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One method for proving inequalities by computer
[article]

2006
*
arXiv
*
pre-print

In this article we consider a

arXiv:math/0608789v7
fatcat:4pknqoyqkbc2vnbhzn7j4nxzmm
*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 ...##
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Some Notes on a Method for Proving Inequalities by Computer

2015
*
Results in Mathematics
*

In this article we consider mathematical fundamentals of

doi:10.1007/s00025-015-0485-8
fatcat:6c4agev4brcnxfhlozoazxni3a
*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. ...##
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One Method for Proving Inequalities by Computer

2007
*
Journal of Inequalities and Applications
*

We consider a numerical

doi:10.1155/2007/78691
fatcat:juysa22acjbdljqjn77y2vsude
*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 ...##
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A Computer Proof of Turan's Inequality
[article]

2005
*
arXiv
*
pre-print

We show how Turan's

arXiv:math/0509468v1
fatcat:77oyhnqrxnhszatoseqttkopza
*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. ...##
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Page 3627 of Mathematical Reviews Vol. , Issue 2000e
[page]

2000
*
Mathematical Reviews
*

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. ...##
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Page 1822 of Mathematical Reviews Vol. , Issue 99c
[page]

1991
*
Mathematical Reviews
*

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 ...##
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A procedure for proving special function inequalities involving a discrete parameter

2005
*
Proceedings of the 2005 international symposium on Symbolic and algebraic computation - ISSAC '05
*

Some difficult well-known

doi:10.1145/1073884.1073907
dblp:conf/issac/GerholdK05
fatcat:7kqn62mlfvaghjn5cz4twfqpoi
*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. ...##
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On the computer solution of symmetric homogeneous triangle inequalities

1989
*
Proceedings of the ACM-SIGSAM 1989 international symposium on Symbolic and algebraic computation - ISSAC '89
*

Consult [ll]

doi:10.1145/74540.74573
dblp:conf/issac/Rabinowitz89
fatcat:p2cc6s5xe5dvtjnsqgfzr22qvm
*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*. ...##
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Linear secret sharing and the automatic search of linear rank inequalities

2015
*
Applied Mathematical Sciences
*

We

doi:10.12988/ams.2015.57478
fatcat:cupeoazxcnd33ea7llhz2zu4mq
*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. ...##
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Page 4321 of Mathematical Reviews Vol. , Issue 81J
[page]

1981
*
Mathematical Reviews
*

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, ...##
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Qualitative Theorem Proving in Linear Constraints
[chapter]

2003
*
Lecture Notes in Computer Science
*

We know, from the classical work of Tarski

doi:10.1007/978-3-540-39910-0_19
fatcat:mijxxmc73bdcrahhwiv7zskdqu
*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*. ...##
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Page 1553 of Automation and Remote Control Vol. 54, Issue 10
[page]

1993
*
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,,. ...##
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The complexity-theoretic Bell inequality

2018
*
National Science Review
*

The

doi:10.1093/nsr/nwy075
pmid:34691825
pmcid:PMC8291561
fatcat:xma3twhxa5fe5inct5speuuagy
*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. ...##
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Page 7379 of Mathematical Reviews Vol. , Issue 2002J
[page]

2002
*
Mathematical Reviews
*

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. ...##
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Sharp affine Sobolev type inequalities via the Busemann-Petty centroid inequality
[article]

2016
*
arXiv
*
pre-print

and Gagliardo-Nirenberg

arXiv:1505.07763v2
fatcat:vm77tadj3jhexiicn2rkboa7t4
*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*...
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