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Volumn 60, Issue , 2008, Pages 559-574

Systems of Random Equations. A Review of Some Recent Results

Author keywords

Random polynomial systems; Rice formula

Indexed keywords


EID: 84889306776     PISSN: 10506977     EISSN: 22970428     Source Type: Book Series    
DOI: 10.1007/978-3-7643-8786-0_27     Document Type: Chapter
Times cited : (2)

References (18)
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    • On the Distribution of the Maximum of a Gaussian Field with d Parameters
    • Azäs J.-M. and Wschebor M. (2005a). On the Distribution of the Maximum of a Gaussian Field with d Parameters. Annals Applied Probability, 15 (1A), 254–278.
    • (2005) Annals Applied Probability , vol.15 1A , pp. 254-278
    • Azäs, J.-M.1    Wschebor, M.2
  • 3
    • 27844574729 scopus 로고    scopus 로고
    • On the roots of a random system of equations. The theorem of Shub and Smale and some extensions
    • Azäs J-M. and Wschebor M. (2005b). On the roots of a random system of equations. The theorem of Shub and Smale and some extensions. Found. Comp. Math., 125–144.
    • (2005) Found. Comp. Math , pp. 125-144
    • Azäs, J.-M.1    Wschebor, M.2
  • 6
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    • On the number of real roots of a random algebraic equation
    • Bloch, A. and Polya, G. (1932) On the number of real roots of a random algebraic equation. Proc. Cambridge Phil. Soc., 33, 102–114.
    • (1932) Proc. Cambridge Phil. Soc , vol.33 , pp. 102-114
    • Bloch, A.1    Polya, G.2
  • 9
    • 84967770230 scopus 로고
    • How many zeros of a random polynomial are real
    • Edelman A. and Kostlan, E. (1995) How many zeros of a random polynomial are real? Bull. Amer. Math. Soc. (N.S.), 32 (1): 1–37.
    • (1995) Bull. Amer. Math. Soc. (N.S.) , vol.32 , Issue.1 , pp. 1-37
    • Edelman, A.1    Kostlan, E.2
  • 10
    • 84966210488 scopus 로고
    • On the average number of real roots of a random algebraic equation
    • Kac, M. (1943) On the average number of real roots of a random algebraic equation. Bull. Amer. Math. Soc., 49:314–320.
    • (1943) Bull. Amer. Math. Soc. , vol.49 , pp. 314-320
    • Kac, M.1
  • 11
    • 27844464014 scopus 로고    scopus 로고
    • On the expected number of real roots of a system of random polynomial equations
    • World Sci. Publishing, River Edge, NJ
    • Kostlan, E. (2002) On the expected number of real roots of a system of random polynomial equations. In Foundations of computational mathematics (Hong Kong, 2000), pages 149–188. World Sci. Publishing, River Edge, NJ.
    • (2002) Foundations of Computational Mathematics (Hong Kong, 2000) , pp. 149-188
    • Kostlan, E.1
  • 12
    • 0000496135 scopus 로고
    • On the number of real roots of a random algebraic equation
    • Littlewood J.E. and Offord A.C.(1938) On the number of real roots of a random algebraic equation. J. London Math. Soc., 13, 288–295.
    • (1938) J. London Math. Soc , vol.13 , pp. 288-295
    • Littlewood, J.E.1    Offord, A.C.2
  • 13
    • 84958737079 scopus 로고
    • On the roots of certain algebraic equation
    • Littlewood, J.E. and Offord, A.C. (1939) On the roots of certain algebraic equation. Proc. London Math. Soc., 35, 133–148.
    • (1939) Proc. London Math. Soc , vol.35 , pp. 133-148
    • Littlewood, J.E.1    Offord, A.C.2
  • 14
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    • Metric spaces and completely monotone functions
    • Schoenberg, I.J. (1938) Metric spaces and completely monotone functions. Ann. Of Math. (2), 39(4):811–841.
    • (1938) Ann. of Math. (2) , vol.39 , Issue.4 , pp. 811-841
    • Schoenberg, I.J.1
  • 17
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    • On the Kostlan-Shub-Smale model for random polynomial systems. Variance of the number of roots
    • Wschebor, M. (2005) On the Kostlan-Shub-Smale model for random polynomial systems. Variance of the number of roots. Journal of Complexity, 21, 773–789.
    • (2005) Journal of Complexity , vol.21 , pp. 773-789
    • Wschebor, M.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.