Felipe Cucker | Academic Influence

Felipe Cucker's AcademicInfluence.com Rankings

Felipe Cucker

Mathematics

#5322

World Rank

#7498

Historical Rank

Linear Algebra

#22

World Rank

#28

Historical Rank

Applied Mathematics

#371

World Rank

#398

Historical Rank

Measure Theory

#2420

World Rank

#2894

Historical Rank

mathematics Degrees

Download Badge

Mathematics

Felipe Cucker's Degrees

PhD Mathematics University of the Republic
Masters Mathematics University of the Republic
Bachelors Mathematics University of the Republic

Similar Degrees You Can Earn

Best Online Bachelor's in Math 2025

Why Is Felipe Cucker Influential?

(Suggest an Edit or Addition)

According to Wikipedia, Juan Felipe Cucker Farkas is an Uruguayan mathematician and theoretical computer scientist who has done research into the complexity theory of the Blum–Shub–Smale computational model and the complexity of numerical algorithms in linear programming and numerical algebraic geometry.

(See a Problem?)

Felipe Cucker's Published Works

Number of citations in a given year to any of this author's works

Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author

Published Works

On the mathematical foundations of learning (2001) (1556)
Emergent Behavior in Flocks (2007) (1472)
Learning Theory: An Approximation Theory Viewpoint (2007) (489)
On the mathematics of emergence (2007) (466)
Best Choices for Regularization Parameters in Learning Theory: On the Bias—Variance Problem (2002) (277)
Flocking in noisy environments (2007) (195)
Avoiding Collisions in Flocks (2010) (178)
Learning Theory: An Approximation Theory Viewpoint (Cambridge Monographs on Applied & Computational Mathematics) (2007) (170)
Condition - The Geometry of Numerical Algorithms (2013) (157)
Learning Theory: An Approximation Theory Viewpoint: Index (2007) (156)
SIAM Journal on Optimization (2012) (152)
A General Collision-Avoiding Flocking Framework (2011) (111)
On mixed and componentwise condition numbers for Moore-Penrose inverse and linear least squares problems (2006) (82)
Complexity estimates depending on condition and round-off error (1998) (82)
Modeling Language Evolution (2004) (81)
On a problem posed by Steve Smale (2009) (81)
Flocking with informed agents (2008) (76)
A new condition number for linear programming (2001) (69)
Counting complexity classes for numeric computations II: algebraic and semialgebraic sets (2003) (56)
COMPLEXITY AND REAL COMPUTATION: A MANIFESTO (1996) (56)
A Polynomial Time Algorithm for Diophantine Equations in One Variable (1999) (54)
ON THE CRITICAL EXPONENT FOR FLOCKS UNDER HIERARCHICAL LEADERSHIP (2009) (52)
A Numerical Algorithm for Zero Counting. I: Complexity and Accuracy (2007) (50)
An alternate proof of the continuity of the roots of a polynomial (1989) (45)
Computing over the Reals with Addition and Order: Higher Complexity Classes (1995) (45)
On real Turing machines that toss coins (1995) (43)
On the Power of Real Turing Machines Over Binary Inputs (1997) (42)
Algebraic Settings for the Problem “P ≠ NP?” (1998) (42)
A Primal-Dual Algorithm for Solving Polyhedral Conic Systems with a Finite-Precision Machine (2002) (42)
The probability that a slightly perturbed numerical analysis problem is difficult (2006) (41)
On the Complexity of Quantifier Elimination: the Structural Approach (1993) (38)
Computing the Homology of Basic Semialgebraic Sets in Weak Exponential Time (2017) (36)
Smoothed analysis of complex conic condition numbers (2006) (36)
Separation of Complexity Classes in Koiran's Weak Model (1994) (35)
Coverage processes on spheres and condition numbers for linear programming (2007) (34)
A numerical algorithm for zero counting. II: Distance to ill-posedness and smoothed analysis (2009) (32)
Computing the Homology of Real Projective Sets (2016) (32)
On the Expected Condition Number of Linear Programming Problems (2003) (32)
A conditional, collision-avoiding, model for swarming (2013) (31)
Smoothed analysis of some condition numbers (2006) (29)
A Numerical Algorithm for Zero Counting. III: Randomization and Condition (2008) (28)
Pr != Ncr (1992) (28)
Exotic Quantifiers, Complexity Classes, and Complete Problems (2007) (25)
Unifying Condition Numbers for Linear Programming (2003) (25)
Probabilistic Analysis of Condition Numbers for Linear Programming (2002) (25)
The Arithmetical Hierarchy over the Reals (1992) (24)
A stable, polynomial-time algorithm for the eigenpair problem (2014) (24)
Solving linear programs with finite precision: I. Condition numbers and random programs (2004) (23)
On algorithms for real algebraic plane curves (1991) (23)
Learning Theory: An Approximation Theory Viewpoint: On the bias–variance problem (2007) (23)
Smoothed Analysis of Moore-Penrose Inversion (2010) (22)
Mixed and componentwise condition numbers for rectangular structured matrices (2007) (21)
Nondeterministic Ω-Computations and the Analytical Hierarchy (1989) (21)
On flocks influenced by closest neighbors (2016) (21)
Solving linear programs with finite precision: II. Algorithms (2006) (20)
Computability over an Arbitrary Structure. Sequential and Parallel Polynomial Time (2003) (20)
Logics which capture complexity classes over the reals (1997) (20)
Approximate Zeros and Condition Numbers (1999) (20)
On the Computation of the Local and Global Analytic Branches of a Real Algebraic Curve (1987) (19)
Two P-Complete Problems in the Theory of the Reals (1991) (19)
Computing the Homology of Semialgebraic Sets. I: Lax Formulas (2018) (19)
On digital nondeterminism (1996) (19)
Real Computations with Fake Numbers (1999) (17)
Counting Complexity Classes for Numeric Computations. III: Complex Projective Sets (2005) (17)
Tail Decay and Moment Estimates of a Condition Number for Random Linear Conic Systems (2003) (16)
Modulated Fourier Expansions for Continuous and Discrete Oscillatory Systems (2012) (16)
The Collected Papers of Stephen Smale (2000) (15)
Condition Length and Complexity for the Solution of Polynomial Systems (2015) (14)
A note on level-2 condition numbers (2005) (14)
Counting Complexity Classes for Numeric Computations I: Semilinear Sets (2003) (13)
Plantinga-Vegter Algorithm takes Average Polynomial Time (2019) (13)
On Flocks Under Switching Directed Interaction Topologies (2019) (12)
Through the Kaleidoscope: Symmetries, Groups and Chebyshev-Approximations from a Computational Point of View (2012) (12)
ON THE COMPUTATION OF GEOMETRIC FEATURES OF SPECTRA OF LINEAR OPERATORS ON HILBERT SPACES (2021) (11)
The complexity of semilinear problems in succinct representation (2005) (11)
Implicit Complexity over an Arbitrary Structure: Sequential and Parallel Polynomial Time (2005) (10)
On the Complexity of Some Problems for the Blum, Shub & Smale Model (1992) (10)
General formulas for the smoothed analysis of condition numbers (2006) (10)
Safe Recursion Over an Arbitrary Structure: PAR, PH and DPH (2003) (10)
A Condition Number for Multifold Conic Systems (2008) (10)
Computing the Homology of Semialgebraic Sets. II: General Formulas (2019) (10)
Time Bounded Computations over the Reals (1992) (10)
Fast computation of zeros of polynomial systems with bounded degree under finite-precision (2012) (10)
A Randomized Homotopy for the Hermitian Eigenpair Problem (2015) (9)
Linear Programming and Condition Numbers under the Real Number Computation Model (2003) (9)
Learning Theory: An Approximation Theory Viewpoint: References (2007) (9)
The Shape of Data (2012) (8)
Complexity Lower Bounds for Approximation Algebraic Computation Trees (1999) (8)
Probabilistic analyses of condition numbers* (2016) (8)
Foundations of Computational Mathematics, Hong Kong 2008 (2009) (7)
Generalized Knapsack Problems and Fixed Degree Separations (1996) (7)
Some Properties of the Global Behaviour of Conservative Low-Dimensional Systems (2009) (7)
Implicit complexity over an arbitrary structure: Quantifier alternations (2006) (7)
Complexity and Dimension (1997) (7)
A THEORY OF COMPLEXITY, CONDITION, AND ROUNDOFF (2014) (7)
Adversarial smoothed analysis (2009) (6)
Recursiveness over the Complex Numbers is Time-Bounded (1993) (6)
The complexity to compute the Euler characteristic of complex varieties (2004) (6)
Recent Advances in the Computation of the Homology of Semialgebraic Sets (2019) (5)
A Theorem on Random Polynomials and Some Consequences in Average Complexity (1990) (5)
On strata of degenerate polyhedral cones I: Condition and distance to strata (2009) (5)
A note on parallel and alternating time (2007) (5)
Tailoring Recursion to Characterize Non-Deterministic Complexity Classes over Arbitrary Structures (2004) (5)
Rigid continuation paths II. structured polynomial systems (2020) (5)
Manifold Mirrors: The Crossing Paths of the Arts and Mathematics (2013) (5)
Modelling Language Evolution ∗† (2003) (4)
Functional norms, condition numbers and numerical algorithms in algebraic geometry (2021) (4)
Componentwise Condition Numbers of Random Sparse Matrices (2008) (4)
On the condition of the zeros of characteristic polynomials (2017) (4)
On the Complexity of the Plantinga–Vegter Algorithm (2020) (4)
NC algorithms for real algebraic numbers (1992) (4)
Solving second-order conic systems with variable precision (2011) (4)
MathematicS In Action (2008) (3)
On local analysis (2019) (3)
Foundations of computational mathematics, Budapest 2011 (2012) (3)
Homotopy Continuation and Newton’s Method (2013) (3)
Manifold Mirrors: Index of concepts (2013) (3)
Decision Problems and Round-Off Machines (2001) (3)
There are No Sparse NPw-Hard Sets (2001) (3)
The Legacy of Turing in Numerical Analysis (2012) (3)
Solving polynomial equations in smoothed polynomial time and a near solution to smale's 17th problem (2010) (3)
Real Polynomial Systems (2013) (2)
Modelling Language Evolution ⁄y (2003) (2)
N A ] 9 O ct 2 00 6 The probability that a small perturbation of a numerical analysis problem is difficult (2021) (2)
The Condition Number for Nonlinear Problems (1998) (2)
The Condition Number in ℙ(H(d)) (1998) (2)
Smoothed analysis of componentwise condition numbers for sparse matrices (2013) (2)
A raw material (2013) (2)
On strata of degenerate polyhedral cones, II: Relations between condition measures (2010) (2)
On the Average Condition of Random Linear Programs (2013) (2)
Machines Over the Reals and Non‐Uniformity (1997) (2)
Solving second-order conic systems with finite precision (2011) (1)
Learning Theory: An Approximation Theory Viewpoint: Support vector machines for classification 157 (2007) (1)
The Collected Papers of Stephen Smale: Volume 3 (2000) (1)
Three lectures on real computation (2001) (1)
Newton’s Method (1998) (1)
Foundations of Computational Mathematics (1997) (1)
Counting Complexity Classes over the Reals I: The Additive Case (2003) (1)
Foundations of computational mathematics: Minneapolis, 2002 (2004) (1)
Learning Theory: An Approximation Theory Viewpoint: The framework of learning (2007) (1)
Selected papers of the workshop on Continuous algorithms and complexity (1994) (1)
Foundations of Computational Mathematics: Minneapolis, 2002: Preface (2004) (1)
Computing the Homology of Semialgebraic Sets. II: General Formulas (2021) (1)
Foundations of computational mathematics : selected papers of a conference held at Rio de Janeiro, January 1997 (1997) (1)
Round-off estimates for second-order conic feasibility problems (2012) (1)
Grid Methods in Computational Real Algebraic (and Semialgebraic) Geometry (2018) (1)
The WORK OF STEVE SMALE ON THE THEORY OF COMPUTATION: 1990–1999 (2002) (1)
A Condition Number for Second Order Conic Systems (2006) (1)
Condition Numbers and Iterative Algorithms (2013) (1)
On weak and weighted computations over the real closure of Q (2001) (1)
Learning Theory: An Approximation Theory Viewpoint: Basic hypothesis spaces (2007) (1)
Computation over a Ring (1998) (0)
The shape of the universe (2013) (0)
Some Separations of Complexity Classes (1998) (0)
Complexity and the Condition Number (1998) (0)
Manifold Mirrors: The vicissitudes of geometry (2013) (0)
ICMAT–China Exploratory Workshop (2014) (0)
Probabilistic Analysis of Conic Condition Numbers: II. The Real Case (2013) (0)
Nonuniform Complexity Classes (1998) (0)
Learning Theory: An Approximation Theory Viewpoint: Least squares regularization (2007) (0)
The Class NP and NP-Complete Problems (1998) (0)
Manifold Mirrors: Motions on the plane (2013) (0)
Foundations of computational mathematics: special volume (2003) (0)
Method for Determining Optimal Laying Arrangement of Infrastructure Link (2017) (0)
A Randomized Homotopy for the Hermitian Eigenpair Problem (2014) (0)
Manifold Mirrors: The dawn of perspective (2013) (0)
Mathematics Sector : Applied Mathematics Research group : Complexity and Foundations of Computational Mathematics (2013) (0)
Nash functions over real spectra (1989) (0)
Error Analysis of Triangular Linear Systems (2013) (0)
Conferences 9 th Workshop on Logic , Language , Information and Computation ( WoLLIC ’ 2002 ) (2002) (0)
Deterministic Lower Bounds (1998) (0)
Learning Theory: An Approximation Theory Viewpoint: Estimating the sample error (2007) (0)
Decision Problems and Complexity over a Ring (1998) (0)
Linear Programs and Their Solution Sets (2013) (0)
Manifold Mirrors: References (2013) (0)
Normwise Condition of Linear Equation Solving (2013) (0)
Appendix: Rule-driven creation (2013) (0)
Solving Linear Problems with Finite Precision III: Sharp Expectation Bounds (2011) (0)
Homogeneous Polynomial Systems (2013) (0)
Fundamental Theorem of Algebra: Complexity Aspects (1998) (0)
Computing the Homology of Real Projective Sets (2017) (0)
Condition Numbers and the Loss of Precision of Linear Equations (1998) (0)
Space and geometry (2013) (0)
Foundations of Computational Mathematics, Budapest 2011: Preface (2012) (0)
Parallel Time and Quantifier Prefixes (2009) (0)
Complexity and Dimension Produced as Part of the Esprit Working Group in Neural and Computational Learning, Neurocolt 8556 (1996) (0)
Average Analysis of the RCC Condition Number (2013) (0)
Characteristic polynomials of typical matrices are ill-conditioned (2015) (0)
Definitions and First Properties of Computation (1998) (0)
A Geometric Framework for Condition Numbers (2013) (0)
Preface (2000) (0)
Smale 17th Problem: Advances and Open Directions (2021) (0)
The many symmetries of planar objects (2013) (0)
Approximation Theory (multi-media version): Singularity Now (2018) (0)
Computing the Homology of Semialgebraic Sets. I: Lax Formulas (2019) (0)
On sparseness, reducibilities, and complexity (2005) (0)
Logarithmic decay of the approximation error (2007) (0)
Solving polynomial systems: a complexity theory viewpoint. (2000) (0)
Symmetries in non-Euclidean geometries (2013) (0)
Condition Length and Complexity for the Solution of Polynomial Systems (2016) (0)
Editor's Foreword (1996) (0)
Condition and Linear Programming Optimization (2013) (0)
Smale’s 17th Problem: II (2013) (0)
N A ] 7 O ct 2 01 0 ON A PROBLEM POSED (2010) (0)
Logical Characterizations of $P_\mathcal{K}$ and $NP_\mathcal{K}$ Over an Arbitrary Structure $K$ (2005) (0)
Complexity of Symbolic and Numerical Problems (Dagstuhl Seminar 15242) (2015) (0)
N A ] 2 3 N ov 2 01 5 On the condition of characteristic polynomials (2018) (0)
Solving polynomial systems (invited talk abstract): a complexity theory viewpoint (2000) (0)
On sparseness and Turing reducibility over the reals (2002) (0)
Probabilistic Analysis of Conic Condition Numbers: I. The Complex Case (2013) (0)
Maple Packages and Java Applets (2004) (0)
Learning Theory: An Approximation Theory Viewpoint: General regularized classifiers (2007) (0)
Probabilistic Analyses of the GCC Condition Number (2013) (0)
Reflections on the mirror (2013) (0)
Nach functions and the structure sheaf (1989) (0)
Real Computation and Complexity (Dagstuhl Seminar 04061) (2021) (0)
The vicissitudes of perspective (2013) (0)
A Condition Number for Polyhedral Conic Systems (2013) (0)
Non Recursive Functions Have Transcendental Generating Series (1989) (0)
Manifold Mirrors: The many objects with planar symmetries (2013) (0)
Entropic Envelope (Mothlight): Frequency Domain Representation (2018) (0)
N A ] 2 0 M ay 2 01 9 On local analysis (2019) (0)
Foundations of computational mathematics : proceedings of the Smalefest 2000, Hon Kong, 13-17 2000 (2002) (0)
COMPLEXITY CLASSES OVER THE REALS: A LOGICIAN’S VIEWPOINT (2003) (0)
Interior-Point Methods (2013) (0)
Real‐Valued Computation and Complexity (2006) (0)
Learning Theory: An Approximation Theory Viewpoint: Polynomial decay of the approximation error (2007) (0)
Probabilistic Analysis of Rectangular Matrices (2013) (0)
Learning Theory: An Approximation Theory Viewpoint: Estimating covering numbers (2007) (0)
The Ellipsoid Method (2013) (0)
Foundations of Computational Mathematics, Hong Kong 2008: Preface (2009) (0)
Solving second-order conic systems with variable precision (2014) (0)
The Linear Programming Feasibility Problem (2013) (0)
Learning from rounded-off data (2003) (0)
Mathematics: user's manual (2013) (0)
Selected papers of a conference on Foundations of computational mathematics (1997) (0)
On the condition of characteristic polynomials (2015) (0)
Grid Methods in Computational Real Algebraic (and Semialgebraic) Geometry (2018) (0)
Manifold Mirrors: Stretching the plane (2013) (0)
A repertoire of drawing systems (2013) (0)
Algebraic Settings for the Problem P 6 = Np?" 1. Statement of Main Theorems (1996) (0)
On the power of real Turing machinesover binary inputsFelipe Cucker (2013) (0)

This paper list is powered by the following services:

Other Resources About Felipe Cucker

en.wikipedia.org

What Schools Are Affiliated With Felipe Cucker?

Felipe Cucker is affiliated with the following schools:

What Are Felipe Cucker's Academic Contributions?

Felipe Cucker is most known for their academic work in the field of mathematics. They are also known for their academic work in the fields of

Felipe Cucker has made the following academic contributions:

Complexity and Real Computation