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Author

임종인

Bio: 임종인 is an academic researcher. The author has an hindex of 1, co-authored 1 publications receiving 262 citations.

Papers
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01 Jun 1995
TL;DR: S-polynomials eliminating the leading term Buchberger's criterion and algorithm andWavelet Design construct wavelet filters proof of the Buchberger criterion termination and elimination.
Abstract: 1 S-polynomials eliminating the leading term Buchberger's criterion and algorithm 2 Wavelet Design construct wavelet filters 3 Proof of the Buchberger Criterion two lemmas proof of the Buchberger criterion termination and elimination

292 citations


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Book
01 Aug 1993
TL;DR: This textbook for invariants theory and research monograph that introduces a new approach to the algorithmic side of invariant theory and students should find the book useful as an introduction to this classical and new area of mathematics.
Abstract: This textbook for invariant theory and research monograph that introduces a new approach to the algorithmic side of invariant theory. The Groebner-based method is the main tool by which the central problems in invariant theory become amenable to algorithmic solutions. Students should find the book useful as an introduction to this classical and new area of mathematics. Researchers in mathematics, symbolic computation and computer science should get access to a wealth of research ideas, hints for applications, outlines and details of algorithms, worked-out examples and research problems.

767 citations

Journal ArticleDOI
TL;DR: This paper gives polynomial complexity algorithms to compute a Gröbner basis, generalizing the Buchberger-Möller algorithm for computing a basis of an ideal vanishing at a set of points and the FGLM basis conversion algorithm.
Abstract: In this paper we study 0-dimensional polynomial ideals defined by a dual basis, i.e. as the set of polynomials which are in the kernel of a set of linear morphisms from the polynomial ring to the base field. For such ideals, we give polynomial complexity algorithms to compute a Grobner basis, generalizing the Buchberger-Moller algorithm for computing a basis of an ideal vanishing at a set of points and the FGLM basis conversion algorithm. As an application to Algebraic Geometry, we show how to compute in polynomial time a minimal basis of an ideal of projective points.

163 citations

BookDOI
01 Jan 2006
TL;DR: Part I Chance-Constrained and Stochastic Optimization Scenario Approximations of Chance Constraints Optimization Models with Probabilistic Constrains Theoretical Framework for Comparing Several Stochastics Optimization Approaches Optimization of Risk Measures.
Abstract: Part I Chance-Constrained and Stochastic Optimization Scenario Approximations of Chance Constraints Optimization Models with Probabilistic Constraints Theoretical Framework for Comparing Several Stochastic Optimization Approaches Optimization of Risk Measures Part II Robust Optimization and Random Sampling Sampled Convex Programs and Probabilistically Robust Design Tetris: A Study of Randomized Constraint Sampling Near Optimal Solutions to Least-Squares Problems with Stochastic Uncertainty The Randomized Ellipsoid Algorithm for Constrained Robust Least Squares Problems Randomized Algorithms for Semi-Infnite Programming Problems Part III Probabilistic Methods in Identifcation and Control A Learning Theory Approach to System Identifcation and Stochastic Adaptive Control Probabilistic Design of a Robust Controller Using a Parameter-Dependent Lyapunov Function Probabilistic Robust Controller Design: Probable Near Minimax Value and Randomized Algorithms Sampling Random Transfer Functions Nonlinear Systems Stability via Random and Quasi-Random Methods Probabilistic Control of Nonlinear Uncertain Systems Fast Randomized Algorithms for Probabilistic Robustness Analysis References

157 citations

Journal ArticleDOI
TL;DR: Effective algorithms which check whether or not a linear control system over some Ore algebra is controllable, parametrizable, flat or π-free are given.
Abstract: In this paper, we study linear control systems over Ore algebras. Within this mathematical framework, we can simultaneously deal with different classes of linear control systems such as time-varying systems of ordinary differential equations (ODEs), differential time-delay systems, underdetermined systems of partial differential equations (PDEs), multidimensional discrete systems, multidimensional convolutional codes, etc. We give effective algorithms which check whether or not a linear control system over some Ore algebra is controllable, parametrizable, flat or π-free.

145 citations

Proceedings ArticleDOI
25 Jul 2010
TL;DR: The theoretical and practical complexity of computing Gröbner bases of two algebraic formulations of the MinRank problem are given and the determinantal ideal formulation is used to break a cryptographic challenge and allow us to evaluate precisely the security of the cryptosystem w.r.t. n, r and k.
Abstract: Computing loci of rank defects of linear matrices (also called the MinRank problem) is a fundamental NP-hard problem of linear algebra which has applications in Cryptology, in Error Correcting Codes and in Geometry Given a square linear matrix (ie a matrix whose entries are k-variate linear forms) of size n and an integer r, the problem is to find points such that the evaluation of the matrix has rank less than r + 1 The aim of the paper is to obtain the most efficient algorithm to solve this problem To this end, we give the theoretical and practical complexity of computing Grobner bases of two algebraic formulations of the MinRank problem Both modelings lead to structured algebraic systemsThe first modeling, proposed by Kipnis and Shamir generates bi-homogeneous equations of bi-degree (1, 1) The second one is classically obtained by the vanishing of the (r + 1)-minors of the given matrix, giving rise to a determinantal ideal In both cases, under genericity assumptions on the entries of the considered matrix, we give new bounds on the degree of regularity of the considered ideal which allows us to estimate the complexity of the whole Grobner bases computations For instance, the exact degree of regularity of the determinantal ideal formulation of a generic well-defined MinRank problem is r(n - r) + 1 We also give optimal degree bounds of the loci of rank defect which are reached under genericity assumptions; the new bounds are much lower than the standard multi-homogeneous Bezout bounds (or mixed volume of Newton polytopes)TAs a by-product, we prove that the generic MinRank problem could be solved in polynomial time in n (when n - r is fixed) as announced in a previous paper of Faugere, Levy-dit-Vehel and Perret Moreover, using the determinantal ideal formulation, these results are used to break a cryptographic challenge (which was untractable so far) and allow us to evaluate precisely the security of the cryptosystem wrt n, r and k Our practical results suggest that, up to the software state of the art, this latter formulation is more adapted in the context of Grobner bases computations

108 citations