Edit Profile Cucker, Felipe Compute Distance To: Compute Author ID: cucker.felipe Published as: Cucker, F.; Cucker, Felipe; Cucker, Filipe External Links: MGP · Wikidata · ORCID · GND Documents Indexed: 145 Publications since 1986, including 12 Books Reviewing Activity: 5 Reviews all top 5 Co-Authors 27 single-authored 24 Bürgisser, Peter 15 Cheung, Dennis 12 Smale, Steve 10 Shub, Michael 8 de Naurois, Paulin Jacobé 8 Peña, Javier F. 7 Lotz, Martin 6 Dong, Jiu-Gang 6 Krick, Teresa 5 Blum, Lenore 5 Bournez, Olivier 5 Marion, Jean-Yves 4 Grigor’ev, Dmitriĭ Yur’evich 4 Koiran, Pascal 4 Malajovich, Gregorio 4 Pardo, Luis Miguel 4 Roy, Marie-Françoise 4 Wschebor, Mario 3 Armentano, Diego 3 Diao, Huaian 3 Montaña, José Luis 3 Roshchina, Vera 2 Beltrán, Carlos 2 Briquel, Irénée 2 Hauser, Raphael Andreas 2 Lickteig, Thomas 2 Matamala, Martín 2 Pinkus, Allan M. 2 Rosselló, Francesc 2 Tonelli-Cueto, Josué 2 Torrecillas, A. 2 Wei, Yimin 2 Zhou, Dingxuan 1 Castro, Jocelyn A. 1 Corbalan, Antonio Gonzalez 1 Dedieu, Jean-Piere 1 DeVore, Ronald A. 1 Ergür, Alperen Ali 1 Gabarró, Joaquim 1 Gonzalez-Vega, Laureano 1 Huepe, Cristián 1 Karpinski, Marek 1 Lairez, Pierre 1 Lanneau, H. 1 Meer, Klaus 1 Mishra, Bhavya 1 Mordecki, Ernesto 1 Olver, Peter John 1 Pedersen, Poul Wulff 1 Raimondo, Mario 1 Recio, Tomas 1 Rocha Cardozo, Elisa 1 Rojas, J. Maurice 1 Süli, Endre E. 1 Szántó, Ágnes 1 Todd, Michael J. 1 Werther, Kai 1 Ye, Yinyu all top 5 Serials 16 Journal of Complexity 8 Foundations of Computational Mathematics 4 Theoretical Computer Science 4 SIAM Journal on Optimization 3 Mathematics of Computation 3 IEEE Transactions on Automatic Control 3 SIAM Journal on Computing 3 Mathematical Programming. Series A. Series B 3 Comptes Rendus. Mathématique. Académie des Sciences, Paris 3 London Mathematical Society Lecture Note Series 2 Journal of Symbolic Computation 2 Information and Computation 2 SIAM Journal on Matrix Analysis and Applications 2 Journal of Logic and Computation 2 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences 2 Journal de Mathématiques Pures et Appliquées. Neuvième Série 2 Computational Complexity 2 Journal of the ACM 1 American Mathematical Monthly 1 Communications in Algebra 1 IMA Journal of Numerical Analysis 1 Information Processing Letters 1 Rocky Mountain Journal of Mathematics 1 The Annals of Probability 1 Calcolo 1 The Computer Journal. Section A / Section B 1 Journal of Optimization Theory and Applications 1 Journal of Pure and Applied Algebra 1 The Journal of Symbolic Logic 1 Mathematics of Operations Research 1 Mathematical Systems Theory 1 Mathematische Zeitschrift 1 Numerische Mathematik 1 Zeitschrift für Mathematische Logik und Grundlagen der Mathematik 1 Comptes Rendus Mathématiques de l’Académie des Sciences 1 Advances in Applied Mathematics 1 Bollettino della Unione Matemàtica Italiana. Serie VI. D. Algebra e Geometria 1 Chinese Annals of Mathematics. Series B 1 Annals of Pure and Applied Logic 1 Extracta Mathematicae 1 International Journal of Algebra and Computation 1 European Journal of Operational Research 1 SIAM Journal on Applied Mathematics 1 Bulletin of the American Mathematical Society. New Series 1 Comptes Rendus de l’Académie des Sciences. Série I 1 RAIRO. Informatique Théorique et Applications 1 Applicable Algebra in Engineering, Communication and Computing 1 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 1 Numerical Linear Algebra with Applications 1 Mathematical Logic Quarterly (MLQ) 1 Discrete and Continuous Dynamical Systems 1 Theory of Computing Systems 1 Publicaciones Matemáticas del Uruguay 1 Annals of Mathematics. Second Series 1 Journal of the European Mathematical Society (JEMS) 1 Acta Numerica 1 Grundlehren der Mathematischen Wissenschaften 1 Cambridge Monographs on Applied and Computational Mathematics 1 Handbook of Numerical Analysis 1 Journal of Fixed Point Theory and Applications 1 Japanese Journal of Mathematics. 3rd Series 1 MathematicS In Action 1 Forum of Mathematics, Sigma all top 5 Fields 76 Computer science (68-XX) 50 Numerical analysis (65-XX) 24 Mathematical logic and foundations (03-XX) 20 Algebraic geometry (14-XX) 19 Operations research, mathematical programming (90-XX) 15 Linear and multilinear algebra; matrix theory (15-XX) 10 General and overarching topics; collections (00-XX) 8 Field theory and polynomials (12-XX) 7 Systems theory; control (93-XX) 5 Functions of a complex variable (30-XX) 4 Number theory (11-XX) 4 Commutative algebra (13-XX) 4 Real functions (26-XX) 4 Global analysis, analysis on manifolds (58-XX) 4 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 4 Biology and other natural sciences (92-XX) 3 Ordinary differential equations (34-XX) 3 Dynamical systems and ergodic theory (37-XX) 3 Convex and discrete geometry (52-XX) 3 Algebraic topology (55-XX) 3 Probability theory and stochastic processes (60-XX) 3 Statistics (62-XX) 2 Several complex variables and analytic spaces (32-XX) 2 Differential geometry (53-XX) 1 History and biography (01-XX) 1 Combinatorics (05-XX) 1 Category theory; homological algebra (18-XX) 1 Group theory and generalizations (20-XX) 1 Approximations and expansions (41-XX) 1 Geometry (51-XX) 1 Manifolds and cell complexes (57-XX) 1 Mechanics of particles and systems (70-XX) 1 Fluid mechanics (76-XX) 1 Statistical mechanics, structure of matter (82-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH 105 Publications have been cited 2,224 times in 1,400 Documents Cited by ▼ Year ▼ Emergent behavior in flocks. Zbl 1366.91116Cucker, Felipe; Smale, Steve 342 2007 On the mathematical foundations of learning. Zbl 0983.68162Cucker, Felipe; Smale, Steve 322 2002 Complexity and real computation: A manifesto. Zbl 0872.68036Blum, Lenore; Cucker, Felipe; Shub, Mike; Smale, Steve 282 1996 Learning theory. An approximation theory viewpoint. Zbl 1274.41001Cucker, Felipe; Zhou, Ding Xuan 196 2007 On the mathematics of emergence. Zbl 1166.92323Cucker, Felipe; Smale, Steve 106 2007 Best choices for regularization parameters in learning theory: on the bias-variance problem. Zbl 1057.68085Cucker, Felipe; Smale, Steve 78 2002 Flocking in noisy environments. Zbl 1273.91404Cucker, Felipe; Mordecki, Ernesto 70 2008 Avoiding collisions in flocks. Zbl 1368.93370Cucker, Felipe; Dong, Jiu-Gang 54 2010 Complexity and real computation. Foreword by Richard M. Karp. Zbl 0948.68068Blum, Leonore; Cucker, Felipe; Shub, Michael; Smale, Steve 53 1997 On mixed and componentwise condition numbers for Moore-Penrose inverse and linear least squares problems. Zbl 1115.15004Cucker, Felipe; Diao, Huaian; Wei, Yimin 39 2007 Condition. The geometry of numerical algorithms. Zbl 1280.65041Bürgisser, Peter; Cucker, Felipe 37 2013 A general collision-avoiding flocking framework. Zbl 1368.93261Cucker, Felipe; Dong, Jiu-Gang 28 2011 On the critical exponent for flocks under hierarchical leadership. Zbl 1202.92089Cucker, Felipe; Dong, Jiu-Gang 27 2009 Flocking with informed agents. Zbl 1163.93306Cucker, Felipe; Huepe, Cristián 27 2008 On a problem posed by Steve Smale. Zbl 1248.65047Bürgisser, Peter; Cucker, Felipe 22 2011 A new condition number for linear programming. Zbl 1072.90564Cheung, Dennis; Cucker, Felipe 21 2001 Complexity estimates depending on condition and round-off error. Zbl 1065.68533Cucker, Felipe; Smale, Steve 19 1999 Counting complexity classes for numeric computations. II: Algebraic and semialgebraic sets. Zbl 1149.68029Bürgisser, Peter; Cucker, Felipe 16 2006 A primal-dual algorithm for solving polyhedral conic systems with a finite-precision machine. Zbl 0996.90052Cucker, Felipe; Peña, Javier 16 2001 Computing over the reals with addition and order: Higher complexity classes. Zbl 0843.68033Cucker, Felipe; Koiran, Pascal 16 1995 Modeling language evolution. Zbl 1083.68131Cucker, Felipe; Smale, Steve; Zhou, Ding-Xuan 15 2004 Separation of complexity classes in Koiran’s weak model. Zbl 0819.68053Cucker, F.; Shub, M.; Smale, S. 15 1994 The probability that a slightly perturbed numerical analysis problem is difficult. Zbl 1195.65018Bürgisser, Peter; Cucker, Felipe; Lotz, Martin 14 2008 On the power of real Turing machines over binary inputs. Zbl 0874.68110Cucker, Felipe; Grigoriev, Dima 14 1997 On the complexity of quantifier elimination: The structural approach. Zbl 0788.68058Cucker, Felipe 13 1993 Smoothed analysis of complex conic condition numbers. Zbl 1113.65044Bürgisser, Peter; Cucker, Felipe; Lotz, Martin 12 2006 Smoothed analysis of some condition numbers. Zbl 1198.65084Cucker, F.; Diao, H.; Wei, Y. 12 2006 Unifying condition numbers for linear programming. Zbl 1082.90061Cheung, Dennis; Cucker, Felipe; Peña, Javier 12 2003 Algebraic settings for the problem ”P\(\neq\)NP?”. Zbl 0856.68068Blum, Lenore; Cucker, Felipe; Shub, Mike; Smale, Steve 12 1996 An alternate proof of the continuity of the roots of a polynomial. Zbl 0708.30010Cucker, Felipe; Corbalan, Antonio Gonzalez 12 1989 On flocks influenced by closest neighbors. Zbl 1354.93069Cucker, Felipe; Dong, Jiu-Gang 11 2016 A numerical algorithm for zero counting. I: Complexity and accuracy. Zbl 1166.65021Cucker, Felipe; Krick, Teresa; Malajovich, Gregorio; Wschebor, Mario 11 2008 On the expected condition number of linear programming problems. Zbl 1030.65039Cucker, Felipe; Wschebor, Mario 11 2003 A polynomial time algorithm for diophantine equations in one variable. Zbl 0920.11085Cucker, Felipe; Koiran, Pascal; Smale, Steve 11 1999 A numerical algorithm for zero counting. II: Distance to ill-posedness and smoothed analysis. Zbl 1215.65218Cucker, Felipe; Krick, Teresa; Malajovich, Gregorio; Wschebor, Mario 10 2009 Mixed and componentwise condition numbers for rectangular structured matrices. Zbl 1168.15304Cucker, Felipe; Diao, Huaian 10 2007 On digital nondeterminism. Zbl 0868.68058Cucker, F.; Matamala, M. 10 1996 On algorithms for real algebraic plane curves. Zbl 0737.14017Cucker, Felipe; González-Vega, Laureano; Rossello, Francesc 10 1991 A numerical algorithm for zero counting. III: Randomization and condition. Zbl 1245.65189Cucker, Felipe; Krick, Teresa; Malajovich, Gregorio; Wschebor, Mario 9 2012 Coverage processes on spheres and condition numbers for linear programming. Zbl 1205.60027Bürgisser, Peter; Cucker, Felipe; Lotz, Martin 9 2010 On real Turing machines that toss coins. Zbl 0938.68648Cucker, Felipe; Karpinski, Marek; Koiran, Pascal; Lickteig, Thomas; Werther, Kai 9 1995 \(P_ \mathbb{R}{}\neq{}NC_ \mathbb{R}\). Zbl 0753.68044Cucker, Felipe 9 1992 Solving linear programs with finite precision. II: Algorithms. Zbl 1105.90042Cheung, Dennis; Cucker, Felipe 8 2006 Variations by complexity theorists on three themes of Euler, Bézout, Betti, and Poincaré. Zbl 1076.68033Bürgisser, Peter; Cucker, Felipe 8 2004 Computability over an arbitrary structure. Sequential and parallel polynomial time. Zbl 1029.68056Bournez, Olivier; Cucker, Felipe; de Naurois, Paulin Jacobé; Marion, Jean-Yves 8 2003 On the computation of the local and global analytic branches of a real algebraic curve. Zbl 0697.14002Cucker, F.; Pardo, L. M.; Raimondo, M.; Recio, T.; Roy, M. F. 8 1989 A conditional, collision-avoiding, model for swarming. Zbl 1273.93087Cucker, Felipe; Dong, Jiu-Gang 7 2014 Exotic quantifiers, complexity classes, and complete problems. Zbl 1185.68343Bürgisser, Peter; Cucker, Felipe 7 2009 Solving linear programs with finite precision. I: Condition numbers and random programs. Zbl 1082.90060Cheung, Dennis; Cucker, Felipe 7 2004 Two \(P\)-complete problems in the theory of the reals. Zbl 0759.68032Cucker, F.; Torrecillas, A. 7 1992 Nondeterministic \(\omega\)-computations and the analytical hierarchy. Zbl 0661.03030Castro, J.; Cucker, F. 7 1989 Counting complexity classes for numeric computations. III: Complex projective sets. Zbl 1100.68032Bürgisser, Peter; Cucker, Felipe; Lotz, Martin 6 2005 A note on level-2 condition numbers. Zbl 1074.15008Cheung, Dennis; Cucker, Felipe 6 2005 Probabilistic analysis of condition numbers for linear programming. Zbl 1041.90028Cheung, D.; Cucker, F. 6 2002 Approximate zeros and condition numbers. Zbl 0967.65063Cucker, Felipe 6 1999 Logics which capture complexity classes over the reals. Zbl 0933.03047Cucker, Felipe; Meer, Klaus 5 1999 The arithmetical hierarchy over the reals. Zbl 0765.03020Cucker, Felipe 5 1992 Condition length and complexity for the solution of polynomial systems. Zbl 1358.65031Armentano, Diego; Beltrán, Carlos; Bürgisser, Peter; Cucker, Felipe; Shub, Michael 4 2016 Fast computation of zeros of polynomial systems with bounded degree under finite-precision. Zbl 1291.65158Briquel, Irénée; Cucker, Felipe; Peña, Javier; Roshchina, Vera 4 2014 Smoothed analysis of Moore-Penrose inversion. Zbl 1227.65035Bürgisser, Peter; Cucker, Felipe 4 2010 The complexity of semilinear problems in succinct representation. Zbl 1113.68057Bürgisser, Peter; Cucker, Felipe; de Naurois, Paulin Jacobé 4 2006 Tail decay and moment estimates of a condition number for random linear conic systems. Zbl 1097.90057Cheung, Dennis; Cucker, Felipe; Hauser, Raphael 4 2005 Counting complexity classes for numeric computations. I: Semilinear sets. Zbl 1069.68049Bürgisser, Peter; Cucker, Felipe 4 2003 Complexity and dimension. Zbl 1337.68117Cucker, Felipe; Koiran, Pascal; Matamala, Martín 4 1997 A stable, polynomial-time algorithm for the eigenpair problem. Zbl 1401.65034Armentano, Diego; Beltrán, Carlos; Bürgisser, Peter; Cucker, Felipe; Shub, Michael 3 2018 On strata of degenerate polyhedral cones. I: Condition and distance to strata. Zbl 1163.90644Cheung, Dennis; Cucker, Felipe; Peña, Javier 3 2009 A condition number for multifold conic systems. Zbl 1168.90572Cheung, Dennis; Cucker, Felipe; Peña, Javier 3 2008 General formulas for the smoothed analysis of condition numbers. Zbl 1121.65041Bürgisser, Peter; Cucker, Felipe; Lotz, Martin 3 2006 Implicit complexity over an arbitrary structure: sequential and parallel polynomial time. Zbl 1077.03021Bounez, Olivier; Cucker, Felipe; Jacobé de Naurois, Paulin; Marion, Jean-Yves 3 2005 The work of Steve Smale on the theory of computation: 1990-1999. Zbl 1050.68042Cucker, Felipe; Blum, Lenore 3 2002 Generalized Knapsack problems and fixed degree separations. Zbl 0900.68212Cucker, Felipe; Shub, Michael 3 1996 Time bounded computations over the reals. Zbl 0788.68043Cucker, F.; Montaña, J. L.; Pardo, L. M. 3 1992 Computing the homology of basic semialgebraic sets in weak exponential time. Zbl 1426.14016Bürgisser, Peter; Cucker, Felipe; Lairez, Pierre 2 2019 On flocks under switching directed interaction topologies. Zbl 1405.93014Cucker, Felipe; Dong, Jiu-Gang 2 2019 A randomized homotopy for the Hermitian eigenpair problem. Zbl 1317.65096Armentano, Diego; Cucker, Felipe 2 2015 Solving second-order conic systems with variable precision. Zbl 1309.90076Cucker, Felipe; Peña, Javier; Roshchina, Vera 2 2015 A theory of complexity, condition, and roundoff. Zbl 1307.68037Cucker, Felipe 2 2015 Adversarial smoothed analysis. Zbl 1232.65071Cucker, Felipe; Hauser, Raphael; Lotz, Martin 2 2010 A note on parallel and alternating time. Zbl 1137.65076Cucker, Felipe; Briquel, Irénée 2 2007 Implicit complexity over an arbitrary structure: Quantifier alternations. Zbl 1093.68041Bournez, Olivier; Cucker, Felipe; de Naurois, Paulin Jacobé; Marion, Jean-Yves 2 2006 Counting complexity classes for numeric computations. II. Algebraic and semialgebraic sets. Zbl 1192.68289Bürgisser, Peter; Cucker, Felipe 2 2004 Real computations with fake numbers. Zbl 1004.68069Cucker, Felipe 2 2002 There are no sparse NP\(_{w}\)-hard sets. Zbl 0992.68061Cucker, Felipe; Grigoriev, Dima 2 2001 Real computations with fake numbers. Zbl 0944.03030Cucker, Felipe 2 1999 NC algorithms for real algebraic numbers. Zbl 0786.12007Cucker, F.; Lanneau, H.; Mishra, B.; Pedersen, P.; Roy, M.-F. 2 1992 Two P-complete problems in the theory of the reals. Zbl 0785.68038Cucker, F.; Torrecillas, A. 2 1991 A theorem on random polynomials and some consequences in average complexity. Zbl 0725.12007Cucker, F.; Roy, M.-F. 2 1990 Sur les anneaux de sections globales du faisceau structural sur le spectre réel. (On the rings of global sections of the structural sheaf over the real spectrum). Zbl 0681.14009Cucker, Felipe 2 1988 Computing the homology of real projective sets. Zbl 07031361Cucker, Felipe; Krick, Teresa; Shub, Michael 1 2018 On the condition of the zeros of characteristic polynomials. Zbl 1372.65103Bürgisser, Peter; Cucker, Felipe; Rocha Cardozo, Elisa 1 2017 Smoothed analysis of componentwise condition numbers for sparse matrices. Zbl 1323.65045Cheung, Dennis; Cucker, Felipe 1 2015 On the average condition of random linear programs. Zbl 1273.90116Cheung, Dennis; Cucker, Felipe 1 2013 Manifold mirrors. The crossing paths of the arts and mathematics. Zbl 1300.00023Cucker, Felipe 1 2013 The legacy of Turing in numerical analysis. Zbl 1274.01074Cucker, Felipe 1 2012 Systems of polynomial equations. Zbl 1361.65031Cucker, Felipe; Malajovich, Gregorio 1 2011 On strata of degenerate polyhedral cones. II: Relations between condition measures. Zbl 1273.90214Cheung, Dennis; Cucker, Felipe; Peña, Javier 1 2010 Foundations of computational mathematics, Hong Kong, China, 2008. Selected papers based on the presentations at the international conference of the Society for the Foundations of Computational Mathematics (FoCM), June 16–26, 2008. Zbl 1170.13001Cucker, Felipe (ed.); Pinkus, Allan (ed.); Todd, Michael J. (ed.) 1 2009 Safe recursion over an arbitrary structure: PAR, PH and DPH. Zbl 1261.68058Bournez, Olivier; Cucker, Felipe; De Naurois, Paulin Jacobé; Marion, Jean-Yves 1 2003 Linear programming and condition numbers under the real number computation model. Zbl 1070.65548Cheung, Dennis; Cucker, Filipe; Ye, Yinyu 1 2003 On weak and weighted computations over the real closure of \(\mathbb{Q}\). Zbl 0977.68034Cucker, Felipe 1 2001 Computing the homology of basic semialgebraic sets in weak exponential time. Zbl 1426.14016Bürgisser, Peter; Cucker, Felipe; Lairez, Pierre 2 2019 On flocks under switching directed interaction topologies. Zbl 1405.93014Cucker, Felipe; Dong, Jiu-Gang 2 2019 A stable, polynomial-time algorithm for the eigenpair problem. Zbl 1401.65034Armentano, Diego; Beltrán, Carlos; Bürgisser, Peter; Cucker, Felipe; Shub, Michael 3 2018 Computing the homology of real projective sets. Zbl 07031361Cucker, Felipe; Krick, Teresa; Shub, Michael 1 2018 On the condition of the zeros of characteristic polynomials. Zbl 1372.65103Bürgisser, Peter; Cucker, Felipe; Rocha Cardozo, Elisa 1 2017 On flocks influenced by closest neighbors. Zbl 1354.93069Cucker, Felipe; Dong, Jiu-Gang 11 2016 Condition length and complexity for the solution of polynomial systems. Zbl 1358.65031Armentano, Diego; Beltrán, Carlos; Bürgisser, Peter; Cucker, Felipe; Shub, Michael 4 2016 A randomized homotopy for the Hermitian eigenpair problem. Zbl 1317.65096Armentano, Diego; Cucker, Felipe 2 2015 Solving second-order conic systems with variable precision. Zbl 1309.90076Cucker, Felipe; Peña, Javier; Roshchina, Vera 2 2015 A theory of complexity, condition, and roundoff. Zbl 1307.68037Cucker, Felipe 2 2015 Smoothed analysis of componentwise condition numbers for sparse matrices. Zbl 1323.65045Cheung, Dennis; Cucker, Felipe 1 2015 A conditional, collision-avoiding, model for swarming. Zbl 1273.93087Cucker, Felipe; Dong, Jiu-Gang 7 2014 Fast computation of zeros of polynomial systems with bounded degree under finite-precision. Zbl 1291.65158Briquel, Irénée; Cucker, Felipe; Peña, Javier; Roshchina, Vera 4 2014 Condition. The geometry of numerical algorithms. Zbl 1280.65041Bürgisser, Peter; Cucker, Felipe 37 2013 On the average condition of random linear programs. Zbl 1273.90116Cheung, Dennis; Cucker, Felipe 1 2013 Manifold mirrors. The crossing paths of the arts and mathematics. Zbl 1300.00023Cucker, Felipe 1 2013 A numerical algorithm for zero counting. III: Randomization and condition. Zbl 1245.65189Cucker, Felipe; Krick, Teresa; Malajovich, Gregorio; Wschebor, Mario 9 2012 The legacy of Turing in numerical analysis. Zbl 1274.01074Cucker, Felipe 1 2012 A general collision-avoiding flocking framework. Zbl 1368.93261Cucker, Felipe; Dong, Jiu-Gang 28 2011 On a problem posed by Steve Smale. Zbl 1248.65047Bürgisser, Peter; Cucker, Felipe 22 2011 Systems of polynomial equations. Zbl 1361.65031Cucker, Felipe; Malajovich, Gregorio 1 2011 Avoiding collisions in flocks. Zbl 1368.93370Cucker, Felipe; Dong, Jiu-Gang 54 2010 Coverage processes on spheres and condition numbers for linear programming. Zbl 1205.60027Bürgisser, Peter; Cucker, Felipe; Lotz, Martin 9 2010 Smoothed analysis of Moore-Penrose inversion. Zbl 1227.65035Bürgisser, Peter; Cucker, Felipe 4 2010 Adversarial smoothed analysis. Zbl 1232.65071Cucker, Felipe; Hauser, Raphael; Lotz, Martin 2 2010 On strata of degenerate polyhedral cones. II: Relations between condition measures. Zbl 1273.90214Cheung, Dennis; Cucker, Felipe; Peña, Javier 1 2010 On the critical exponent for flocks under hierarchical leadership. Zbl 1202.92089Cucker, Felipe; Dong, Jiu-Gang 27 2009 A numerical algorithm for zero counting. II: Distance to ill-posedness and smoothed analysis. Zbl 1215.65218Cucker, Felipe; Krick, Teresa; Malajovich, Gregorio; Wschebor, Mario 10 2009 Exotic quantifiers, complexity classes, and complete problems. Zbl 1185.68343Bürgisser, Peter; Cucker, Felipe 7 2009 On strata of degenerate polyhedral cones. I: Condition and distance to strata. Zbl 1163.90644Cheung, Dennis; Cucker, Felipe; Peña, Javier 3 2009 Foundations of computational mathematics, Hong Kong, China, 2008. Selected papers based on the presentations at the international conference of the Society for the Foundations of Computational Mathematics (FoCM), June 16–26, 2008. Zbl 1170.13001Cucker, Felipe (ed.); Pinkus, Allan (ed.); Todd, Michael J. (ed.) 1 2009 Flocking in noisy environments. Zbl 1273.91404Cucker, Felipe; Mordecki, Ernesto 70 2008 Flocking with informed agents. Zbl 1163.93306Cucker, Felipe; Huepe, Cristián 27 2008 The probability that a slightly perturbed numerical analysis problem is difficult. Zbl 1195.65018Bürgisser, Peter; Cucker, Felipe; Lotz, Martin 14 2008 A numerical algorithm for zero counting. I: Complexity and accuracy. Zbl 1166.65021Cucker, Felipe; Krick, Teresa; Malajovich, Gregorio; Wschebor, Mario 11 2008 A condition number for multifold conic systems. Zbl 1168.90572Cheung, Dennis; Cucker, Felipe; Peña, Javier 3 2008 Emergent behavior in flocks. Zbl 1366.91116Cucker, Felipe; Smale, Steve 342 2007 Learning theory. An approximation theory viewpoint. Zbl 1274.41001Cucker, Felipe; Zhou, Ding Xuan 196 2007 On the mathematics of emergence. Zbl 1166.92323Cucker, Felipe; Smale, Steve 106 2007 On mixed and componentwise condition numbers for Moore-Penrose inverse and linear least squares problems. Zbl 1115.15004Cucker, Felipe; Diao, Huaian; Wei, Yimin 39 2007 Mixed and componentwise condition numbers for rectangular structured matrices. Zbl 1168.15304Cucker, Felipe; Diao, Huaian 10 2007 A note on parallel and alternating time. Zbl 1137.65076Cucker, Felipe; Briquel, Irénée 2 2007 Counting complexity classes for numeric computations. II: Algebraic and semialgebraic sets. Zbl 1149.68029Bürgisser, Peter; Cucker, Felipe 16 2006 Smoothed analysis of complex conic condition numbers. Zbl 1113.65044Bürgisser, Peter; Cucker, Felipe; Lotz, Martin 12 2006 Smoothed analysis of some condition numbers. Zbl 1198.65084Cucker, F.; Diao, H.; Wei, Y. 12 2006 Solving linear programs with finite precision. II: Algorithms. Zbl 1105.90042Cheung, Dennis; Cucker, Felipe 8 2006 The complexity of semilinear problems in succinct representation. Zbl 1113.68057Bürgisser, Peter; Cucker, Felipe; de Naurois, Paulin Jacobé 4 2006 General formulas for the smoothed analysis of condition numbers. Zbl 1121.65041Bürgisser, Peter; Cucker, Felipe; Lotz, Martin 3 2006 Implicit complexity over an arbitrary structure: Quantifier alternations. Zbl 1093.68041Bournez, Olivier; Cucker, Felipe; de Naurois, Paulin Jacobé; Marion, Jean-Yves 2 2006 Counting complexity classes for numeric computations. III: Complex projective sets. Zbl 1100.68032Bürgisser, Peter; Cucker, Felipe; Lotz, Martin 6 2005 A note on level-2 condition numbers. Zbl 1074.15008Cheung, Dennis; Cucker, Felipe 6 2005 Tail decay and moment estimates of a condition number for random linear conic systems. Zbl 1097.90057Cheung, Dennis; Cucker, Felipe; Hauser, Raphael 4 2005 Implicit complexity over an arbitrary structure: sequential and parallel polynomial time. Zbl 1077.03021Bounez, Olivier; Cucker, Felipe; Jacobé de Naurois, Paulin; Marion, Jean-Yves 3 2005 Modeling language evolution. Zbl 1083.68131Cucker, Felipe; Smale, Steve; Zhou, Ding-Xuan 15 2004 Variations by complexity theorists on three themes of Euler, Bézout, Betti, and Poincaré. Zbl 1076.68033Bürgisser, Peter; Cucker, Felipe 8 2004 Solving linear programs with finite precision. I: Condition numbers and random programs. Zbl 1082.90060Cheung, Dennis; Cucker, Felipe 7 2004 Counting complexity classes for numeric computations. II. Algebraic and semialgebraic sets. Zbl 1192.68289Bürgisser, Peter; Cucker, Felipe 2 2004 Unifying condition numbers for linear programming. Zbl 1082.90061Cheung, Dennis; Cucker, Felipe; Peña, Javier 12 2003 On the expected condition number of linear programming problems. Zbl 1030.65039Cucker, Felipe; Wschebor, Mario 11 2003 Computability over an arbitrary structure. Sequential and parallel polynomial time. Zbl 1029.68056Bournez, Olivier; Cucker, Felipe; de Naurois, Paulin Jacobé; Marion, Jean-Yves 8 2003 Counting complexity classes for numeric computations. I: Semilinear sets. Zbl 1069.68049Bürgisser, Peter; Cucker, Felipe 4 2003 Safe recursion over an arbitrary structure: PAR, PH and DPH. Zbl 1261.68058Bournez, Olivier; Cucker, Felipe; De Naurois, Paulin Jacobé; Marion, Jean-Yves 1 2003 Linear programming and condition numbers under the real number computation model. Zbl 1070.65548Cheung, Dennis; Cucker, Filipe; Ye, Yinyu 1 2003 On the mathematical foundations of learning. Zbl 0983.68162Cucker, Felipe; Smale, Steve 322 2002 Best choices for regularization parameters in learning theory: on the bias-variance problem. Zbl 1057.68085Cucker, Felipe; Smale, Steve 78 2002 Probabilistic analysis of condition numbers for linear programming. Zbl 1041.90028Cheung, D.; Cucker, F. 6 2002 The work of Steve Smale on the theory of computation: 1990-1999. Zbl 1050.68042Cucker, Felipe; Blum, Lenore 3 2002 Real computations with fake numbers. Zbl 1004.68069Cucker, Felipe 2 2002 A new condition number for linear programming. Zbl 1072.90564Cheung, Dennis; Cucker, Felipe 21 2001 A primal-dual algorithm for solving polyhedral conic systems with a finite-precision machine. Zbl 0996.90052Cucker, Felipe; Peña, Javier 16 2001 There are no sparse NP\(_{w}\)-hard sets. Zbl 0992.68061Cucker, Felipe; Grigoriev, Dima 2 2001 On weak and weighted computations over the real closure of \(\mathbb{Q}\). Zbl 0977.68034Cucker, Felipe 1 2001 Complexity estimates depending on condition and round-off error. Zbl 1065.68533Cucker, Felipe; Smale, Steve 19 1999 A polynomial time algorithm for diophantine equations in one variable. Zbl 0920.11085Cucker, Felipe; Koiran, Pascal; Smale, Steve 11 1999 Approximate zeros and condition numbers. Zbl 0967.65063Cucker, Felipe 6 1999 Logics which capture complexity classes over the reals. Zbl 0933.03047Cucker, Felipe; Meer, Klaus 5 1999 Real computations with fake numbers. Zbl 0944.03030Cucker, Felipe 2 1999 Complexity lower bounds for approximation algebraic computation trees. Zbl 0959.68143Cucker, Felipe; Grigoriev, Dima 1 1999 Complexity and real computation. Foreword by Richard M. Karp. Zbl 0948.68068Blum, Leonore; Cucker, Felipe; Shub, Michael; Smale, Steve 53 1997 On the power of real Turing machines over binary inputs. Zbl 0874.68110Cucker, Felipe; Grigoriev, Dima 14 1997 Complexity and dimension. Zbl 1337.68117Cucker, Felipe; Koiran, Pascal; Matamala, Martín 4 1997 Machines over the reals and non-uniformity. Zbl 0941.03038Cucker, Felipe 1 1997 Complexity and real computation: A manifesto. Zbl 0872.68036Blum, Lenore; Cucker, Felipe; Shub, Mike; Smale, Steve 282 1996 Algebraic settings for the problem ”P\(\neq\)NP?”. Zbl 0856.68068Blum, Lenore; Cucker, Felipe; Shub, Mike; Smale, Steve 12 1996 On digital nondeterminism. Zbl 0868.68058Cucker, F.; Matamala, M. 10 1996 Generalized Knapsack problems and fixed degree separations. Zbl 0900.68212Cucker, Felipe; Shub, Michael 3 1996 Computing over the reals with addition and order: Higher complexity classes. Zbl 0843.68033Cucker, Felipe; Koiran, Pascal 16 1995 On real Turing machines that toss coins. Zbl 0938.68648Cucker, Felipe; Karpinski, Marek; Koiran, Pascal; Lickteig, Thomas; Werther, Kai 9 1995 Models for parallel computation with real numbers. Zbl 0921.68056Cucker, F.; Montaña, J. L.; Pardo, L. M. 1 1995 Separation of complexity classes in Koiran’s weak model. Zbl 0819.68053Cucker, F.; Shub, M.; Smale, S. 15 1994 On the complexity of quantifier elimination: The structural approach. Zbl 0788.68058Cucker, Felipe 13 1993 \(P_ \mathbb{R}{}\neq{}NC_ \mathbb{R}\). Zbl 0753.68044Cucker, Felipe 9 1992 Two \(P\)-complete problems in the theory of the reals. Zbl 0759.68032Cucker, F.; Torrecillas, A. 7 1992 The arithmetical hierarchy over the reals. Zbl 0765.03020Cucker, Felipe 5 1992 Time bounded computations over the reals. Zbl 0788.68043Cucker, F.; Montaña, J. L.; Pardo, L. M. 3 1992 NC algorithms for real algebraic numbers. Zbl 0786.12007Cucker, F.; Lanneau, H.; Mishra, B.; Pedersen, P.; Roy, M.-F. 2 1992 On algorithms for real algebraic plane curves. Zbl 0737.14017Cucker, Felipe; González-Vega, Laureano; Rossello, Francesc 10 1991 Two P-complete problems in the theory of the reals. Zbl 0785.68038Cucker, F.; Torrecillas, A. 2 1991 A theorem on random polynomials and some consequences in average complexity. Zbl 0725.12007Cucker, F.; Roy, M.-F. 2 1990 An alternate proof of the continuity of the roots of a polynomial. Zbl 0708.30010Cucker, Felipe; Corbalan, Antonio Gonzalez 12 1989 ...and 5 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 1,680 Authors 66 Ha, Seung-Yeal 58 Cucker, Felipe 31 Zhou, Dingxuan 23 Choi, Young-Pil 22 Carrillo de la Plata, José Antonio 21 Chen, Dirong 20 Bürgisser, Peter 20 Sun, Hongwei 19 Meer, Klaus 18 Sheng, Baohuai 17 Pardo, Luis Miguel 17 Wei, Yimin 16 Degond, Pierre 16 Kim, Jeongho 16 Koiran, Pascal 15 Bellomo, Nicola 15 Beltrán, Carlos 15 Li, Luoqing 15 Pillonetto, Gianluigi 15 Xiang, Dao-Hong 14 Peña, Javier F. 14 Shub, Michael 14 Wu, Qiang 13 Chen, Hong 13 Smale, Steve 13 Xu, Zongben 12 Fornasier, Massimo 12 Guo, Zheng-Chu 12 Zhang, Xiongtao 11 Diao, Huaian 11 Dong, Jiu-Gang 11 Ko, Dongnam 11 Rosasco, Lorenzo A. 11 Sanguineti, Marcello 11 Tong, Hongzhi 10 Cao, Feilong 10 Li, Zhuchun 10 Lotz, Martin 10 Malajovich, Gregorio 10 Zhang, Haizhang 10 Zou, Bin 9 Dedieu, Jean-Pierre 9 Feng, Yunlong 9 Ferreira, Orizon Pereira 9 Kim, Doheon 9 Lv, Shaogao 9 Peszek, Jan 9 Shi, Lei 9 Tan, Changhui 8 Armentano, Diego 8 Bae, Hyeong-Ohk 8 Basu, Saugata 8 Gnecco, Giorgio 8 Kang, Moon-Jin 8 Kim, Dohyun 8 Li, Chong 8 Rojas, J. 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