n .CONJECTURE. A multipoint iteration without memory based on n evaluations has optimal order 2 n

ASSTRACT. Let U1 , U2, . . . , Ud be totally ordered sets and let V be a set of n d-dimensional vectors In U~ X Us. . X Ud . A partial ordering is defined on V in a natural way The problem of finding all maximal elements of V with respect to the partial ordering ~s considered The computational complexity of the problem is defined to be the number of required comparisons of two components and is denoted by Cd(n). It is tnwal that C~(n) = n -1 and C,~(n) < O(n 2) for d _~ 2 In this paper we show: (1) C2(n) = O(n logan) for d = 2, 3 and Cd(n) ~ O(n(log2n) ~-~) for d ~ 4, (2) C,t(n) >_ flog2 n!l for d _> 2 KEY WORDS AND PHRASES: maxima of a set of vectors, computattonal complexity, number of comparisons, algorithm, recurrence CR CATEaOmES. 5.25, 5,31, 5.39

Most current approaches to concurrency control in database systems rely on locking of data objects as a control mechanism. In this paper, two families of nonlocking concurrency controls are presented. The methods used are "optimistic" in the sense that they rely mainly on transaction backup as a control mechanism, "hoping" that conflicts between transactions will not occur. Applications for which these methods should be more efficient than locking are discussed.

ABSTRACT.A maximal vector of a set ~s one which is not less than any other vector m all components We derive a recurrence relation for computing the average number of maxunal vectors m a set of n vectors m d-space under the assumpUon that all (nl) a relative ordermgs are equally probable. Solving the recurrence shows that the average number of maxmaa is O((ln n) a-~) for fixed d We use this result to construct an algorithm for finding all the maxima that have expected running tmae hnear m n (for sets of vectors drawn under our assumptions) We then use the result to find an upper bound on the expected number of convex hull points m a random point set KE~ WORDS AND eHRASES maxtma of a set of vectors, average number of maxtma, expected-tsme algorithms, analysts of algorithms, convex hulls, dynamtc programming CR CATEGORIES" 5 25, 5.39, 5.42

No abstract