The Internet Archive has a preservation copy of this work in our general collections.
The file type is
In this article we consider a method for proving a class of analytical inequalities via minimax rational approximations. All numerical calculations in this paper are given by Maple computer program. ... A numerical method for proving inequalities In this section we expose a numerical method for proving inequalities in following form: f (x) ≥ 0 (29) for the continuous function f : [a, b] −→ R. ... For the function of one variable the previous method can be applied to the inequality the infinite interval using the appropriate substitute variable, which transforms inequality to the new one over the ...arXiv:math/0608789v7 fatcat:4pknqoyqkbc2vnbhzn7j4nxzmm
In this article we consider mathematical fundamentals of one method for proving inequalities by computer, based on the Remez algorithm. ... We give some improvements of the inequalities considered in the theorems for which the existing proofs have been based on the numerical verifications of Remez algorithm. ... The authors would like to thank anonymous reviewer for his/her valuable comments and suggestions, which were helpful in improving the article. ...doi:10.1007/s00025-015-0485-8 fatcat:6c4agev4brcnxfhlozoazxni3a
We consider a numerical method for proving a class of analytical inequalities via minimax rational approximations. All numerical calculations in this paper are given by Maple computer program. ... Acknowledgment The research was partially supported by the MNTRS, Serbia, Grant no. 144020. ... ] . 6 Journal of Inequalities and Applications A method for proving inequalities In this section we expose a numerical method for proving inequalities in following form: f (x) ≥ 0 (2.1) for the continuous ...doi:10.1155/2007/78691 fatcat:juysa22acjbdljqjn77y2vsude
We show how Turan's inequality P_n(x)^2-P_n-1(x)P_n+1(x)≥ 0 for Legendre polynomials and related inequalities can be proven by means of a computer procedure. ... For instance, we have found the stronger inequality |x|P_n(x)^2-P_n-1(x)P_n+1(x)≥ 0, -1≤ x≤ 1, effortlessly with the aid of our method. ... The Proving Method We exemplify our proving method on the classical Turán inequality (1.1). The idea underlying the method is complete induction on n. ...arXiv:math/0509468v1 fatcat:77oyhnqrxnhszatoseqttkopza
This paper describes an algorithm for proving geometric inequali- ties by using the computer algebra software Maple and cylindrical algebraic decomposition technique. ... Jingzhong Zhang (PRC-ASCD; Chengdu) 2000e:68151 68T15 26Dxx Yang, Lu (PRC-GZT-ESF; Guangzhou) Practical automated reasoning on inequalities: generic programs for inequality proving and discovering. ...
He’s method [“A class of new methods for monotone variational inequalities”, Tech. Rep., Inst. ... The note deals with the Halley method Yn = Xn F'(xn)7'F (xn), H (Xn, Yn) = —F'(xn)F" (xn) Wn = ta) Xn+1 -= Yn — SF'(xn)7'U = SH (Xn, ¥n)J FE" (Xn) (On a7 ta) for solving equations F(x) = 0, where F is ...
Some difficult well-known inequalities such as the Askey-Gasper inequality and Vietoris's inequality lie in our class as well, but we do not know if our proving procedure terminates for them. ... We define a class of special function inequalities that contains many classical examples, such as the Cauchy-Schwarz inequality, and introduce a proving procedure based on induction and Cylindrical Algebraic ... In this paper, we have contributed a simple but powerful method for proving special function inequalities, based on a connection of CAD with difference algebra. ...doi:10.1145/1073884.1073907 dblp:conf/issac/GerholdK05 fatcat:7kqn62mlfvaghjn5cz4twfqpoi
Consult [ll] for a guide to the literature in this area. Even the method of cylindrical decomposition may be too slow for proving the types of inequalities we are interested in. ... A COMPUTER ALGORITHM In this section, we describe an algorithm (more technically a set of heuristics) for proving certain polynomial inequalities. ...doi:10.1145/74540.74573 dblp:conf/issac/Rabinowitz89 fatcat:p2cc6s5xe5dvtjnsqgfzr22qvm
We prove that if one knows a generating set for the cone of linear rank inequalities on n + 1 variables, then he can use this generating set and linear programming (or semi-infinite programming) to compute ... This theorem shows that it is useful and important to compute generating sets for the cones of linear rank inequalities on a given number of variables. ... Acknowledgment This research was developed thanks to the financial support provided by COL-CIENCIAS. ...doi:10.12988/ams.2015.57478 fatcat:cupeoazxcnd33ea7llhz2zu4mq
We justify a two-stage method for the problem which is a development of the adaptive method earlier proposed by us. ... Parameter management from situation features by pattern-recogni- tion methods is illustrated by a problem in linear programming, mixed strategies for a finite set of iterative operators are indicated, ...
Lecture Notes in Computer Science
We know, from the classical work of Tarski on real closed elds, that elimination is, in principle, a fundamental engine for mechanized deduction. ... We advocate qualitative theorem proving, where elimination is attractive since most processes of reasoning take place through the elimination of middle terms, and because the computational complexity of ... Qualitative Theorem Proving In this paper we will focus on the non-computational or non-automated aspects of theorem proving. ...doi:10.1007/978-3-540-39910-0_19 fatcat:mijxxmc73bdcrahhwiv7zskdqu
Automation and Remote Control
The method of optimization of a description of an arbitrary (parenthetical) BF in the basis AND, OR, NOT does not allow one to compute them with maximal plausibility by means of ranging and goal-driven ... By induction, this leads to the statement r; > R for y = y; for an arbitrary n. We prove that R > r,,. ...
The inequality proves Einstein wrong and provides a concrete method to tell apart quantum mechanics and classical theories. ... The standard Bell inequality tells us that the classical and quantum values can be different for a fixed game; our result instead establishes that the computational complexities for approximating the classical ... The inequality proves Einstein wrong and provides a concrete method to tell apart quantum mechanics and classical theories. ...doi:10.1093/nsr/nwy075 pmid:34691825 pmcid:PMC8291561 fatcat:xma3twhxa5fe5inct5speuuagy
Summary: “In this paper, we suggest and analyze a class of predictor-corrector methods for computing the fixed-points of general mixed variational inequalities. ... (English summary) Comput. Methods Appl. Math. 1 (2001), no. 3, 242-264. ...
and Gagliardo-Nirenberg inequalities. ... We show that the Busemann-Petty centroid inequality provides an elementary and powerful tool to the study of some sharp affine functional inequalities with a geometric content, like log-Sobolev, Sobolev ... Schuster for pointing out several references and useful comments on a previous version of this work and as well to the referee for several valuable comments and for proposing the study with our method ...arXiv:1505.07763v2 fatcat:vm77tadj3jhexiicn2rkboa7t4
« Previous Showing results 1 — 15 out of 473,580 results