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Volumn 13, Issue 2, 1985, Pages 87-121

On the efficiency of algorithms of analysis

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EID: 84967770163     PISSN: 02730979     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0273-0979-1985-15391-1     Document Type: Article
Times cited : (229)

References (55)
  • 5
    • 0039802226 scopus 로고
    • Über die Divergenzpunkte des Newtonschen Verfahrens zur Bestimmung von Wurzeln Algebraischer Gleichungen. II
    • B. Barna, Über die Divergenzpunkte des Newtonschen Verfahrens zur Bestimmung von Wurzeln Algebraischer Gleichungen. II, Publ. Math. Debrecen 4 (1956), 384–397.
    • (1956) Publ. Math. Debrecen , vol.4 , pp. 384-397
    • Barna, B.1
  • 6
    • 84968494997 scopus 로고
    • Complex analytic dynamics on the Riemann sphere
    • P. Blanchard, Complex analytic dynamics on the Riemann sphere, Bull. Amer. Math. Soc. (N.S.) 11 (1984), 85–141.
    • (1984) Bull. Amer. Math. Soc. (N.S.) , vol.11 , pp. 85-141
    • Blanchard, P.1
  • 7
    • 84913283825 scopus 로고    scopus 로고
    • Evaluating rational functions: Infinite precision is finite cost and tractable on average
    • (to appear)
    • L. Blum and M. Shub, Evaluating rational functions: Infinite precision is finite cost and tractable on average, SIAM J. Comput. (to appear).
    • SIAM J. Comput.
    • Blum, L.1    Shub, M.2
  • 8
    • 0020179461 scopus 로고
    • The average number of pivot steps required by the simplex-method is polynomial
    • K. H. Borgwardt, The average number of pivot steps required by the simplex-method is polynomial, Z. Oper. Res. 26 (1982), 157–177.
    • (1982) Z. Oper. Res. , vol.26 , pp. 157-177
    • Borgwardt, K.H.1
  • 10
    • 0000519586 scopus 로고
    • On the iteration of a rational function: Computer experiments with Newton’s method
    • J. Curry, L. Garnett and D. Sullivan, On the iteration of a rational function: Computer experiments with Newton’s method, Comm. Math. Phys. 91 (1983), 267–277.
    • (1983) Comm. Math. Phys. , vol.91 , pp. 267-277
    • Curry, J.1    Garnett, L.2    Sullivan, D.3
  • 15
    • 0009068559 scopus 로고
    • Systèmes dynamiques holomorphes
    • A. Douady, Systèmes dynamiques holomorphes, Séminaire Bourbaki, No. 599, 1982.
    • (1982) Séminaire Bourbaki , Issue.599
    • Douady, A.1
  • 16
    • 0016918552 scopus 로고
    • The solution of systems of piecewise linear equations
    • C. Eaves and H. Scarf, The solution of systems of piecewise linear equations, Math. Oper. Res. 1 (1976), 1–27.
    • (1976) Math. Oper. Res. , vol.1 , pp. 1-27
    • Eaves, C.1    Scarf, H.2
  • 17
    • 0041197143 scopus 로고
    • Gaussian measures on Banach spaces and manifolds
    • International Atomic Energy Agency, Vienna
    • D. Elworthy, Gaussian measures on Banach spaces and manifolds, Global Analysis and its Applications, Vol. II, International Atomic Energy Agency, Vienna, 1974, pp. 151–166.
    • (1974) Global Analysis and Its Applications, Vol. II , pp. 151-166
    • Elworthy, D.1
  • 18
    • 0000888015 scopus 로고
    • Sur les equations fonctionnelles
    • P. Fatou, Sur les equations fonctionnelles, Bull. Soc. Math. France 47, 48 (1919–1920), 161–211; 33–94; 208–314.
    • (1919) Bull. Soc. Math. France , vol.47-48
    • Fatou, P.1
  • 21
    • 0040417842 scopus 로고
    • Endomorphisms of the Riemann sphere
    • (Chern and Smale, eds.), Amer. Math. Soc., Providence, R. I
    • J. Guckenheimer, Endomorphisms of the Riemann sphere, Global Analysis (Chern and Smale, eds.), Amer. Math. Soc., Providence, R. I., 1970, pp. 95–123.
    • (1970) Global Analysis , pp. 95-123
    • Guckenheimer, J.1
  • 25
    • 0002413379 scopus 로고
    • Mémoire sur l’itération des fonctions rationnelles
    • G. Julia, Mémoire sur l’itération des fonctions rationnelles, J. Math. Pures Appl. 4 (1918), 47–245.
    • (1918) J. Math. Pures Appl. , vol.4 , pp. 47-245
    • Julia, G.1
  • 27
    • 0021375962 scopus 로고
    • On the cost of computing roots of polynomials
    • H. Kuhn, Z. Wang and Senlin Xu, On the cost of computing roots of polynomials, Math. Programming 28 (1984), 156–163.
    • (1984) Math. Programming , vol.28 , pp. 156-163
    • Kuhn, H.1    Wang, Z.2    Senlin, X.3
  • 28
    • 0003225839 scopus 로고
    • Gaussian measures in Banach spaces
    • Springer-Verlag, Berlin and New York
    • H. H. Kuo, Gaussian measures in Banach spaces, Lecture Notes in Math., vol. 463, Springer-Verlag, Berlin and New York, 1975.
    • (1975) Lecture Notes in Math. , vol.463
    • Kuo, H.H.1
  • 29
    • 0003956970 scopus 로고
    • Addison-Wesley, Reading, Mass
    • S. Lang, Algebra, Addison-Wesley, Reading, Mass., 1963.
    • (1963) Algebra
    • Lang, S.1
  • 30
    • 0042260766 scopus 로고
    • Newton’s algorithm and chaotic dynamical systems
    • C. Martin and R. Hurley, Newton’s algorithm and chaotic dynamical systems, SIAM J. Math. Anal. 16 (1984), 238–252.
    • (1984) SIAM J. Math. Anal. , vol.16 , pp. 238-252
    • Martin, C.1    Hurley, R.2
  • 35
    • 84968500881 scopus 로고    scopus 로고
    • On the complexity of a piecewise linear algorithm for approximating roots of complex polynomials
    • (to appear)
    • J. Renegar I, On the complexity of a piecewise linear algorithm for approximating roots of complex polynomials, Math. Programming (to appear).
    • Math. Programming
    • Renegar, J.1
  • 36
    • 84968487440 scopus 로고    scopus 로고
    • On the cost of approximating all roots of a complex polynomial
    • (to appear)
    • J. Renegar II, On the cost of approximating all roots of a complex polynomial, Math. Programming (to appear).
    • Math. Programming
    • Renegar, J.1
  • 38
    • 0041760030 scopus 로고
    • Newton’s method, circle maps, and chaotic motion
    • D. Saari and J. Urenko, Newton’s method, circle maps, and chaotic motion, Amer. Math. Monthly 91 (1984), 3–17.
    • (1984) Amer. Math. Monthly , vol.91 , pp. 3-17
    • Saari, D.1    Urenko, J.2
  • 42
    • 84968503240 scopus 로고    scopus 로고
    • Computational complexity: On the geometry of polynomials and a theory of cost, Part I
    • (to appear)
    • M. Shub and S. Smale I, Computational complexity: On the geometry of polynomials and a theory of cost, Part I, Ann. Sci. École Norm. Sup. (4) (to appear).
    • Ann. Sci. École Norm. Sup. , Issue.4
    • Shub, M.1    Smale, S.2
  • 43
    • 84968519591 scopus 로고    scopus 로고
    • Computational complexity: On the geometry of polynomials and a theory of cost: Part II
    • (to appear)
    • M. Shub and S. Smale II, Computational complexity: On the geometry of polynomials and a theory of cost: Part II, SIAM J. Computing (to appear).
    • SIAM J. Computing
    • Shub, M.1    Smale, S.2
  • 44
    • 84966238914 scopus 로고
    • The Mathematics of Time, Springer-Verlag, New York and Berlin
    • S. Smale I, Differentiable dynamical systems, The Mathematics of Time, Springer-Verlag, New York and Berlin, 1980.
    • (1980) Differentiable Dynamical Systems
    • Smale, S.1
  • 45
    • 49549130863 scopus 로고
    • A convergent process of price adjustment and global Newton methods
    • S. Smale II, A convergent process of price adjustment and global Newton methods, J. Math. Econom. 3 (1976), 107–120.
    • (1976) J. Math. Econom. , vol.3 , pp. 107-120
    • Smale, S.1
  • 46
    • 84966209344 scopus 로고
    • The fundamental theorem of algebra and complexity theory
    • S. Smale III, The fundamental theorem of algebra and complexity theory, Bull. Amer. Math. Soc. (N. S.) 4 (1981), 1–36.
    • (1981) Bull. Amer. Math. Soc. (N. S.) , vol.4 , pp. 1-36
    • Smale, S.1
  • 47
    • 0020881843 scopus 로고
    • On the average number of steps in the simplex method of linear programming
    • S. Smale IV, On the average number of steps in the simplex method of linear programming, Math. Programming 27 (1983), 241–262.
    • (1983) Math. Programming , vol.27 , pp. 241-262
    • Smale, S.1
  • 48
    • 84909725471 scopus 로고
    • The problem of the average speed of the Simplex method
    • The State of the Art (Bonn, 1982) (Bachem et al., eds.), Springer-Verlag, Berlin and New York
    • S. Smale V, The problem of the average speed of the Simplex method, Mathematical Programming, The State of the Art (Bonn, 1982) (Bachem et al., eds.), Springer-Verlag, Berlin and New York, 1983.
    • (1983) Mathematical Programming
    • Smale, S.1
  • 49
    • 84968502180 scopus 로고    scopus 로고
    • Quasiconformal homeomorphisms and dynamics III: Topological conjugacy classes of analytic endomorphisms
    • (to appear)
    • D. Sullivan, Quasiconformal homeomorphisms and dynamics III: Topological conjugacy classes of analytic endomorphisms, Ann. of Math, (to appear).
    • Ann. of Math
    • Sullivan, D.1
  • 50
    • 84910526091 scopus 로고
    • Polynomial expected behavior of a pivoting algorithm for linear complementary and linear programming problems
    • School of Operations Research and Industrial Engineering, Cornell University, Ithaca, New York
    • M. J. Todd, Polynomial expected behavior of a pivoting algorithm for linear complementary and linear programming problems, Technical Report No. 595, School of Operations Research and Industrial Engineering, Cornell University, Ithaca, New York, 1983.
    • (1983) Technical Report No. 595
    • Todd, M.J.1
  • 51
    • 0021661665 scopus 로고
    • Advances in Computers, vol. 23 (M. C. Yovits, ed.), Academic Press, N. Y
    • J. Traub and H. Wozniakowski, Information and computation, in Vol. 23, Advances in Computers, vol. 23 (M. C. Yovits, ed.), Academic Press, N. Y., 1984.
    • (1984) Information and Computation , vol.23
    • Traub, J.1    Wozniakowski, H.2
  • 52
    • 84936686040 scopus 로고
    • An estimate of the average number of steps in the simplex method and problems in asymptotic integral geometry
    • (Russian)
    • A. Vershik and P. Sporyshev, An estimate of the average number of steps in the simplex method and problems in asymptotic integral geometry, Soviet Math. Dokl. 28 (1983). (Russian)
    • (1983) Soviet Math. Dokl. , vol.28
    • Vershik, A.1    Sporyshev, P.2
  • 53
    • 84972559506 scopus 로고
    • A. Taub, ed., MacMillan, N. Y
    • J. Von Neumann, Collected works, vol. V (A. Taub, ed.), MacMillan, N. Y., 1963.
    • (1963) Collected Works , vol.5
    • Von Neumann, J.1


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