منابع مشابه
Two Algorithms for Root Finding in
We present two algorithms for computing the root, or equivalently the xed point, of a function in exact real arithmetic. The rst algorithm uses the iteration of the expression tree representing the function in real arithmetic based on linear fractional transformations and exact oating point. The second and more general algorithm is based on a trisection of intervals and can be compared with the...
متن کاملPolynomial Root-Finding Algorithms and Branched Covers
Introduction. The problem of devising optimal methods for numerically approximating the roots of a polynomial has been of interest for several centuries, and is far from solved. There are numerous recent works on root-finding algorithms and their cost, for example, the work of Jenkins and Traub [JT70], Renegar [Ren87], Schönhage [Sch82], and Shub and Smale [SS85, SS86, Sma85]. This list is far ...
متن کاملOn finding optimum paths in computer networks
1 Supported in part by a grant from the Texas Advanced Research Program. Abstract-We consider the problem of finding an optimum path from each node in the network to a destination node in the network. Typically, each edge in the network is assigned a weight value (e.g. bandwidth or delay), and a metric function (e.g. min or +) is applied consecutively to the edges in the path. The result is the...
متن کاملFinding optimum branchings
Chu and Liu, Ecbnonds, and Bock have independently devised an ef f ic ient aZgorYithm to f i n d an optimum branching i n a d i rected haph. runs i n O(m2ogn) time i f the problem graph has n vertices and m edges. A modification for dense graphs gives a running time 2 of O(n 1. We also show that the unmodified algorithm runs i n 2 O(n(Zog n) + m) time on an average graph, asswning a uniform pro...
متن کاملA note on finding optimum branchings
The subject of t h i s note i s Tarjan's aZgorithm for finding an optimum branching in a directed graph. ed out, namely (i) an incorrect cZaim invoZving branching uniqueness, and (ii) an imprecise way of updating edge vaZues i n each i terat ion. val idi ty of the algorithm. I t is s h m here that they may be f ixed v i a a simpZe modification, which Zeaves unchanged the overall time and space ...
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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 1971
ISSN: 0022-247X
DOI: 10.1016/0022-247x(71)90031-x