Felipe Cucker

发表

On weak and weighted computations over the real closure of Q

Felipe Cucker, 2001, Theor. Comput. Sci..

Computation over a Ring

Felipe Cucker, Lenore Blum, Michael Shub, 1998 .

Counting complexity classes for numeric computations II: algebraic and semialgebraic sets

Felipe Cucker, Peter Bürgisser, F. Cucker, 2003, STOC '04.

Solving linear programs with finite precision: II. Algorithms

Felipe Cucker, Dennis Cheung, F. Cucker, 2006, J. Complex..

On the Complexity of Some Problems for the Blum, Shub & Smale Model

Felipe Cucker, Francesc Rosselló, 1992, LATIN.

Safe Recursion Over an Arbitrary Structure: PAR, PH and DPH

Felipe Cucker, Olivier Bournez, Jean-Yves Marion, 2003, Electron. Notes Theor. Comput. Sci..

A Randomized Homotopy for the Hermitian Eigenpair Problem

Felipe Cucker, Diego Armentano, F. Cucker, 2015, Found. Comput. Math..

Non Recursive Functions Have Transcendental Generating Series

Felipe Cucker, Joaquim Gabarró, J. Gabarró, 1989, RAIRO Theor. Informatics Appl..

On real Turing machines that toss coins

Marek Karpinski, Thomas Lickteig, Felipe Cucker, 1995, STOC '95.

Complexity estimates depending on condition and round-off error

Felipe Cucker, Stephen Smale, S. Smale, 1998, JACM.

Appendix: Rule-driven creation

Felipe Cucker, 2013 .

Probabilistic analyses of condition numbers*

Felipe Cucker, F. Cucker, 2016, Acta Numerica.

A note on parallel and alternating time

Felipe Cucker, Irénée Briquel, 2007, J. Complex..

Smoothed analysis of some condition numbers

Yimin Wei, Felipe Cucker, Huaian Diao, 2006, Numer. Linear Algebra Appl..

Approximate Zeros and Condition Numbers

Felipe Cucker, F. Cucker, 1999, J. Complex..

A new condition number for linear programming

Felipe Cucker, Dennis Cheung, F. Cucker, 2001, Math. Program..

Learning Theory: An Approximation Theory Viewpoint: References

Felipe Cucker, Ding-Xuan Zhou, Ding-Xuan Zhou, 2007 .

COMPLEXITY AND REAL COMPUTATION: A MANIFESTO

Felipe Cucker, Steve Smale, Michael Shub, 1996 .

Solving polynomial equations in smoothed polynomial time and a near solution to smale's 17th problem

Felipe Cucker, Peter Bürgisser, 2010, STOC '10.

On the Computation of the Local and Global Analytic Branches of a Real Algebraic Curve

Felipe Cucker, Tomás Recio, Luis M. Pardo, 1987, AAECC.

Exotic Quantifiers, Complexity Classes, and Complete Problems

Felipe Cucker, Peter Bürgisser, 2007, ICALP.

Learning Theory: An Approximation Theory Viewpoint: On the bias–variance problem

Felipe Cucker, Ding-Xuan Zhou, Ding-Xuan Zhou, 2007 .

The Complexity of Semilinear Problems in Succinct Representation

Felipe Cucker, Peter Bürgisser, Paulin Jacobé de Naurois, 2005, FCT.

Componentwise Condition Numbers of Random Sparse Matrices

Felipe Cucker, Dennis Cheung, F. Cucker, 2008, SIAM J. Matrix Anal. Appl..

Linear Programming and Condition Numbers under the Real Number Computation Model

Felipe Cucker, Yinyu Ye, Dennis Cheung, 2003 .

Foundations of Computational Mathematics, Hong Kong 2008: Preface

Felipe Cucker, Allan Pinkus, Michael J. Todd, 2009 .

Method for Determining Optimal Laying Arrangement of Infrastructure Link

Moshe Zukerman, Yu Wang, Felipe Cucker, 2017 .

Foundations of computational mathematics: special volume

Felipe Cucker, Philippe G. Ciarlet, 2003 .

On strata of degenerate polyhedral cones I: Condition and distance to strata

Felipe Cucker, Javier Peña, Dennis Cheung, 2009, Eur. J. Oper. Res..

Solving polynomial systems: a complexity theory viewpoint.

Felipe Cucker, 2000, ISSAC 2000.

A Condition Number for Polyhedral Conic Systems

Felipe Cucker, Peter Bürgisser, 2013 .

Two P-Complete Problems in the Theory of the Reals

Felipe Cucker, A. Torrecillas, 1991, ICALP.

Manifold Mirrors: The many objects with planar symmetries

Felipe Cucker, F. Cucker, 2013 .

On strata of degenerate polyhedral cones, II: Relations between condition measures

Felipe Cucker, Javier Peña, Dennis Cheung, 2010, J. Complex..

Selected papers of a conference on Foundations of computational mathematics

Felipe Cucker, Michael Shub, 1997 .

The probability that a slightly perturbed numerical analysis problem is difficult

Felipe Cucker, Martin Lotz, Peter Buergisser, 2006, Math. Comput..

On the Expected Condition Number of Linear Programming Problems

Felipe Cucker, Mario Wschebor, F. Cucker, 2003, Numerische Mathematik.

Probabilistic Analysis of Conic Condition Numbers: II. The Real Case

Felipe Cucker, Peter Bürgisser, 2013 .

Recursiveness over the Complex Numbers is Time-Bounded

Felipe Cucker, Francesc Rosselló, Felipe Cucker, 1993, FSTTCS.

There Are No Sparse NPW-Hard Sets

Dima Grigoriev, Felipe Cucker, 2001, MFCS.

Adversarial smoothed analysis

Felipe Cucker, Raphael Hauser, Martin Lotz, 2010, J. Complex..

On digital nondeterminism

Martín Matamala, Felipe Cucker, F. Cucker, 1996, Mathematical systems theory.

A Primal-Dual Algorithm for Solving Polyhedral Conic Systems with a Finite-Precision Machine

Felipe Cucker, Javier Peña, Javier F. Pena, 2002, SIAM J. Optim..

A numerical algorithm for zero counting. II: Distance to ill-posedness and smoothed analysis

Felipe Cucker, Teresa Krick, Mario Wschebor, 2009, ArXiv.

SIAM Journal on Optimization

Nicholas I. M. Gould, Stefan Ulbrich, Masao Fukushima, 2012 .

Avoiding Collisions in Flocks

Felipe Cucker, Jiu-Gang Dong, F. Cucker, 2010, IEEE Transactions on Automatic Control.

Foundations of Computational Mathematics

Felipe Cucker, Michael Shub, 1997 .

A Numerical Algorithm for Zero Counting. I: Complexity and Accuracy pdf

Felipe Cucker, Teresa Krick, Mario Wschebor, 2007, J. Complex..

Solving linear programs with finite precision: I. Condition numbers and random programs

Felipe Cucker, Dennis Cheung, F. Cucker, 2004, Math. Program..

Modeling Language Evolution

Felipe Cucker, Stephen Smale, Ding-Xuan Zhou, 2004, Found. Comput. Math..

On sparseness, reducibilities, and complexity

Felipe Cucker, 2005, Ann. Pure Appl. Log..

Fast computation of zeros of polynomial systems with bounded degree under finite-precision

Felipe Cucker, Javier Peña, Vera Roshchina, 2014, Math. Comput..

Computing the Homology of Real Projective Sets

Felipe Cucker, Michael Shub, Teresa Krick, 2016, Foundations of Computational Mathematics.

Computability over an Arbitrary Structure. Sequential and Parallel Polynomial Time

Felipe Cucker, Olivier Bournez, Jean-Yves Marion, 2003, FoSSaCS.

The Shape of Data

Felipe Cucker, Allan Pinkus, Teresa Krick, 2012 .

Computing the Homology of Basic Semialgebraic Sets in Weak Exponential Time

Peter Bürgisser, Felipe Cucker, Pierre Lairez, 2017, J. ACM.

Foundations of Computational Mathematics, Budapest 2011: Preface

Felipe Cucker, Allan Pinkus, Teresa Krick, 2012 .

Learning Theory: An Approximation Theory Viewpoint (Cambridge Monographs on Applied & Computational Mathematics)

Felipe Cucker, Ding-Xuan Zhou, Ding-Xuan Zhou, 2007 .

On algorithms for real algebraic plane curves

Felipe Cucker, Francesc Rosselló, Laureano González Vega, 1991 .

Real Computations with Fake Numbers

Felipe Cucker, 1999, ICALP.

Preface

Thomas Lickteig, Felipe Cucker, F. Cucker, 2000, Journal of Complexity.

There are No Sparse NPw-Hard Sets

Dima Grigoriev, Felipe Cucker, 2001, SIAM J. Comput..

Foundations of Computational Mathematics: Minneapolis, 2002: Preface

Endre Süli, Felipe Cucker, Ronald A. DeVore, 2004 .

Counting Complexity Classes over the Reals I: The Additive Case

Felipe Cucker, Peter Bürgisser, F. Cucker, 2003, ISAAC.

A THEORY OF COMPLEXITY, CONDITION, AND ROUNDOFF pdf

Felipe Cucker, F. Cucker, 2014, Forum of Mathematics, Sigma.

Solving polynomial systems (invited talk abstract): a complexity theory viewpoint

Felipe Cucker, 2000, ISSAC.

A Condition Number for Multifold Conic Systems

Felipe Cucker, Javier Peña, Dennis Cheung, 2008, SIAM J. Optim..

Pr != Ncr

Felipe Cucker, F. Cucker, 1992, Journal of Complexity.

Complexity of Symbolic and Numerical Problems (Dagstuhl Seminar 15242)

Marek Karpinski, Felipe Cucker, Peter Bürgisser, 2015, Dagstuhl Reports.

The Linear Programming Feasibility Problem

Felipe Cucker, Peter Bürgisser, 2013 .

Learning Theory: An Approximation Theory Viewpoint: Index

Felipe Cucker, Ding-Xuan Zhou, Ding-Xuan Zhou, 2007 .

Tailoring Recursion to Characterize Non-Deterministic Complexity Classes over Arbitrary Structures

Felipe Cucker, Olivier Bournez, Jean-Yves Marion, 2004, IFIP TCS.

On the mathematical foundations of learning

Felipe Cucker, Steve Smale, S. Smale, 2001 .

Two P-complete problems in the theory of the reals

Felipe Cucker, A. Torrecillas, 1992, J. Complex..

Definitions and First Properties of Computation

Felipe Cucker, Lenore Blum, Michael Shub, 1998 .

Implicit complexity over an arbitrary structure: Quantifier alternations

Felipe Cucker, Olivier Bournez, Jean-Yves Marion, 2006, Inf. Comput..

Unifying Condition Numbers for Linear Programming

Felipe Cucker, Javier Peña, Dennis Cheung, 2003, Math. Oper. Res..

Modelling Language Evolution ⁄y

Felipe Cucker, Steve Smale, Ding-Xuan Zhou, 2003 .

Complexity and Dimension

Martín Matamala, Felipe Cucker, Pascal Koiran, 1997, Inf. Process. Lett..

On the Average Condition of Random Linear Programs

Felipe Cucker, Dennis Cheung, 2013, SIAM J. Optim..

Recent Advances in the Computation of the Homology of Semialgebraic Sets

Felipe Cucker, F. Cucker, 2019, CiE.

On Flocks Under Switching Directed Interaction Topologies

Felipe Cucker, Jiu-Gang Dong, F. Cucker, 2019, SIAM J. Appl. Math..

Machines Over the Reals and Non Uniformity

Felipe Cucker, 1997, Math. Log. Q..

Manifold Mirrors: References

Felipe Cucker, 2013 .

Real Computations with Fake Numbers

Felipe Cucker, 2002, J. Complex..

Counting Complexity Classes for Numeric Computations. III: Complex Projective Sets

Felipe Cucker, Peter Bürgisser, Martin Lotz, 2005, Found. Comput. Math..

Foundations of Computational Mathematics, Hong Kong 2008

Felipe Cucker, Allan Pinkus, Michael J. Todd, 2009 .

Time Bounded Computations over the Reals

Felipe Cucker, José Luis Montaña, Luis M. Pardo, 1992, Int. J. Algebra Comput..

Plantinga-Vegter Algorithm takes Average Polynomial Time

Felipe Cucker, Alperen Ali Ergür, Josué Tonelli-Cueto, 2019, ISSAC.

Tail Decay and Moment Estimates of a Condition Number for Random Linear Conic Systems

Felipe Cucker, Dennis Cheung, Raphael Hauser, 2005, SIAM J. Optim..

On mixed and componentwise condition numbers for Moore-Penrose inverse and linear least squares problems

Yimin Wei, Felipe Cucker, Huaian Diao, 2006, Math. Comput..

A General Collision-Avoiding Flocking Framework

Felipe Cucker, Jiu-Gang Dong, F. Cucker, 2011, IEEE Transactions on Automatic Control.

A note on level-2 condition numbers

Felipe Cucker, Dennis Cheung, 2005, J. Complex..

A Theorem on Random Polynomials and Some Consequences in Average Complexity

Felipe Cucker, Marie-Françoise Roy, 1990, J. Symb. Comput..

Smoothed Analysis of Moore-Penrose Inversion

Felipe Cucker, Peter Bürgisser, F. Cucker, 2010, SIAM J. Matrix Anal. Appl..

Approximation Theory (multi-media version): Singularity Now

Felipe Cucker, Hector Rodriguez, Sam Chan, 2018 .

Logics Which Capture Complexity Classes Over The Reals

Klaus Meer, Felipe Cucker, 1999, J. Symb. Log..

On the condition of the zeros of characteristic polynomials

Felipe Cucker, Peter Bürgisser, Elisa Rocha Cardozo, 2017, J. Complex..

Rigid continuation paths II. Structured polynomial systems pdf

Peter Bürgisser, Felipe Cucker, Pierre Lairez, 2020, ArXiv.

Condition - The Geometry of Numerical Algorithms

Felipe Cucker, Peter Bürgisser, F. Cucker, 2013, Grundlehren der mathematischen Wissenschaften.

Counting complexity classes for numeric computations II: Algebraic and semialgebraic sets

Felipe Cucker, Peter Bürgisser, 2006, J. Complex..

NC algorithms for real algebraic numbers

Felipe Cucker, Bud Mishra, Marie-Françoise Roy, 1992, Applicable Algebra in Engineering, Communication and Computing.

Solving second-order conic systems with variable precision

Felipe Cucker, Javier Peña, Vera Roshchina, 2015, Math. Program..

Condition Length and Complexity for the Solution of Polynomial Systems

Felipe Cucker, Michael Shub, Peter Bürgisser, 2015, Found. Comput. Math..

On sparseness and Turing reducibility over the reals

Felipe Cucker, 2002, Electron. Notes Theor. Comput. Sci..

The Arithmetical Hierarchy over the Reals

Felipe Cucker, 1992, J. Log. Comput..

Nondeterministic Ω-Computations and the Analytical Hierarchy

Felipe Cucker, J. Castro, 1989, Math. Log. Q..

On the Complexity of Quantifier Elimination: the Structural Approach

Felipe Cucker, 1993, Comput. J..

Learning from rounded-off data

Felipe Cucker, Dennis Cheung, F. Cucker, 2003, Inf. Comput..

Some Separations of Complexity Classes

Felipe Cucker, Lenore Blum, Michael Shub, 1998 .

Separation of Complexity Classes in Koiran's Weak Model

Felipe Cucker, Stephen Smale, Michael Shub, 1994, Theor. Comput. Sci..

Exotic Quantifiers, Complexity Classes, and Complete Problems

Felipe Cucker, Peter Bürgisser, F. Cucker, 2007, ICALP.

Parallel Time and Quantifier Prefixes

Felipe Cucker, Paulin Jacobé de Naurois, 2009, computational complexity.

Complexity Lower Bounds for Approximation Algebraic Computation Trees

Dima Grigoriev, Felipe Cucker, F. Cucker, 1999, J. Complex..

Computing the Homology of Semialgebraic Sets. II: General Formulas

Felipe Cucker, Peter Bürgisser, Josué Tonelli-Cueto, 2019, Foundations of Computational Mathematics.

On local analysis

Felipe Cucker, Teresa Krick, 2020, J. Complex..

Emergent Behavior in Flocks

Felipe Cucker, Steve Smale, S. Smale, 2007, IEEE Transactions on Automatic Control.

On the Power of Real Turing Machines Over Binary Inputs

Dima Grigoriev, Felipe Cucker, 1997, SIAM J. Comput..

Computing over the Reals with Addition and Order: Higher Complexity Classes

Felipe Cucker, Pascal Koiran, 1995, J. Complex..

Generalized Knapsack Problems and Fixed Degree Separations

Felipe Cucker, Michael Shub, M. Shub, 1996, Theor. Comput. Sci..

Implicit Complexity over an Arbitrary Structure: Sequential and Parallel Polynomial Time

Felipe Cucker, Olivier Bournez, Jean-Yves Marion, 2005, J. Log. Comput..

Editor's Foreword

Felipe Cucker, Michael Shub, 1996, J. Complex..

Decision Problems and Complexity over a Ring

Felipe Cucker, Lenore Blum, Michael Shub, 1998 .

Best Choices for Regularization Parameters in Learning Theory: On the Bias—Variance Problem

Felipe Cucker, Stephen Smale, S. Smale, 2002, Found. Comput. Math..

The Collected Papers of Stephen Smale

Felipe Cucker, Stephen Smale, Roderick Wong, 2000 .

Computing the Homology of Semialgebraic Sets. I: Lax Formulas

Felipe Cucker, Peter Bürgisser, Josué Tonelli-Cueto, 2018, Foundations of Computational Mathematics.

The complexity of semilinear problems in succinct representation

Felipe Cucker, Peter Bürgisser, Paulin Jacobé de Naurois, 2005, computational complexity.

The Legacy of Turing in Numerical Analysis

Felipe Cucker, 2012, SOFSEM.

Mathematics: user's manual

Felipe Cucker, 2013 .

Foreword

James Renegar, Felipe Cucker, Tomaso A. Poggio, 2005, Found. Comput. Math..

On the Complexity of the Plantinga-Vegter Algorithm pdf

Felipe Cucker, Alperen A. Ergur, Josu'e Tonelli-Cueto, 2020, ArXiv.

Maple Packages and Java Applets

Endre Süli, Felipe Cucker, Ronald A. DeVore, 2004 .

A Polynomial Time Algorithm for Diophantine Equations in One Variable

Felipe Cucker, Stephen Smale, Pascal Koiran, 1999, J. Symb. Comput..

Complexity Estimates Depending on Condition and Round-Off Error

Felipe Cucker, Steve Smale, 1998, ESA.

Counting Complexity Classes for Numeric Computations I: Semilinear Sets

Felipe Cucker, Peter Bürgisser, F. Cucker, 2003, SIAM J. Comput..

A Numerical Algorithm for Zero Counting. III: Randomization and Condition

Felipe Cucker, Teresa Krick, Mario Wschebor, 2008, Adv. Appl. Math..

Real Computation and Complexity (Dagstuhl Seminar 04061)

Thomas Lickteig, Felipe Cucker, Michael Shub, 2021 .

Functional norms, condition numbers and numerical algorithms in algebraic geometry pdf

Felipe Cucker, Alperen A. Ergur, Josu'e Tonelli-Cueto, 2021, ArXiv.

Foundations of computational mathematics: Minneapolis, 2002

Endre Süli, Felipe Cucker, Ronald A. DeVore, 2004 .

General formulas for the smoothed analysis of condition numbers

Felipe Cucker, Peter Bürgisser, Martin Lotz, 2006 .

MathematicS In Action

Felipe Cucker, Cristián Huepe, C. Huepe, 2008 .

ON THE CRITICAL EXPONENT FOR FLOCKS UNDER HIERARCHICAL LEADERSHIP

Felipe Cucker, Jiu-Gang Dong, F. Cucker, 2009 .

Manifold Mirrors: The Crossing Paths of the Arts and Mathematics

Felipe Cucker, 2013 .

Newton’s Method

Felipe Cucker, Michael Shub, Lenore Blum, 1998 .

A stable, polynomial-time algorithm for the eigenpair problem

Felipe Cucker, Peter Burgisser, F. Cucker, 2014, 1505.03290.

Condition Numbers and Iterative Algorithms

Felipe Cucker, Peter Bürgisser, 2013 .

Homotopy Continuation and Newton’s Method

Felipe Cucker, Peter Bürgisser, 2013 .

Algebraic Settings for the Problem “P ≠ NP?”

Felipe Cucker, Michael Shub, Lenore Blum, 1998 .

On a problem posed by Steve Smale

Felipe Cucker, F. Cucker, Peter Buergisser, 2009, 0909.2114.

Learning Theory: An Approximation Theory Viewpoint: Basic hypothesis spaces

Felipe Cucker, Ding-Xuan Zhou, 2007 .

Mixed and componentwise condition numbers for rectangular structured matrices

Felipe Cucker, Huaian Diao, 2007 .

Smoothed analysis of componentwise condition numbers for sparse matrices

Felipe Cucker, Dennis Cheung, 2013 .

Probabilistic Analysis of Condition Numbers for Linear Programming

Felipe Cucker, D. Cheung, F. Cucker, 2002 .

Manifold Mirrors: Contents

Felipe Cucker, 2013 .

Modelling Language Evolution ∗†

Felipe Cucker, Ding-Xuan Zhou, S. Smale, 2003 .

The complexity to compute the Euler characteristic of complex varieties

Felipe Cucker, Peter Bürgisser, Martin Lotz, 2004 .

A conditional, collision-avoiding, model for swarming

Felipe Cucker, Jiu-Gang Dong, 2013 .

Manifold Mirrors: Index of concepts

Felipe Cucker, 2013 .

Logics which capture complexity classes over the reals

Klaus Meer, Felipe Cucker, 1999 .