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Volumn 24, Issue 4, 2008, Pages 524-544

Effective Pólya semi-positivity for non-negative polynomials on the simplex

Author keywords

Homogeneous polynomials; P lya semi positivity; Simplex; Zeros

Indexed keywords

COMPUTATIONAL COMPLEXITY; NUMERICAL ANALYSIS;

EID: 47949115480     PISSN: 0885064X     EISSN: 10902708     Source Type: Journal    
DOI: 10.1016/j.jco.2008.01.003     Document Type: Article
Times cited : (3)

References (16)
  • 2
    • 47949109577 scopus 로고    scopus 로고
    • M. Castle, V. Powers, B. Reznick, A quantitative Pólya's theorem with zeros. MEGA 2007. Preprint 〈http://www.mathcs.emory.edu/~vicki/preprint/polya3.pdf〉.
    • M. Castle, V. Powers, B. Reznick, A quantitative Pólya's theorem with zeros. MEGA 2007. Preprint 〈http://www.mathcs.emory.edu/~vicki/preprint/polya3.pdf〉.
  • 3
    • 0000463583 scopus 로고
    • Über die Zerlegung strikte definter Formen in Quadrate
    • Habicht W. Über die Zerlegung strikte definter Formen in Quadrate. Comment. Math. Helv. 12 (1940) 317-322
    • (1940) Comment. Math. Helv. , vol.12 , pp. 317-322
    • Habicht, W.1
  • 4
    • 0041093366 scopus 로고
    • Deciding eventual positivity of polynomials
    • Handelman D. Deciding eventual positivity of polynomials. Ergodic Theory Dynam. Systems 6 (1986) 57-79
    • (1986) Ergodic Theory Dynam. Systems , vol.6 , pp. 57-79
    • Handelman, D.1
  • 5
    • 84972584455 scopus 로고
    • Representing polynomials by positive linear functions on compact convex polyhedra
    • Handelman D. Representing polynomials by positive linear functions on compact convex polyhedra. Pacific J. Math. 132 (1988) 35-62
    • (1988) Pacific J. Math. , vol.132 , pp. 35-62
    • Handelman, D.1
  • 6
    • 0036433723 scopus 로고    scopus 로고
    • Approximation of the stability number of a graph via copositive programming
    • de Klerk E., and Pasechnik D. Approximation of the stability number of a graph via copositive programming. SIAM J. Optim. 12 (2002) 875-892
    • (2002) SIAM J. Optim. , vol.12 , pp. 875-892
    • de Klerk, E.1    Pasechnik, D.2
  • 7
    • 0030581992 scopus 로고    scopus 로고
    • An effective version of Pólya's theorem on positive definite forms
    • de Loera J.A., and Santos F. An effective version of Pólya's theorem on positive definite forms. J. Pure Appl. Algebra 108 (1996) 231-240
    • (1996) J. Pure Appl. Algebra , vol.108 , pp. 231-240
    • de Loera, J.A.1    Santos, F.2
  • 8
    • 85028641736 scopus 로고    scopus 로고
    • Erratum to "an effective version of Pólya's theorem on positive definite forms"
    • de Loera J.A., and Santos F. Erratum to "an effective version of Pólya's theorem on positive definite forms". J. Pure Appl. Algebra 155 (2000) 309-310
    • (2000) J. Pure Appl. Algebra , vol.155 , pp. 309-310
    • de Loera, J.A.1    Santos, F.2
  • 9
    • 84972541849 scopus 로고
    • Divisors of polynomials and power series with positive coefficients
    • Motzkin T.S., and Strauss E.G. Divisors of polynomials and power series with positive coefficients. Pacific J. Math. 29 (1969) 641-652
    • (1969) Pacific J. Math. , vol.29 , pp. 641-652
    • Motzkin, T.S.1    Strauss, E.G.2
  • 10
    • 47949094921 scopus 로고    scopus 로고
    • G. Pólya, Über positive Darstellung von Polynomen, in: Vierterhartschrigt d. Naturforschenden Gessellschaft in Zürich 73 (1928) 141-145; see: Collected Papers, vol. 2, MIT Press, Cambridge, 1974, pp. 309-313.
    • G. Pólya, Über positive Darstellung von Polynomen, in: Vierterhartschrigt d. Naturforschenden Gessellschaft in Zürich 73 (1928) 141-145; see: Collected Papers, vol. 2, MIT Press, Cambridge, 1974, pp. 309-313.
  • 11
    • 0001276275 scopus 로고    scopus 로고
    • A new bound for Pólya's theorem with applications to polynomials positive on polyhedra
    • Powers V., and Reznick B. A new bound for Pólya's theorem with applications to polynomials positive on polyhedra. J. Pure Appl. Algebra 164 (2001) 221-229
    • (2001) J. Pure Appl. Algebra , vol.164 , pp. 221-229
    • Powers, V.1    Reznick, B.2
  • 12
    • 33748973180 scopus 로고    scopus 로고
    • V. Powers, B. Reznick, A quantitative Pólya's theorem with corner zeros, in: ISSAC 2006, ACM, New York, 2006, pp. 285-289.
    • V. Powers, B. Reznick, A quantitative Pólya's theorem with corner zeros, in: ISSAC 2006, ACM, New York, 2006, pp. 285-289.
  • 13
    • 3242670750 scopus 로고    scopus 로고
    • An algorithmic approach to Schmüdgen's Positivstellensatz
    • Schweighofer M. An algorithmic approach to Schmüdgen's Positivstellensatz. J. Pure Appl. Algebra 166 (2002) 307-319
    • (2002) J. Pure Appl. Algebra , vol.166 , pp. 307-319
    • Schweighofer, M.1
  • 14
    • 3242670924 scopus 로고    scopus 로고
    • On the complexity of Schmüdgen's Positivstellensatz
    • Schweighofer M. On the complexity of Schmüdgen's Positivstellensatz. J. Complexity 20 (2004) 529-543
    • (2004) J. Complexity , vol.20 , pp. 529-543
    • Schweighofer, M.1
  • 15
    • 23944437404 scopus 로고    scopus 로고
    • Certificates for nonnegativity of polynomials with zeros on compact semialgebraic sets
    • Schweighofer M. Certificates for nonnegativity of polynomials with zeros on compact semialgebraic sets. Manuscripta Math. 117 (2005) 407-428
    • (2005) Manuscripta Math. , vol.117 , pp. 407-428
    • Schweighofer, M.1
  • 16
    • 23844493105 scopus 로고    scopus 로고
    • Optimization of polynomials on compact semialgebraic sets
    • Schweighofer M. Optimization of polynomials on compact semialgebraic sets. SIAM J. Optim. 15 (2005) 805-825
    • (2005) SIAM J. Optim. , vol.15 , pp. 805-825
    • Schweighofer, M.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.