Allan M. Pinkus

Allan M. Pinkus's AcademicInfluence.com Rankings

Allan M. Pinkus

Computer Science

#8721

World Rank

#9170

Historical Rank

Machine Learning

#3644

World Rank

#3689

Historical Rank

computer-science Degrees

Allan M. Pinkus

Mathematics

#7244

World Rank

#9880

Historical Rank

Applied Mathematics

#312

World Rank

#337

Historical Rank

Measure Theory

#1977

World Rank

#2402

Historical Rank

mathematics Degrees

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Computer Science
Mathematics

Allan M. Pinkus's Degrees

PhD Mathematics University of California, Berkeley

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Allan M. Pinkus'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

Multilayer Feedforward Networks with a Non-Polynomial Activation Function Can Approximate Any Function (1991) (1742)
Approximation theory of the MLP model in neural networks (1999) (956)
n-Widths in Approximation Theory (1985) (915)
On L[1]-approximation (1991) (157)
Lower bounds for approximation by MLP neural networks (1999) (129)
Progress in Approximation Theory (1991) (118)
Fundamentality of Ridge Functions (1993) (102)
On L1-Approximation (1989) (101)
Backward error analysis for totally positive linear systems (1976) (94)
Weierstrass and Approximation Theory (2000) (88)
Totally Positive Matrices (2009) (82)
Proof of the conjectures of Bernstein and Erdös concerning the optimal nodes for polynomial interpolation (1978) (81)
On Ridge Functions (2013) (78)
Multivariate Approximation and Applications: Index (2001) (66)
Encyclopaedia of Mathematics, Supplement III (2002) (59)
Some Problems in the Approximation of Functions of Two Variables and n-Widths of Integral Operators (1978) (59)
Moment Theory for Weak Chebyshev Systems with Applications to Monosplines, Quadrature Formulae and Best One-Sided $L^1 $-Approximation by Spline Functions with Fixed Knots (1977) (57)
Interpolation by ridge functions (1993) (51)
The Approximation of a Totally Positive Band Matrix by a Strictly Banded Totally Positive One (1982) (51)
Approximating by Ridge Functions (1997) (45)
Foundations of Computational Mathematics, Santander 2005 (London Mathematical Society Lecture Note Series) (2006) (44)
Functions that preserve families of positive semidefinite matrices (1995) (44)
Spectral Properties of Totally Positive Kernels and Matrices (1996) (41)
n-Widths of Sobolev spaces inLp (1985) (40)
Onn-widths of periodic functions (1979) (40)
Identifying Linear Combinations of Ridge Functions (1999) (39)
Introduction to shift-invariant spaces. Linear independence (2001) (39)
A simple proof of the Hobby-Rice theorem (1976) (38)
Strictly Positive Definite Functions on a Real Inner Product Space (2004) (36)
Variations on the Chebyshev and Lq theories of best approximation (1982) (35)
TDI-Subspaces ofC(Rd) and Some Density Problems from Neural Networks (1996) (32)
Some Extremal Properties of Perfect Splines and the Pointwise Landau Problem on the Finite Interval (1978) (32)
On n-Widths in L ∞ (1977) (31)
Fourier Series and Integral Transforms (2019) (30)
Approximation of Multivariate Functions (2004) (29)
Density in Approximation Theory (2005) (28)
Strictly Hermitian positive definite functions (2004) (27)
Interlacing properties of the zeros of the error functions in best Lp-approximations (1979) (26)
On -widths in ^{∞} (1977) (26)
Unicity subspaces in L 1 -approximation (1986) (26)
On smoothest interpolants (1988) (25)
Descartes systems from corner cutting (1991) (24)
approximation with constraints (1990) (24)
Uniqueness in Vector-Valued Approximation (1993) (23)
Preface / Préface (2000) (23)
Sparse Grids for Higher Dimensional Problems (2006) (22)
Some Remarks on Nonnegative Polynomials on Polyhedra (1989) (22)
On the Erdös Conjecture Concerning Minimal Norm Interpolation on the Unit Circle (1980) (22)
Strong Uniqueness (2010) (21)
On some zero-increasing operators (2002) (21)
INTERPOLATION BY MATRICES (2004) (20)
Interpolation on lines by ridge functions (2013) (20)
Oscillation Properties of Generalized Characteristic Polynomials for Totally Positive and Positive Definite Matrices (1974) (18)
Functional inequalities for spectral radii of nonnegative matrices (1990) (16)
The B-spline recurrence relations of Chakalov and of Popoviciu (2003) (16)
Structure of Invertible (Bi)infinite Totally Positive Matrices (1982) (16)
Modulated Fourier Expansions for Continuous and Discrete Oscillatory Systems (2012) (16)
On a recovery problem (1995) (14)
Positive and minimal projections in function spaces (1983) (13)
Through the Kaleidoscope: Symmetries, Groups and Chebyshev-Approximations from a Computational Point of View (2012) (12)
One-sided L1 approximation by splines with fixed knots (1976) (12)
Some extremal problems for strictly totally positive matrices (1985) (12)
Sparse representations and approximation theory (2011) (11)
A problem of approximation using multivariate polynomials (1995) (11)
Matrices and n-Widths (1979) (11)
Total positivity and the exact $n$-width of certain sets in $L^1$. (1977) (11)
Smoothness and uniqueness in ridge function representation (2013) (11)
INVERSES OF INFINITE SIGN REGULAR MATRICES (1982) (10)
Foundations of computational mathematics : Santander 2005 (2006) (10)
Necessary conditions for uniqueness in L 1 -approximation (1988) (10)
Negative Theorems in Approximation Theory (2003) (10)
Extending n-convex functions (2005) (8)
The Shape of Data (2012) (8)
Best mean approximation to a 2-dimensional kernel by tensor products (1977) (8)
An interlacing property of eigenvalues of strictly totally positive matrices (1998) (8)
Density methods and results in approximation theory (2004) (7)
Best Approximations by Smooth Functions (1981) (7)
Some Properties of the Global Behaviour of Conservative Low-Dimensional Systems (2009) (7)
Foundations of Computational Mathematics, Hong Kong 2008 (2009) (7)
Asymptotic minimum norm quadrature formulae (1975) (6)
Some Density Problems in Multivariate Approximation (2004) (5)
Bernstein's comparison theorem and a problem of Braess (1981) (5)
Spectral Properties and Oscillation Theorems for Mixed Boundary-Value Problems of Sturm-Liouville Type. (1978) (5)
The alternating algorithm in a uniformly convex and uniformly smooth Banach space (2015) (5)
On Stability of the Metric Projection Operator (2013) (4)
Nonlinear eigenvalue problems for a class of ordinary differential equations (2002) (4)
On Zero-Preserving Linear Transformations☆ (2002) (4)
Some Remarks on Zero-Increasing Transformations (2004) (3)
Best Approximation and Cyclic Variation Diminishing Kernels (1997) (3)
Dominating Subsets under Projections (2010) (3)
On Some Zero-Increasing Operators (2002) (3)
Rank restricting functions (2003) (3)
Best Approximation with Coefficient Constraints (1988) (3)
Continuous selections for the metric projection onC1 (1988) (3)
Uniqueness of Smoothest Interpolants (2004) (3)
Zero minors of total positive matrices (2008) (3)
Foundations of computational mathematics, Budapest 2011 (2012) (3)
Book Review: S. Bagdasarov, Chebyshev Splines and Kolmogorov Inequalities (2000) (2)
One-Sided L1 -Approximation (1986) (2)
On best rank n matrix approximations (2012) (2)
Representation theorems for Tchebycheffian polynomials with boundary conditions and their applications (1974) (2)
Non-linear Eigenvalue Problems for a Class of Ordinary Differential Equations (2002) (1)
Zero Minors of Totally Positive Matrices * (2008) (1)
Nonlinear eigenvalue–eigenvector problems for STP matrices (2002) (1)
Preface to the Special Issue on Sparse Approximate Solution of Linear Systems (2014) (1)
On a Best Estimator For the Class (M sup r) Using Only Function Values. (1976) (1)
Polynomial Ridge Functions (2015) (1)
Bernstein's comparison theorem and a problem of Braess (1981) (1)
Interlacing Properties of the Zeros of the Error Function in Best Lp-Approximation, 1 Less Than or Equal to p Less Than or Equal to Infinity. (1976) (1)
On a Problem of G. G. Lorentz (2000) (1)
Entropy, compactness and the approximation of operators: B. Carl and I. Stephani, Cambridge University Press, 1990, 277 pp (1991) (0)
Progress in Approximation Theory. (1992) (0)
Existence and Characterization of Best Approximations (2015) (0)
Spline functions and total pasitivity (2014) (0)
Foundations of Computational Mathematics, Budapest 2011: Preface (2012) (0)
Notation and Terminology (1997) (0)
Fourier Series and Integral Transforms: Fourier Series (1997) (0)
Glossary of Selected Symbols (2015) (0)
Continuous selections for metric projections and interpolating subspaces: W. Li, Verlag Peter Lang, 1991, 108 pp (1991) (0)
Totally Positive Matrices: Variation diminishing (2009) (0)
Foundations of Computational Mathematics, Hong Kong 2008: Preface (2009) (0)
Tchebycheff Systems and Total Positivity (1985) (0)
On «-widths in L00 (2010) (0)
Ratio and Relative Asymptotics of Polynomials Orthogonal on an Arc of the Unit Circle (1998) (0)
Fourier Series and Integral Transforms: The Laplace Transform (1997) (0)
On L 1–approximation: Convexity Cones and L1-Approximation (1989) (0)
Fourier Series and Integral Transforms: The Residue Theorem and Related Results (1997) (0)
Totally Positive Matrices: Factorizations of totally positive matrices (2009) (0)
n -Widths of Analytic Functions (1985) (0)
n-Widths in Hilbert Spaces (1985) (0)
Totally Positive Matrices: Foreword (2009) (0)
Ridge Functions: Approximation Algorithms (2015) (0)
On Ridge Functions (pp.122-130) (2013) (0)
Unicity Subspaces and Property A (1989) (0)
The closed linear span of {Xk − Ck}∞1 (1985) (0)
Approximation from Finite-Dimensional Subspaces ofL1 (1989) (0)
Interpolation on Lines (2015) (0)
Fourier Series and Integral Transforms: The Fourier Transform (1997) (0)
One-SidedL1-Approximation (1989) (0)
Approximation from Finite-Dimensional Subspaces inC1(K, μ) (1989) (0)
The multi-dimensional Von Neumann alternating direction search algorithm in C(B) and L1 (1992) (0)
Fourier Series and Integral Transforms: Background: Inner Product Spaces (1997) (0)
George G. Lorentz Turns 90 (2000) (0)
Density and Representation (2015) (0)
On L 1–approximation: Discrete l1m-Approximation (1989) (0)
Totally Positive Matrices: Criteria for total positivity and strict total positivity (2009) (0)
ANU volume 8 issue 1 Cover and Front matter (1999) (0)
On nonnegative sign equivalent and sign similar factorizations of matrices. (2007) (0)
Optimal Reconstructions and n-Widths. (1983) (0)
On $n$-widths in $L\sp{\infty }$ (1977) (0)
On N-widths in L? 1. Introduction. Let X = (x,ii * 11) Be a Normal Linear Space, a a Subset of X (2008) (0)
Inverses of Infinite Sign Regular Matrices Author ( s ) : (1980) (0)
On Chebyshev-Markov-Krein inequalities (2012) (0)
INVERSES OF INFINITE SIGN REGULAR MATRICES' BY C. DE BOOR, S. FRIEDLAND AND A. PINKUS (2010) (0)
Fourier Series and Integral Transforms: Leibniz's Rule and Fubinfs Theorem (1997) (0)
Totally Positive Matrices: Basic properties of totally positive and strictly totally positive matrices (2009) (0)
On L 1–approximation: Algorithms (1989) (0)
Asymptotic Estimates for n-Widths of Sobolev Spaces (1985) (0)
Totally Positive Matrices: Eigenvalues and eigenvectors (2009) (0)
A Factorization of Totally Positive Band Matrices. (1980) (0)
A ] 2 0 Ja n 20 05 Density in Approximation Theory (2005) (0)
Multivariate Approximation and Applications: Preface (2001) (0)
Borislav D. Bojanov: 18 November 1944-8 April 2009 (2010) (0)
Interpolation at Points (2015) (0)
Exact n-Widths of Integral Operators (1985) (0)
Totally Positive Matrices: Afterword (2009) (0)
Identifying Functions and Directions (2015) (0)
Basic Properties of n-Widths (1985) (0)

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Allan M. Pinkus's Academic­Influence.com Rankings

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Allan M. Pinkus's Published Works

Published Works

Allan M. Pinkus's AcademicInfluence.com Rankings