Kaltofen, Erich - Department of Mathematics, North Carolina State University

• On the complexity of computing determinants Erich Kaltofen
• Fast algorithms for factoring polynomials Erich Kaltofen
• Appears in Journal of Symbolic Computation (2000) 29, 891919 Challenges of Symbolic Computation
• SIAM J. COMPUT. Vol. 17, No. 4, August 1988
• Proceedings of PASCO'94 c 1994 by World Scientific Publishing Company
• Asymptotically Fast Solution of Toeplitz-Like Singular Linear Systems*
• On Wiedemann's Method of Solving Sparse Linear Systems* Erich Kaltofen
• J. Symbolic Computation (2008) 23, 503515 Teaching Computational Abstract Algebra
• A Note on the Risch Differential Equation* Erich Kaltofen
• Efficient Algorithms for Computing the Nearest Polynomial With Parametrically Constrained Roots and Factors
• Approximate Greatest Common Divisors of Several Polynomials with Linearly Constrained Coefficients
• J. Symbolic Computation (1995) 19, 269282 Process Scheduling in DSC and the Large Sparse
• Early Termination in Ben-Or/Tiwari Sparse Interpolation and a Hybrid of Zippel's Algorithm
• An Improved Las Vegas Primality Test Erich Kaltofen and Thomas Valente
• Phase determination of an amplitude modulated complex wavefront
• The nature ("art") of symbolic computation Erich Kaltofen
• Processor Efficient Parallel Solution of Linear Systems over an Abstract Field*
• Computation Appraisement
• 1. Statement of Problem One generic parallel evaluation scheme for algebraic objects, that of evaluating algebraic
• Factoring HighDegree Polynomials by the Black Box Berlekamp Algorithm*
• Effective Hilbert Irreducibility* Erich Kaltofen+
• Approximate Greatest Common Divisors of Several Multivariate Polynomials
• Sparse Hensel Lifting Erich Kaltofen
• Fifteen years after DSC and WLSS2 What parallel computations I do today
• A DISTRIBUTED APPROACH TO PROBLEM SOLVING IN MAPLE
• Asymptotically Toeplitzlike
• Exact Certification of Global Optimality of Approximate Factorizations Via Rationalizing Sums-Of-Squares
• Prediction Based Task Scheduling in Distributed Computing \Lambda
• Factorization of Polynomials by E. Kaltofen
• Computation www.math.ncsu.edu/kaltofen
• Fast algorithms for factoring polynomials A selection
• Lower Bounds for Approximate Factorizations via Semidefinite Programming (extended abstract)*
• An output-sensitive variant of the baby steps/ giant steps determinant algorithm
• On the complexity of the determinant Erich Kaltofen
• Contemporary Mathematics Symmetric Determinantal Representation
• Approximate Factorization of Complex Multivariate Polynomials
• Early Termination in Ben-Or/Tiwari Sparse Interpolation and a Hybrid of Zippel's Algorithm
• Symbolic Computation in Java: an Appraisement* Laurent Bernardin1 Bruce Char2 Erich Kaltofen3
• Polynomials Composition
• Algebraic algorithms Angel D'iaz 1;5
• Early Termination in Sparse Interpolation Erich Kaltofen a
• Proc. Latin '92, I. Simon (Ed.), Springer Lect. Notes Comput. Sci., vol. 583, pp. 294313 (1992). Polynomial Factorization 19871991*
• Acta Informatica vol. 28, nr. 7, pp. 693701 (1991) ON FAST MULTIPLICATION OF
• Subquadratic-Time Factoring of Polynomials over Finite Fields
• FOXBOX: A System for Manipulating Symbolic Objects in Black Box Representation*
• Approximate Factorization of Multivariate Polynomials via Differential Equations
• Appears in Journal of Computer and System Sciences, 50/2 pp. 274295 (1995). Effective Noether Irreducibility Forms and Applications*
• Approximate Factorization of Complex Multivariate Polynomials
• Maple generic code with Domains package GCD := proc(A,B,P,G,phi,NextPrime,SymRem)
• Finding Small Degree Factors of Multivariate Supersparse (Lacunary) Polynomials
• Blocked Iterative Sparse Linear System Solvers for Finite Fields \Lambda
• Parallel Algebraic Algorithm Design* Lecture Notes for a Tutorial
• Algorithms: www.math.ncsu.edu/kaltofen
• Efficient linear algebra algorithms in symbolic computation
• SIAM COMPUT. Vol. 14, No. 2, May 1985
• ON THE COMPLEXITY OF COMPUTING DETERMINANTS* (Extended abstract)
• SubquadraticTime Factoring of Polynomials over Finite Fields *
• ProcessorEfficient Parallel Computation of Polynomial Greatest Common Divisors*
• Constrained approximate
• EFFICIENT LINEAR ALGEBRA ALGORITHMS IN SYMBOLIC COMPUTATION
• factorization irreducible
• Finding Small Degree Factors of Multivariate Supersparse (Lacunary) Polynomials Over Algebraic Number Fields*
• Size Efficient Parallel Algebraic Circuits for Partial Derivatives*
• Approximate Factorization of Multivariate Polynomials via Differential Equations*
• Solving Systems of Non-Linear Polynomial Equations Faster John F. Canny
• Algebraic Algorithms 1 Angel D'iaz
• Integer Division in Residue Number Systems Markus A. Hitz and Erich Kaltofen
• 112 Computer Algebra Handbook 2.12.3 Hybrid Methods
• Explicit Construction of the Hilbert Class Fields of Imaginary Quadratic Fields with Class Numbers 7 and 11
• POLYNOMIALTIME FACTORIZATION OF MULTIVARIATE POLYNOMIALS OVER FINITE FIELDS
• Programming kaltofen@math.ncsu.edu
• EFFICIENTLY CERTIFYING NON-INTEGER POWERS
• Exact certification in global polynomial optimization via sums-of-squares of rational functions
• Symbolic computation in the new century The road ahead
• The Algebraic Theory of Integration Draft Lecture Notes
• The Art of Symbolic Computation Erich Kaltofen
• Algorithmica (1999) 24: 331348 Algorithmica
• Deterministic Irreducibility Testing of Polynomials over Large Finite Fields*
• Algorithms for sparse and black box matrices over finite fields
• www.math.ncsu.edu/kaltofen University)
• Computing the radius of positive semidefiniteness of a multivariate real polynomial via a
• Polynomial Factorization: a Success Story [Plenary Lecture]
• On probabilistic analysis of randomization in hybrid symbolic-numeric algorithms*
• Uniform Closure Properties of P-Computable Functions* Erich Kaltofen
• Symmetric Determinantal Representation of Weakly-Skew Circuits
• The "Seven Dwarfs" of Symbolic Computation* Erich L. Kaltofen
• A Proof of the Monotone Column Permanent (MCP) Conjecture for Dimension 4 via Sums-Of-Squares
• Journal of Symbolic Computation 43 (2008) 359376 Computation
• ACM Communications in Computer Algebra, Issue 162, Number 4, December 2007 Formally reviewed communication Irreducible polynomials and Barker sequences
• Hybrid Symbolic-Numeric Computation* Erich Kaltofen
• On the Complexity of Factoring Bivariate Supersparse (Lacunary) Polynomials*
• Generic Matrix Multiplication and Memory Management in Erich Kaltofen
• Generic Matrix Multiplication and Memory Management Erich Kaltofen
• Symbolic-Numeric Computation D. Wang and L. Zhi, Eds.
• comput. complex. 13 (2004), 91 130 1016-3328/04/03009140
• Computing the sign or the value of the determinant of an integer matrix,
• On Approximate Irreducibility of Polynomials in Several Variables
• An output-sensitive variant of the baby steps/giant steps determinant algorithm*
• Algorithms for sparse and black box matrices over finite fields (Invited talk)
• Efficient Algorithms for Computing the Nearest Polynomial with a Real Root and Related Problems*
• Efficient Algorithms for Computing the Nearest Polynomial with Constrained Roots
• On Randomized Lanczos Algorithms Wayne Eberly
• On Rank Properties of Toeplitz Matrices over Finite Fields E. KALTOFEN1 and A. LOBO2
• Generic Gram-Schmidt Orthogonalization by Exact Division
• Proc. DISCO '93, Springer Lect. Notes Comput. Sci., vol. 722, pp. 6680 (1993). Process Scheduling in DSC and the Large
• Computational Differentiation and Algebraic Complexity Theory* Erich Kaltofen
• On Computing Determinants of Matrices Without Divisions* Erich Kaltofen
• Computing with Black Boxes 301 Computing with Polynomials Given By
• Parallel Algorithms for Matrix Normal Forms Erich Kaltofen
• Appears in SIGSAM Bulletin 22(2):41-49 (April 1988). Analysis of the Binary Complexity of Asymptotically Fast
• Greatest Common Divisors of Polynomials Given by Straight-Line Programs*
• Fast Parallel Computation of Hermite and Smith Forms
• ON THE COMPLEXITY OF FACTORING POLYNOMIALS WITH INTEGER COEFFICIENTS
• Publications by Erich Kaltofen July 3, 2011
• On the complexity of factoring sparse polynomials Erich Kaltofen
• Algorithms for Computing the Sparsest Shifts of Polynomials via the Berlekamp/Massey Algorithm
• FoxBox: A System for Manipulating Symbolic Objects in Black Box Representation
• The Seven Dwarfs of Symbolic Computation and the Discovery of Reduced Symbolic Models
• On probabilistic analysis of randomization in hybrid symbolic-numeric Erich Kaltofen
• Factoring Supersparse (Lacunary) Polynomials Erich Kaltofen
• Hybrid Symbolic-Numeric Computation Erich Kaltofen
• Tellegen's principle and the synthesis of algorithms Erich Kaltofen
• Polynomial Factorization: a Success Story Erich Kaltofen
• Efficient Problem Reductions in Linear Algebra
• Algorithms for sparse and black box matrices over finite fields
• Efficient Algorithms for Computing the Nearest Polynomial With Parametrically Constrained Roots and Factors
• The Art of Symbolic Computation Erich Kaltofen
• The art of symbolic computation Erich Kaltofen
• On the complexity of computing determinants Erich Kaltofen
• Generic programming: C++ vs. Java Erich Kaltofen
• J. Symbolic Computation (1997) subm., 000000 The Kharitonov theorem and its applications in
• Fast Polynomial Factorization Over High Algebraic Extensions of Finite Fields
• Dagstuhl 2004 Approximate Factorization of Multivariate
• A System for Distributed Symbolic Computation* A. Diaz, E. Kaltofen, K. Schmitz, and T. Valente
• Computer algebra in the new century The road ahead
• The Art of Symbolic Computation Erich Kaltofen
• Enabling Breakthrough: Manuel Bronstein's Impact on the Infrastructure of
• LINBOX: A GENERIC LIBRARY FOR EXACT LINEAR J.-G. DUMASa
• D. V. Chudnovsky G. V. Chudnovsky H. Cohn M. B. Nathanson
• On the Genericity of the Modular Polynomial GCD Algorithm* Erich Kaltofen
• Single-Factor Hensel Lifting and its Application to the Straight-Line Complexity of Certain Polynomials*
• A Polynomial-Time Reduction from Bivariate to Univariate Integral Polynomial Factorization*
• Coppersmith's Polytechnic
• "Using Maple to Grade Maple" Assessment Software
• On the complexity of the determinant Erich Kaltofen
• Computing the Irreducible Real Factors and Components of an Algebraic Curve*
• On Exact and Approximate Interpolation of Sparse Rational Functions*
• COMPUTER ALGEBRA ALGORITHMS* Erich Kaltofen
• Improved Sparse Multivariate Polynomial Interpolation Algorithms*
• Polynomial Factorization 19821986* Erich Kaltofen
• Analysis of Coppersmith's Block Wiedemann Algorithm for the Parallel Solution
• Computing with Polynomials Given by StraightLine Programs II Sparse Factorization*
• Early Termination in Ben-Or/Tiwari Sparse Interpolation and a Hybrid of Zippel's Algorithm*
• Appears in the Proc. of the 33rd Annual Symp. on Foundations of Comput. Sci., IEEE, 714723 (1992). Processor-Efficient Parallel Solution of Linear Systems II
• Distributed Matrix-Free Solution of Large Sparse Linear Systems over Finite Fields
• PolynomialTime Reductions from Multivariate to * Bi and Univariate Integral Polynomial Factorization
• Polynomials Evaluations
• On Computing Greatest Common Divisors with Polynomials Given By Black Boxes for Their Evaluations *
• www.math.ncsu.edu/kaltofen distributable
• Deterministic distinct-degree factorization of polynomials over finite fields
• On the complexity of factoring sparse polynomials Erich Kaltofen
• Factoring Supersparse (Lacunary) Polynomials Erich Kaltofen
• The role of algorithms in symbolic computation Erich Kaltofen
• SubquadraticTime Polynomials
• Polytechnic nonsingular
• Constrained approximate
• Fifteen years after DSC and WLSS2 What parallel computations I do today*
• Expressing a Fraction of Two Determinants as a Determinant*
• Algorithms for Computing the Sparsest Shifts of Polynomials via the Berlekamp/Massey Algorithm*
• Computing Greatest Common Divisors and Factorizations in Quadratic Number Fields*
• Complexity Theory in the Service of Algorithm Design
• Algorithms for Computing Sparsest Shifts of Polynomials in Power, Chebyshev, and
• My lecture at the Conference on Algebraic Complexity in the memory of Jacques Morgenstern, INRIA Sophia Antipolis, France May 1995.
• SIGSAM Bulletin, vol. 27, nr. 4, p. 2 (1993). Direct Proof of a Theorem by Kalkbrener, Sweedler, and Taylor*
• Factorization of Polynomials Given by Straight-Line Programs*
• Fast Estimates of Hankel Matrix Condition Numbers and Numeric Sparse Interpolation*
• Supersparse Black Box Rational Function Interpolation* Erich L. Kaltofen
• Quadratic-Time Certificates in Linear Algebra* Erich L. Kaltofen
• Handbook of Finite Fields Gary L. Mullen
• Encyclopedia of Applied and Computational Mathematics, Bjorn Enquist, ed., Mathematics of Computer Science, Discrete Math-