S. Smale

发表

Differential Equations, Dynamical Systems, and Linear Algebra

M. Hirsch, S. Smale, 1974 .

ESTIMATING THE APPROXIMATION ERROR IN LEARNING THEORY

S. Smale, Ding-Xuan Zhou, 2003 .

Shannon sampling and function reconstruction from point values

S. Smale, Ding-Xuan Zhou, 2004 .

ONLINE LEARNING WITH MARKOV SAMPLING

S. Smale, Ding-Xuan Zhou, 2009 .

Learning Theory Estimates via Integral Operators and Their Approximations

S. Smale, Ding-Xuan Zhou, 2007 .

On Algorithms for Solving f(x)=0

M. Hirsch, S. Smale, 1979 .

Convergent process of price adjust-ment and global newton methods

S. Smale, 1976 .

Global analysis and economics VI: Geometric analysis of Pareto Optima and price equilibria under classical hypotheses

S. Smale, 1976 .

Shannon sampling II: Connections to learning theory

S. Smale, Ding-Xuan Zhou, 2005 .

On the differential equations of species in competition

S. Smale, 1976, Journal of mathematical biology.

The Condition Number in ℙ(H(d))

S. Smale, M. Shub, L. Blum, 1998 .

On the average number of steps of the simplex method of linear programming

Stephen Smale, S. Smale, 1983, Math. Program..

The fundamental theorem of algebra and complexity theory

S. Smale, 1981 .

On the efficiency of algorithms of analysis

S. Smale, 1985 .

Newton’s Method Estimates from Data at One Point

S. Smale, 1986 .

Global analysis and economics

S. Smale, 1975, Synthese.

On a theory of computation and complexity over the real numbers; np-completeness

S. Smale, M. Shub, L. Blum, 1989 .

On the mathematics of emergence

S. Smale, F. Cucker, 2007 .

Generalized Poincare's Conjecture in Dimensions Greater Than Four

S. Smale, 1961 .

RKHS Representation of Measures Applied to Homogeneity, Independence, and Fourier Optics

Bharath K. Sriperumbudur, S. Smale, B. Schölkopf, 2008 .

Lecture III Dynamical systems and turbulence

S. Smale, 1977 .

Differential Equations, Dynamical Systems, and an Introduction to Chaos

M. Hirsch, S. Smale, R. Devaney, 2003 .

Online Learning Algorithms

Yuan Yao, Stephen Smale, S. Smale, 2006, Found. Comput. Math..

Geometry on Probability Spaces

S. Smale, Ding-Xuan Zhou, 2009 .

On the existence of generally convergent algorithms

Stephen Smale, Michael Shub, S. Smale, 1986, J. Complex..

Differentiable dynamical systems

S. Smale, 1967 .

On a model of visual cortex: learning invariance and selectivity

S. Smale, T. Poggio, A. Caponnetto, 2008 .

Mathematical problems for the next century

S. Smale, 1998 .

Morse inequalities for a dynamical system

S. Smale, 1960 .

Exchange processes with price adjustment

S. Smale, S. Smale, 1976 .

The mathematics of numerical analysis

S. Smale, M. Shub, J. Renegar, 1996 .

The mathematics of numerical analysis : 1995 AMS-SIAM Summer Seminar in Applied Mathematics, July 17-August 11, 1995, Park City, Utah

S. Smale, M. Shub, J. Renegar, 1996 .

Emergent Behavior in Flocks

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

From Topology to Computation: Proceedings of the Smalefest

Jerrold E. Marsden, Stephen Smale, Michael Shub, 2011 .

The Mathematics of Learning: Dealing with Data

T. Poggio, S. Smale, S. Smale, 2005, 2005 International Conference on Neural Networks and Brain.

Reproducing kernel hilbert spaces in learning theory

S. Smale, M. H. Quang, 2006 .

Complexity of Bezout's theorem IV: probability of success; extensions

S. Smale, M. Shub, 1996 .

Computational complexity: on the geometry of polynomials and a theory of cost. I

S. Smale, M. Shub, 1985 .

Complexity of Bezout’s Theorem II Volumes and Probabilities

S. Smale, M. Shub, 1993 .

Algebraic Settings for the Problem P 6 = Np?" 1. Statement of Main Theorems

S. Smale, M. Shub, L. Blum, 1996 .

On the complexity of path-following newton algorithms for solving systems of polynomial equations with integer coefficients

S. Smale, Gregorio Malajovich-Munoz, 1993 .

The Gödel Incompleteness Theorem and Decidability over a Ring

S. Smale, L. Blum, 1993 .

Complexity of Bézout’s theorem. I. Geometric aspects

S. Smale, M. Shub, 1993 .

The Prisoner's Dilemma and Dynamical Systems Associated to Non-Cooperative Games

S. Smale, 1980 .

On a theory of computation over the real numbers; NP completeness, recursive functions and universal machines

Stephen Smale, Michael Shub, Lenore Blum, 1988, [Proceedings 1988] 29th Annual Symposium on Foundations of Computer Science.

On the mathematical foundations of learning

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

Discrete Dynamical Systems

M. Hirsch, S. Smale, R. Devaney, 2013 .

Modeling Language Evolution

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

On the topology of algorithms, I

Stephen Smale, S. Smale, 1987, J. Complex..

On Gradient Dynamical Systems

S. Smale, 1961 .

Stable Manifolds for Differential Equations and Diffeomorphisms

S. Smale, 2011 .

On a theory of computation and complexity over the real numbers; np-completeness

S. Smale, M. Shub, L. Blum, 1989 .

Diffeomorphisms with Many Periodic Points

S. Smale, 1965 .

NP and mathematics – a computational complexity perspective

S. Smale, 2006 .

Complexity and RealComputation : A Manifesto Lenore

S. Smale, M. Shub, L. Blum, 1995 .

The Mathematics of Learning: Dealing With Data

S. Smale, 2005, 2005 International Conference on Neural Networks and Brain.

Genome Architecture Leads a Bifurcation in Cell Identity

Gerald A. Higgins, S. Smale, P. Baldi, 2017, bioRxiv.

A Topological View of Unsupervised Learning from Noisy Data

Stephen Smale, Partha Niyogi, Shmuel Weinberger, 2011, SIAM J. Comput..

On the mathematical foundations of electrical circuit theory

S. Smale, 1972 .

THE DYNAMICAL SYSTEMS APPROACH TO DIFFERENTIAL EQUATIONS

Stephen Smale, Xavier Mora, S. Smale, 2007 .

Dynamics of the Genome

S. Smale, I. Rajapakse, 2015 .

A Mathematical Model of Two Cells Via Turing’s Equation

S. Smale, Steve Smale, 1976 .

Global Analysis and Economics I: Pareto Optimum and a Generalization of Morse Theory†

S. Smale, Steve Smale, 1975 .

Functional organization of the human 4D Nucleome

Stephen Smale, Jie Chen, Thomas Ried, 2015, Proceedings of the National Academy of Sciences.

Modelling Language Evolution ∗†

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

Neurons That Confuse Mirror-Symmetric Object Views

Joel Z. Leibo, S. Smale, T. Poggio, 2010 .

Comparative Statics and Algorithms for Finding Economic Equilibria

S. Smale, 1995 .

Emergence of Function

S. Smale, I. Rajapakse, 2016, 1610.04224.

A Vietoris mapping theorem for homotopy

Stephen Smale, S. Smale, 1957 .

Professional Biography, Bibliography, and Graduate Students

S. Smale, 1993 .

A NOTE ON OPEN MAPS

S. Smale, 1957 .

On the Structure of 5-Manifolds

S. Smale, 1962 .

First-Order Equations

M. Hirsch, S. Smale, R. Devaney, 2013 .

Topology and mechanics. II

S. Smale, Steve Smale, 1970 .

Stability and genericity in dynamical systems

S. Smale, 1971 .

Global stability questions in dynamical systems

S. Smale, 1969 .

On the steps of Moscow University

S. Smale, 1984 .

Gerard Debreu wins the Nobel Prize

S. Smale, 1984 .

On the Immersion of Manifolds in Euclidean Space

S. Smale, R. Lashof, 1958 .

Problems on the nature of relative equilibria in celestial mechanics

S. Smale, 1971 .

Complexity of Bezout's Theorem: III. Condition Number and Packing

Stephen Smale, Michael Shub, S. Smale, 1993, J. Complex..

Emergence of function from coordinated cells in a tissue

S. Smale, I. Rajapakse, 2017, Proceedings of the National Academy of Sciences.

Data-Guided Controllability : Learning from the Human Genome

S. Smale, A. Bloch, M. Mesbahi, 2015 .

Chapter 8 Global analysis and economics

S. Smale, 1981 .

PSEUDO-DIVISION MACHINE (I): A MODEL OF SYMBOLIC COMPUTATION

Blum, S. Smale, M. Shub, 2007 .

Real‐Valued Computation and Complexity

S. Smale, F. Cucker, 2006 .

A Structurally Stable Differentiable Homeomorphism with an Infinite Number of Periodic Points

S. Smale, 2007 .

The Condition Number for Nonlinear Problems

S. Smale, M. Shub, L. Blum, 1998 .

ON THE PROBLEM OF REVIVING THE ERGODIC HYPOTHESIS OF BLOTZMANN AND BIRKHOFF

S. Smale, Steve Smale, 1980 .

Differentiable dynamical systems

S. Smale, 1967 .

Some Lower Bounds for the Complexity of Continuation Methods

Stephen Smale, Jean-Pierre Dedieu, S. Smale, 1998, J. Complex..

Surveys in Modern Mathematics: On problems of computational complexity

Stephen Smale, S. Smale, 2005 .

Smale horseshoe

Stephen Smale, Michael Shub, S. Smale, 2007, Scholarpedia.

Learning Theory: An Approximation Theory Viewpoint: Foreword

Stephen Smale, S. Smale, 2007 .

Smooth solutions of the heat and wave equations

Stephen Smale, S. Smale, 1980 .

Review: E. C. Zeeman, Catastrophe theory: Selected papers, 1972–1977

Stephen Smale, S. Smale, 1978 .

DIFFEOMORPHISMS OF THE 2-SPHERE

Stephen Smale, S. Smale, 1959 .

Complexity aspects of numerical analysis

Stephen Smale, S. Smale, 1986 .

Hodge Theory on Metric Spaces

Laurent Bartholdi, Stephen Smale, Thomas Schick, 2009, Found. Comput. Math..

The mathematics of time

Stephen Smale, S. Smale, 1980 .

Regular curves on Riemannian manifolds

Stephen Smale, S. Smale, 1958 .

THE STRUCTURE OF COMPLETE MANIFOLDS OF NONNEGATIVE CURVATURE BY JEFF CHEEGER AND DETLEF GROMOLL

S. Smale, 2007 .

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

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

Computational Complexity: On the Geometry of Polynomials and a Theory of Cost: II

Stephen Smale, Michael Shub, S. Smale, 1986, SIAM J. Comput..

Genome Architecture Mediates Transcriptional Control of Human Myogenic Reprogramming

Pierre Baldi, Alfred Hero, Gerald A. Higgins, 2018, iScience.

The Classification of Immersions of Spheres in Euclidean Spaces

S. Smale, 1959 .

The generalized Poincaré conjecture in higher dimensions

S. Smale, 1960 .

Self-Intersections of Immersed Manifolds

S. Smale, R. Lashof, 1959 .

Global analysis and economics III: Pareto Optima and price equilibria

S. Smale, Steve Smale, 1974 .

Topology and mechanics. I

S. Smale, S. Smale, Steve Smale, 1970 .

Finding the Homology of Submanifolds with High Confidence from Random Samples

Stephen Smale, Partha Niyogi, Shmuel Weinberger, 2008, Discret. Comput. Geom..

Finding a horseshoe on the beaches of Rio

S. Smale, Steve Smale, 1998 .

Generalization and Properties of the Neural Response

Andre Wibisono, Tomaso Poggio, Lorenzo Rosasco, 2010 .

A classification of immersions of the two-sphere

Stephen Smale, S. Smale, 1959 .

Remembering Raoul Bott

S. Smale, David Mumford, S. Yau, 2013 .

Complexity theory and numerical analysis

Steve Smale, S. Smale, 1997, Acta Numerica.

On the Structure of Manifolds

S. Smale, Steve Smale, 1962 .

An Infinite Dimensional Version of Sard's Theorem

S. Smale, Steve Smale, 1965 .

On the Problem of Reviving the Ergodic Hypothesis of Boltzmann and Birkhoff: Dedicated to the memory of Rufus Bowen

S. Smale, 1980 .

Dynamical systems and the topological conjugacy problem for diffeomorphisms

S. Smale, 1963 .

Dynamics retrospective: great problems, attempts that failed

Steve Smale, S. Smale, 1991 .

A Dynamic Theory of Learning

S. Smale, Y. Yao, 2008 .

The qualitative analysis of a difference equation of population growth

R. F. Williams, S. Smale, 1976, Journal of mathematical biology.

Existence and Uniqueness Revisited

M. Hirsch, S. Smale, R. Devaney, 2013 .

Dynamics in General Equilibrium Theory

S. Smale, 1976 .

Global analysis and economics IV: Finiteness and stability of equilibria with general consumption sets and production

S. Smale, 1974 .

ALGEBRAIC TOPOLOGY AT THE STEKLOV MATHEMATICAL INSTITUTE OF THE ACADEMY OF SCIENCES OF THE USSR

S. Smale, J. Milnor, N. Steenrod, 2008 .

Complexity of Bezout's Theorem V: Polynomial Time

Stephen Smale, Michael Shub, S. Smale, 1994, Theor. Comput. Sci..

Complexity estimates depending on condition and round-off error

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

Publisher Accessed Terms of Use Detailed Terms Mathematics of the Neural Response

Lorenzo Rosasco, Tomaso A. Poggio, Stephen Smale, 2022 .

Some Remarks on the Foundations of Numerical Analysis

Stephen Smale, S. Smale, 1990, SIAM Rev..

Lectures of Smale on differential topology

S. Smale, R. Abraham, 1963 .

The story of the higher dimensional poincaré conjecture (what actually happened on the beaches of rio)

S. Smale, 1990 .

ON INVOLUTIONS OF THE 3-SPHERE.*

M. Hirsch, S. Smale, 1959 .

On How I Got Started in Dynamical Systems

S. Smale, Steve Smale, 1980 .

Differentiable and Combinatorial Structures on Manifolds

S. Smale, 1961 .

Stability and genericity in dynamical systems

S. Smale, 1971 .

ABSTRACT AND CLASSICAL HODGE–DE RHAM THEORY

S. Smale, Steve Smale, Nathan Smale, 2012 .

A generalized Morse theory

S. Smale, Richard S. Palais, S. Smale, 1964 .

Algorithms for Solving Equations

Steve Smale, S. Smale, 2010 .

Continuation methods.

S. Smale, 1979, Science.

Sufficient conditions for an optimum

S. Smale, Steve Smale, 1975 .

A survey of some recent developments in differential topology

S. Smale, 1963 .

P , NP and mathematics – a computational complexity perspective

Avi Wigderson, S. Smale, A. Wigderson, 2006 .

Derived Distance : towards a mathematical theory of visual cortex

Tomaso Poggio, Jake V. Bouvrie, Andrea Caponnetto, 2007 .

The Problem of the Average Speed of the Simplex Method

Steve Smale, S. Smale, 1982, ISMP.

Structurally Stable Systems are not Dense

S. Smale, S. Smale, 1966 .

Best choices for regularization parameters in learning theory

S. Smale, F. Cucker, 2003 .

Mathematics of the Genome

Steve Smale, Indika Rajapakse, S. Smale, 2015, Found. Comput. Math..

Stable Manifolds for Differential Equations and Diffeomorphisms

S. Smale, 2011 .

Online Learning Algorithms

S. Smale, Y. Yao, 2006, Found. Comput. Math..

S . S MALE Stable manifolds for differential equations and diffeomorphisms

S. Smale, S. Superiore, 2018 .

DIFFERENTIABLE AND COMBINATORIAL STRUCTURES

S. Smale, O. Manifolds, 2016 .

Morse theory and a non-linear generalization of the Dirichlet problem

S. Smale, 1964 .

On Involutions of the 3-Sphere Author ( s ) :

M. Hirsch, S. Smale, 2017 .

A classification of immersions of the two-sphere

S. Smale, 1959 .

REGULAR CURVES ON RIEMANNIAN MANIFOLDS ( J )

S. Smale, 2010 .

Stability and Isotopy in Discrete Dynamical Systems

S. Smale, Steve Smale, 1973 .

ON COMPARATIVE STATICS AND BIFURCATION IN ECONOMIC EQUILIBRIUM THEORY

S. Smale, 1979 .

Modeling Language Evolution

S. Smale, Ding-Xuan Zhou, F. Cucker, 2004, Found. Comput. Math..

Global analysis and economics IIA: Extension of a theorem of Debreu

S. Smale, Steve Smale, 1974 .

On the mathematics of emergence

S. Smale, F. Cucker, 2007 .

Global analysis and economics V: Pareto theory with constraints

S. Smale, Steve Smale, 1974 .

CBCL Paper April 4 , 2008 On a model of visual cortex : learning invariance and selectivity from image sequences

S. Smale, T. Poggio, A. Caponnetto, 2008 .

Algebraic Settings for the Problem “P ≠ NP?”

Felipe Cucker, Michael Shub, Lenore Blum, 1998 .