메뉴 건너뛰기




Volumn 55, Issue 1, 2008, Pages 445-461

A tutorial on Gröbner bases with applications in signals and systems

Author keywords

Algebra; Book reviews; Circuits and systems; Control systems; Gr bner bases; Matrix factorization; Multidimensional systems; Multivariate polynomial; Polynomials; Signal processing; Signal processing algorithms; Tutorials

Indexed keywords

CONTROL SYSTEMS; FACTORIZATION; MATRIX ALGEBRA; MULTIVARIABLE SYSTEMS; NETWORKS (CIRCUITS); POLYNOMIALS; ROBOTICS; SIGNAL ENCODING;

EID: 42949122508     PISSN: 10577122     EISSN: None     Source Type: Journal    
DOI: 10.1109/TCSI.2007.914007     Document Type: Article
Times cited : (50)

References (148)
  • 1
    • 4444246858 scopus 로고    scopus 로고
    • A serial-in-serial-out hardware architecture for systematic encoding of Hermitian codes via Grobner bases
    • J.-P. Chen C.-C. Lu A serial-in-serial-out hardware architecture for systematic encoding of Hermitian codes via Grobner bases IEEE Trans. Commun. 52 8 1322 1332 Aug. 2004
    • (2004) IEEE Trans. Commun. , vol.52 , Issue.8 , pp. 1322-1332
    • Chen, J.-P.1    Lu, C.-C.2
  • 2
    • 85177110250 scopus 로고    scopus 로고
    • CoCoA, a System for Doing Computations in Commuatative Algebra. CoCoA Team http://www.cocoa.dima.unige.it
  • 3
    • 0003908675 scopus 로고
    • Ideals, Varieties, and Algorithms
    • Springer-Verlag Germany, Berlin
    • D. Cox J. Little D. O'Shea Ideals, Varieties, and Algorithms 1992 Springer-Verlag Germany, Berlin
    • (1992)
    • Cox, D.1    Little, J.2    O'Shea, D.3
  • 5
    • 0003527787 scopus 로고
    • Commutative Algebra With a View Towards Algebraic Geometry
    • Springer-Verlag New York
    • D. Eisenbud Commutative Algebra With a View Towards Algebraic Geometry 1995 Springer-Verlag New York
    • (1995)
    • Eisenbud, D.1
  • 6
    • 0004154214 scopus 로고
    • Syzygies
    • Cambridge Univ. Press U.K., Cambridge
    • E. G. Evans P. Griffith Syzygies 1985 Cambridge Univ. Press U.K., Cambridge
    • (1985)
    • Evans, E.G.1    Griffith, P.2
  • 7
    • 85177142464 scopus 로고    scopus 로고
    • Flat multidimensional linear systems with constant coefficients are equivalent to controllable 1-D linear systems
    • A. Fabiaska A. Quadrat Flat multidimensional linear systems with constant coefficients are equivalent to controllable 1-D linear systems Proc. MTNS 24 28 Proc. MTNS Kyoto Japan 2006-Jul.
    • (2006) , pp. 24-28
    • Fabiaska, A.1    Quadrat, A.2
  • 8
    • 46649116471 scopus 로고    scopus 로고
    • Applications of the Quillen-Suslin Theorem to Multidimensional Systems Theory
    • A. Fabiaska A. Quadrat Applications of the Quillen-Suslin Theorem to Multidimensional Systems Theory 2007 INRIA Rep. 6126
    • (2007)
    • Fabiaska, A.1    Quadrat, A.2
  • 9
    • 9144273964 scopus 로고    scopus 로고
    • Design of regular nonseparable bidimensional wavelets using Gröbner basis techniques
    • J.-C. Faugere F. M. de Saint-Martin F. Rouillier Design of regular nonseparable bidimensional wavelets using Gröbner basis techniques IEEE Trans. Signal Process. 46 6 845 856 Jun. 1998
    • (1998) IEEE Trans. Signal Process. , vol.46 , Issue.6 , pp. 845-856
    • Faugere, J.-C.1    de Saint-Martin, F.M.2    Rouillier, F.3
  • 10
    • 0023826499 scopus 로고
    • A note on output feedback stabilizability of multivariable 2-D systems
    • E. Fornasini A note on output feedback stabilizability of multivariable 2-D systems Syst. Control Lett. 10 45 50 1988
    • (1988) Syst. Control Lett. , vol.10 , pp. 45-50
    • Fornasini, E.1
  • 11
    • 0031257022 scopus 로고    scopus 로고
    • $n$D polynomial matrices with applications to multidimensional signal analysis
    • E. Fornasini M. E. Valcher $n$D polynomial matrices with applications to multidimensional signal analysis Multidimensional Syst. Signal Process. 8 387 408 Oct. 1997
    • (1997) Multidimensional Syst. Signal Process. , vol.8 , pp. 387-408
    • Fornasini, E.1    Valcher, M.E.2
  • 12
    • 33747590758 scopus 로고    scopus 로고
    • Parametric optimization and optimal control using algebraic geometry methods
    • I. A. Fotiou P. Rostalski P. A. Parrilo M. Morari Parametric optimization and optimal control using algebraic geometry methods Int. J. Control 79 11 1340 1358 Nov. 2006
    • (2006) Int. J. Control , vol.79 , Issue.11 , pp. 1340-1358
    • Fotiou, I.A.1    Rostalski, P.2    Parrilo, P.A.3    Morari, M.4
  • 13
    • 0032156647 scopus 로고    scopus 로고
    • Continuous time-varying linear systems
    • S. Frhler U. Oberst Continuous time-varying linear systems Syst. Control Lett. 35 2 97 110 1998
    • (1998) Syst. Control Lett. , vol.35 , Issue.2 , pp. 97-110
    • Frhler, S.1    Oberst, U.2
  • 14
    • 0038532904 scopus 로고
    • Gröbner basis of a module over $K[x_{1},\\ldots,x_{n}]$ and polynomial solutions of a system of linear equations
    • ON
    • A. Furukawa T. Sasaki H. Kobayashi Gröbner basis of a module over $K[x_{1},\\ldots,x_{n}]$ and polynomial solutions of a system of linear equations Proc. SYMSAC 222 224 Proc. SYMSAC Waterloo Canada ON 1986
    • (1986) , pp. 222-224
    • Furukawa, A.1    Sasaki, T.2    Kobayashi, H.3
  • 15
    • 0038349656 scopus 로고    scopus 로고
    • On codes from norm-trace curves
    • O. Geil On codes from norm-trace curves Finite Fields Their Appl. 9 351 371 2003
    • (2003) Finite Fields Their Appl. , vol.9 , pp. 351-371
    • Geil, O.1
  • 16
    • 0004056503 scopus 로고
    • Algorithms for Computer Algebra
    • Kluwer The Netherlands, Dordrecht
    • K. O. Geddes S. R. Czapor G. Labahn Algorithms for Computer Algebra 1992 Kluwer The Netherlands, Dordrecht
    • (1992)
    • Geddes, K.O.1    Czapor, S.R.2    Labahn, G.3
  • 17
    • 0020192573 scopus 로고
    • Polynomial matrix primitive factorization over arbitrary coefficient field and related results
    • J. P. Guiver N. K. Bose Polynomial matrix primitive factorization over arbitrary coefficient field and related results IEEE Trans. Circuits Syst. CST-29 3 649 657 May 1982
    • (1982) IEEE Trans. Circuits Syst. , vol.CST-29 , Issue.3 , pp. 649-657
    • Guiver, J.P.1    Bose, N.K.2
  • 18
    • 0003913372 scopus 로고    scopus 로고
    • Multidimensional Systems Theory: Progress, Directions and Open Problems
    • Causal and weakly causal 2-D filters with applications in stabilizations Reidel The Netherlands, Dordrecht
    • J. P. Guiver N. K. Bose Multidimensional Systems Theory: Progress, Directions and Open Problems 52 100 1985 Reidel The Netherlands, Dordrecht Causal and weakly causal 2-D filters with applications in stabilizations
    • (1985) , pp. 52-100
    • Guiver, J.P.1    Bose, N.K.2
  • 19
    • 0030388221 scopus 로고    scopus 로고
    • Constructive algebra methods for the L2-problem for stable linear systems
    • B. Hanzon J. M. Maciejowski Constructive algebra methods for the L2-problem for stable linear systems Automatica 32 12 1645 1657 1996
    • (1996) Automatica , vol.32 , Issue.12 , pp. 1645-1657
    • Hanzon, B.1    Maciejowski, J.M.2
  • 20
    • 0032021829 scopus 로고    scopus 로고
    • Computer simplification of formulas in linear systems theory
    • J. W. Helton M. Stankus J. J. Wavrik Computer simplification of formulas in linear systems theory IEEE Trans. Autom. Control 43 3 302 314 Mar. 1998
    • (1998) IEEE Trans. Autom. Control , vol.43 , Issue.3 , pp. 302-314
    • Helton, J.W.1    Stankus, M.2    Wavrik, J.J.3
  • 22
    • 0000554923 scopus 로고
    • Resolution of singularities of an algebraic variety over a field of characteristic zero: I
    • H. Hironaka Resolution of singularities of an algebraic variety over a field of characteristic zero: I Annals Math. 2 79 1 109 203 Jan. 1964
    • (1964) Annals Math. , vol.79 , Issue.1 , pp. 109-203
    • Hironaka, H.1
  • 23
    • 0030129003 scopus 로고    scopus 로고
    • Annihilation of loading parameters in classical numerical methods with differential equations
    • N. I. Ioakimidis E. G. Anastasselou Annihilation of loading parameters in classical numerical methods with differential equations Comput. Structures 59 2 265 271 1996
    • (1996) Comput. Structures , vol.59 , Issue.2 , pp. 265-271
    • Ioakimidis, N.I.1    Anastasselou, E.G.2
  • 24
    • 0027626135 scopus 로고
    • An implementation of Buchbergers' algorithm with applications to robotics
    • C. M. Kalker-Kalkman An implementation of Buchbergers' algorithm with applications to robotics Mechanism Mach. Theory 28 4 523 537 1993
    • (1993) Mechanism Mach. Theory , vol.28 , Issue.4 , pp. 523-537
    • Kalker-Kalkman, C.M.1
  • 26
    • 0002526507 scopus 로고    scopus 로고
    • Transfer operators and state spaces for discrete multidimensional linear systems
    • S. Kleon U. Oberst Transfer operators and state spaces for discrete multidimensional linear systems Acta Applicandae Mathematicae 57 1 82 1999
    • (1999) Acta Applicandae Mathematicae , vol.57 , pp. 1-82
    • Kleon, S.1    Oberst, U.2
  • 27
    • 0004334181 scopus 로고    scopus 로고
    • Computational Commutative Algebra 1
    • Springer-Verlag Germany, Berlin
    • M. Kreuzer L. Robbiano Computational Commutative Algebra 1 2000 Springer-Verlag Germany, Berlin
    • (2000)
    • Kreuzer, M.1    Robbiano, L.2
  • 28
    • 0003921180 scopus 로고    scopus 로고
    • Advanced Engineering Mathematics
    • 9th Wiley New York
    • E. Kreyszig Advanced Engineering Mathematics 9th 2006 Wiley New York
    • (2006)
    • Kreyszig, E.1
  • 29
    • 0003267890 scopus 로고
    • Serre's Conjecture
    • Springer-Verlag Germany, Berlin
    • T. Y. Lam Serre's Conjecture 635 1978 Springer-Verlag Germany, Berlin
    • (1978) , vol.635
    • Lam, T.Y.1
  • 30
    • 12144265033 scopus 로고    scopus 로고
    • Serre's Problem on Projective Modules
    • Springer-Verlag Germany, Berlin
    • T. Y. Lam Serre's Problem on Projective Modules 2006 Springer-Verlag Germany, Berlin
    • (2006)
    • Lam, T.Y.1
  • 31
    • 1942445291 scopus 로고    scopus 로고
    • Gröbner bases and wavelet design
    • J. Lebrun I. Selesnick Gröbner bases and wavelet design J. Symbol. Computat. 37 2 227 259 2004
    • (2004) J. Symbol. Computat. , vol.37 , Issue.2 , pp. 227-259
    • Lebrun, J.1    Selesnick, I.2
  • 32
    • 39049154297 scopus 로고    scopus 로고
    • An interpolation algorithm using Gröbner bases for soft-decision decoding of Reed–Solomon codes
    • K. Lee M. E. O'Sullivan An interpolation algorithm using Gröbner bases for soft-decision decoding of Reed–Solomon codes Proc. IEEE Int. Symp. Inf. Theory 2032 2036 Proc. IEEE Int. Symp. Inf. Theory 2006-Jul.
    • (2006) , pp. 2032-2036
    • Lee, K.1    O'Sullivan, M.E.2
  • 33
    • 0024701149 scopus 로고
    • Simultaneous amplitude and phase approximation for FIR filter design
    • F. Leeb T. Henk Simultaneous amplitude and phase approximation for FIR filter design Int. J. Circuit Theory Appl. 17 363 374 Jul. 1989
    • (1989) Int. J. Circuit Theory Appl. , vol.17 , pp. 363-374
    • Leeb, F.1    Henk, T.2
  • 34
    • 0024091436 scopus 로고
    • On matrix fraction descriptions of multivariable linear $n$-D systems
    • Z. Lin On matrix fraction descriptions of multivariable linear $n$-D systems IEEE Trans. Circuits Syst. 35 11 1317 1322 Nov. 1988
    • (1988) IEEE Trans. Circuits Syst. , vol.35 , Issue.11 , pp. 1317-1322
    • Lin, Z.1
  • 35
    • 0033348016 scopus 로고    scopus 로고
    • Notes on $n$-d polynomial matrix factorizations
    • Z. Lin Notes on $n$-d polynomial matrix factorizations Multidimensional Syst. Signal Process. 10 379 393 1999
    • (1999) Multidimensional Syst. Signal Process. , vol.10 , pp. 379-393
    • Lin, Z.1
  • 36
    • 0035889741 scopus 로고    scopus 로고
    • A generalization of Serre's conjecture and some related issues
    • Z. Lin N. K. Bose A generalization of Serre's conjecture and some related issues Linear Algebra Appl. 338 125 138 2001
    • (2001) Linear Algebra Appl. , vol.338 , pp. 125-138
    • Lin, Z.1    Bose, N.K.2
  • 38
    • 0035385641 scopus 로고    scopus 로고
    • A constructive approach to stabilizability and stabilization of a class of $n$D systems
    • Z. Lin J. Lam K. Galkowski S. Xu A constructive approach to stabilizability and stabilization of a class of $n$D systems Multidimensional Syst. Signal Process. 12 329 343 2001
    • (2001) Multidimensional Syst. Signal Process. , vol.12 , pp. 329-343
    • Lin, Z.1    Lam, J.2    Galkowski, K.3    Xu, S.4
  • 40
    • 4644288218 scopus 로고    scopus 로고
    • Applications of Gröbner bases to signal and image processing: A survey
    • Z. Lin L. Xu Q. Wu Applications of Gröbner bases to signal and image processing: A survey Linear Algebra Appl. 391 1 169 202 2004
    • (2004) Linear Algebra Appl. , vol.391 , Issue.1 , pp. 169-202
    • Lin, Z.1    Xu, L.2    Wu, Q.3
  • 41
    • 26844534519 scopus 로고    scopus 로고
    • On minor prime factorization for $n$-D polynomial matrices
    • Z. Lin L. Xu H. Fan On minor prime factorization for $n$-D polynomial matrices IEEE Trans. Circuits Syst. II, Exp. Briefs 52 9 568 571 Sep. 2005
    • (2005) IEEE Trans. Circuits Syst. II, Exp. Briefs , vol.52 , Issue.9 , pp. 568-571
    • Lin, Z.1    Xu, L.2    Fan, H.3
  • 42
    • 0141503448 scopus 로고    scopus 로고
    • Solving the Selesnick-Burrus filter design equations using computational algebra and algebraic geometry
    • J. B. Little Solving the Selesnick-Burrus filter design equations using computational algebra and algebraic geometry Adv. Appl. Math. 31 2 463 500 2003
    • (2003) Adv. Appl. Math. , vol.31 , Issue.2 , pp. 463-500
    • Little, J.B.1
  • 43
    • 38249015275 scopus 로고
    • Algorithms for the Quillen-Suslin theorem
    • A. Logar B. Sturmfels Algorithms for the Quillen-Suslin theorem J. Algebra 145 231 239 1992
    • (1992) J. Algebra , vol.145 , pp. 231-239
    • Logar, A.1    Sturmfels, B.2
  • 44
    • 17344368857 scopus 로고    scopus 로고
    • Suslin's algorithms for reduction of unimodular rows
    • H. Lombardia I. Yengui Suslin's algorithms for reduction of unimodular rows J. Symbol. Computat. 39 707 717 2005
    • (2005) J. Symbol. Computat. , vol.39 , pp. 707-717
    • Lombardia, H.1    Yengui, I.2
  • 45
    • 0038110908 scopus 로고    scopus 로고
    • Singular: A computer algebra system
    • C. Lossen Singular: A computer algebra system Computi. Sci. Eng. 5 4 45 55 Jul.August 2003
    • (2003) Computi. Sci. Eng. , vol.5 , Issue.4 , pp. 45-55
    • Lossen, C.1
  • 46
    • 85177115736 scopus 로고    scopus 로고
    • D. Grayson M. Stillman Macaulay 2: A Software System for Algebraic Geometry and Commutative Algebra www.math.uiuc.edu/Macaulay2
    • Grayson, D.1    Stillman, M.2
  • 47
    • 0034630653 scopus 로고    scopus 로고
    • Automation of the lifting factorisation of wavelet transforms
    • M. Maslen P. Abbott Automation of the lifting factorisation of wavelet transforms Comput. Phys. Commun. 127 23 309 326 2000
    • (2000) Comput. Phys. Commun. , vol.127 , Issue.23 , pp. 309-326
    • Maslen, M.1    Abbott, P.2
  • 48
    • 27744470380 scopus 로고    scopus 로고
    • Systolic array architecture implementing Berlekamp–Massey–Sakata algorithm for decoding codes on a class of algebraic curves
    • H. Matsui S. Sakata M. Kurihara S. Mita Systolic array architecture implementing Berlekamp–Massey–Sakata algorithm for decoding codes on a class of algebraic curves IEEE Trans. Inf. Theory 51 11 3856 3871 Nov. 2005
    • (2005) IEEE Trans. Inf. Theory , vol.51 , Issue.11 , pp. 3856-3871
    • Matsui, H.1    Sakata, S.2    Kurihara, M.3    Mita, S.4
  • 49
    • 0004218317 scopus 로고
    • Algorithmic Algebra
    • Springer-Verlag New York
    • B. Mishra Algorithmic Algebra 1993 Springer-Verlag New York
    • (1993)
    • Mishra, B.1
  • 50
    • 0031675109 scopus 로고    scopus 로고
    • Algebraic solution of the load-flow problem for a 4-nodes electrical network
    • A. Montes Algebraic solution of the load-flow problem for a 4-nodes electrical network Math. Comput. Simulation 45 12 163 174 1998
    • (1998) Math. Comput. Simulation , vol.45 , Issue.12 , pp. 163-174
    • Montes, A.1
  • 51
    • 0000520304 scopus 로고
    • New constructive methods in classical ideal theory
    • F. Mora H. M. Mller New constructive methods in classical ideal theory J. Algebra 100 1 138 178 1986
    • (1986) J. Algebra , vol.100 , Issue.1 , pp. 138-178
    • Mora, F.1    Mller, H.M.2
  • 52
    • 0037331726 scopus 로고    scopus 로고
    • On the Gröbner bases of some symmetric systems and their application to coding theory
    • T. Mora M. Sala On the Gröbner bases of some symmetric systems and their application to coding theory J. Symbol. Computat. 35 2 177 194 2003
    • (2003) J. Symbol. Computat. , vol.35 , Issue.2 , pp. 177-194
    • Mora, T.1    Sala, M.2
  • 53
    • 0037744794 scopus 로고    scopus 로고
    • A new parameterization method for all stabilizing controllers of $n$D systems without coprime factorizability
    • K. Mori A new parameterization method for all stabilizing controllers of $n$D systems without coprime factorizability Proc. IEEE Symp. Circuits Syst. III 678 681 Proc. IEEE Symp. Circuits Syst. Bangkok Thailand 2003
    • (2003) , vol.III , pp. 678-681
    • Mori, K.1
  • 54
    • 0031997017 scopus 로고    scopus 로고
    • Dead beat controllability of polynomial systems: Symbolic computation approaches
    • D. Nesi I. M. Y. Mareels Dead beat controllability of polynomial systems: Symbolic computation approaches IEEE Trans. Autom. Control 43 2 162 175 Feb. 1998
    • (1998) IEEE Trans. Autom. Control , vol.43 , Issue.2 , pp. 162-175
    • Nesi, D.1    Mareels, I.M.Y.2
  • 55
    • 0032635583 scopus 로고    scopus 로고
    • Controllability of structured polynomial systems
    • D. Nesi I. M. Y. Mareels Controllability of structured polynomial systems IEEE Trans. Autom. Control 44 4 761 764 Apr. 1999
    • (1999) IEEE Trans. Autom. Control , vol.44 , Issue.4 , pp. 761-764
    • Nesi, D.1    Mareels, I.M.Y.2
  • 56
    • 85090348707 scopus 로고    scopus 로고
    • Strong Gröbner bases and cyclic codes over a finite-chain ring
    • G. H. Norton A. Slgean Strong Gröbner bases and cyclic codes over a finite-chain ring Electron. Notes Discrete Math. 6 240 250 2001
    • (2001) Electron. Notes Discrete Math. , vol.6 , pp. 240-250
    • Norton, G.H.1    Slgean, A.2
  • 57
    • 0003034426 scopus 로고
    • Multidimensional constant linear systems
    • U. Oberst Multidimensional constant linear systems Acta Applicandae Mathematicae 20 1 175 1990
    • (1990) Acta Applicandae Mathematicae , vol.20 , pp. 1-175
    • Oberst, U.1
  • 58
    • 0035385623 scopus 로고    scopus 로고
    • The constructive solution of linear systems of partial difference and differential equations with constant coefficients
    • U. Oberst F. Pauer The constructive solution of linear systems of partial difference and differential equations with constant coefficients Multidimensional Syst. Signal Process. 12 253 308 2001
    • (2001) Multidimensional Syst. Signal Process. , vol.12 , pp. 253-308
    • Oberst, U.1    Pauer, F.2
  • 59
    • 33750545583 scopus 로고    scopus 로고
    • Canonical state representations and Hilbert functions of multidimensional systems
    • U. Oberst Canonical state representations and Hilbert functions of multidimensional systems Acta Appl Math 94 83 135 2006
    • (2006) Acta Appl Math , vol.94 , pp. 83-135
    • Oberst, U.1
  • 60
    • 0038809434 scopus 로고    scopus 로고
    • Gröbner bases of certain zero-dimensional ideals arising in coding theory
    • H. Ohsugi D. Ikegami T. Kitamura T. Hibi Gröbner bases of certain zero-dimensional ideals arising in coding theory Adv. Appl. Math. 31 2 420 432 2003
    • (2003) Adv. Appl. Math. , vol.31 , Issue.2 , pp. 420-432
    • Ohsugi, H.1    Ikegami, D.2    Kitamura, T.3    Hibi, T.4
  • 61
    • 0010185809 scopus 로고    scopus 로고
    • Gröbner basis solutions of constrained interpolation problems
    • H. O'Keeffe P. Fitzpatrick Gröbner basis solutions of constrained interpolation problems Linear Algebra Appl. 351352 533 551 2002
    • (2002) Linear Algebra Appl. , vol.351352 , pp. 533-551
    • O'Keeffe, H.1    Fitzpatrick, P.2
  • 62
    • 0003921178 scopus 로고    scopus 로고
    • Advanced Engineering Mathematics
    • 6th Thomson FL, Tampa
    • P. V. O'Neil Advanced Engineering Mathematics 6th 2007 Thomson FL, Tampa
    • (2007)
    • O'Neil, P.V.1
  • 63
    • 33745632233 scopus 로고    scopus 로고
    • Algebraic Statistics for Computational Biology
    • Cambridge Univ. Press U.K., Cambridge
    • Algebraic Statistics for Computational Biology 2005 Cambridge Univ. Press U.K., Cambridge
    • (2005)
  • 64
    • 85177108870 scopus 로고
    • Univ. California Berkeley
    • H. Park A computational theory of Laurent polynomial rings and multidimensional FIR systems 1995 Univ. California Berkeley
    • (1995)
    • Park, H.1
  • 65
    • 0000533389 scopus 로고
    • An algorithmic proof of Suslin's stability theorem for polynomial rings
    • H. Park C. Woodburn An algorithmic proof of Suslin's stability theorem for polynomial rings J. Algebra 178 277 298 1995
    • (1995) J. Algebra , vol.178 , pp. 277-298
    • Park, H.1    Woodburn, C.2
  • 67
    • 0035385773 scopus 로고    scopus 로고
    • Parametrized family of 2-D non-factorable FIR lossless systems and Gröbner bases
    • H. Park Parametrized family of 2-D non-factorable FIR lossless systems and Gröbner bases Multidimensional Syst. Signal Process. 12 345 364 2001
    • (2001) Multidimensional Syst. Signal Process. , vol.12 , pp. 345-364
    • Park, H.1
  • 68
    • 0036601293 scopus 로고    scopus 로고
    • Optimal design of synthesis filters in multidimensional perfect reconstruction FIR filter banks using Gröbner bases
    • H. Park Optimal design of synthesis filters in multidimensional perfect reconstruction FIR filter banks using Gröbner bases IEEE Trans. Circuits Syst. I, Fundam. Theory Appl. 49 5 843 851 May 2002
    • (2002) IEEE Trans. Circuits Syst. I, Fundam. Theory Appl. , vol.49 , Issue.5 , pp. 843-851
    • Park, H.1
  • 69
    • 0038758936 scopus 로고    scopus 로고
    • Prime factorization of $n$-D polynomial matrices
    • H. Park Prime factorization of $n$-D polynomial matrices Proc. IEEE ISCAS III 666 669 Proc. IEEE ISCAS Bangkok Thailand 2003-May
    • (2003) , vol.III , pp. 666-669
    • Park, H.1
  • 70
    • 1942477555 scopus 로고    scopus 로고
    • Symbolic computation and signal processing
    • H. Park Symbolic computation and signal processing J. Symbol. Computat. 37 2 209 226 2004
    • (2004) J. Symbol. Computat. , vol.37 , Issue.2 , pp. 209-226
    • Park, H.1
  • 71
    • 42949166773 scopus 로고    scopus 로고
    • Optimal construction of compactly-supported multidimensional wavelets
    • H. Park Optimal construction of compactly-supported multidimensional wavelets Proc. IEEE ISCAS 2417 2420 Proc. IEEE ISCAS Kobe Japan 2005-May
    • (2005) , pp. 2417-2420
    • Park, H.1
  • 72
    • 33645416609 scopus 로고    scopus 로고
    • Positive Polynomials in Control
    • Exploiting algebraic structure in sum of squares programs Springer-Verlag Germany, Berlin
    • P. Parrilo Positive Polynomials in Control 181 194 2005 Springer-Verlag Germany, Berlin Exploiting algebraic structure in sum of squares programs
    • (2005) , pp. 181-194
    • Parrilo, P.1
  • 73
    • 42949152392 scopus 로고    scopus 로고
    • Gröbner bases and constructive multidimensional behavioural theory
    • H. Pillai J. Wood E. Rogers Gröbner bases and constructive multidimensional behavioural theory Proc. 2nd Int. Workshop Multidimensional (D) Syst. 83 89 Proc. 2nd Int. Workshop Multidimensional (D) Syst. Czocha Castle Poland 2000-Jun.
    • (2000) , pp. 83-89
    • Pillai, H.1    Wood, J.2    Rogers, E.3
  • 74
    • 0037518862 scopus 로고    scopus 로고
    • Solving Bose conjecture on linear multidimensional systems
    • J. F. Pommaret Solving Bose conjecture on linear multidimensional systems Proc. Eur. Control Conf. 1853 1855 Proc. Eur. Control Conf. 2001
    • (2001) , pp. 1853-1855
    • Pommaret, J.F.1
  • 75
    • 33746862889 scopus 로고    scopus 로고
    • A lattice approach to analysis and synthesis problems
    • A. Quadrat A lattice approach to analysis and synthesis problems Math. Control, Signals Syst. 18 2 147 186 May 2006
    • (2006) Math. Control, Signals Syst. , vol.18 , Issue.2 , pp. 147-186
    • Quadrat, A.1
  • 76
    • 0000074293 scopus 로고
    • Projective modules over polynomial rings
    • D. Quillen Projective modules over polynomial rings Invent. Math 36 167 171 1976
    • (1976) Invent. Math , vol.36 , pp. 167-171
    • Quillen, D.1
  • 77
    • 22544438171 scopus 로고    scopus 로고
    • Symbolic Computation for Moments and Filter Coefficients of Scaling Functions
    • G. Regensburger O. Scherzer Symbolic Computation for Moments and Filter Coefficients of Scaling Functions Annals Combinator. 9 223 243 2005
    • (2005) Annals Combinator. , vol.9 , pp. 223-243
    • Regensburger, G.1    Scherzer, O.2
  • 79
    • 1542678669 scopus 로고    scopus 로고
    • The geometry of algebraic systems and their exact solving using Gröbner bases
    • E. Roanes-Lozano E. Roanes-Macas L. M. Laita The geometry of algebraic systems and their exact solving using Gröbner bases Computi. Sci. Eng. 6 2 76 79 Mar.Apr. 2004
    • (2004) Computi. Sci. Eng. , vol.6 , Issue.2 , pp. 76-79
    • Roanes-Lozano, E.1    Roanes-Macas, E.2    Laita, L.M.3
  • 81
    • 27544488516 scopus 로고    scopus 로고
    • Certified solving of the forward kinematics problem with an exact algebraic method for the general parallel manipulator
    • L. Rolland Certified solving of the forward kinematics problem with an exact algebraic method for the general parallel manipulator J. Adv. Robot. 19 9 995 1025 Oct. 2005
    • (2005) J. Adv. Robot. , vol.19 , Issue.9 , pp. 995-1025
    • Rolland, L.1
  • 82
    • 33750174384 scopus 로고    scopus 로고
    • Synthesis on forward kinematics problem algebraic modeling for the planar parallel manipulator: Displacement-based equation systems
    • L. Rolland Synthesis on forward kinematics problem algebraic modeling for the planar parallel manipulator: Displacement-based equation systems J. Adv. Robot. 20 9 1035 1065 Sep. 2006
    • (2006) J. Adv. Robot. , vol.20 , Issue.9 , pp. 1035-1065
    • Rolland, L.1
  • 83
    • 0025383036 scopus 로고
    • Extension of the Berlekamp-Massey algorithm to $N$ dimensions
    • S. Sakata Extension of the Berlekamp-Massey algorithm to $N$ dimensions Inf. Computat. 84 2 207 239 1990
    • (1990) Inf. Computat. , vol.84 , Issue.2 , pp. 207-239
    • Sakata, S.1
  • 84
    • 84927088892 scopus 로고
    • Algebraic-geometric codes and multidimensional cyclic codes: A unified theory and algorithms for decoding using Grobner bases
    • K. Saints C. Heegard Algebraic-geometric codes and multidimensional cyclic codes: A unified theory and algorithms for decoding using Grobner bases IEEE Trans. Inf. Theory 41 6 1733 1751 Nov. 1995
    • (1995) IEEE Trans. Inf. Theory , vol.41 , Issue.6 , pp. 1733-1751
    • Saints, K.1    Heegard, C.2
  • 87
    • 0028539247 scopus 로고
    • Feedback stabilization over commutative rings: The matrix case
    • V. R. Sule Feedback stabilization over commutative rings: The matrix case SIAM J. Control Optim. 32 1675 1695 1994
    • (1994) SIAM J. Control Optim. , vol.32 , pp. 1675-1695
    • Sule, V.R.1
  • 88
    • 85177120778 scopus 로고    scopus 로고
    • Germany
    • G. M. Greuel G. Pfister H. Schonemann Singular Reference Manual 12 Germany Centre of Algebra http://www.mathematik.uni-kl.de/~zca/Singular
    • , Issue.12
    • Greuel, G.M.1    Pfister, G.2    Schonemann, H.3
  • 89
    • 3242784209 scopus 로고    scopus 로고
    • A generalized Serre problem
    • V. Srinivas A generalized Serre problem J. Algebra 278 2 621 627 Aug. 2004
    • (2004) J. Algebra , vol.278 , Issue.2 , pp. 621-627
    • Srinivas, V.1
  • 90
    • 0001631923 scopus 로고
    • Projective modules over a polynomial ring are free
    • A. A. Suslin Projective modules over a polynomial ring are free Sov. Math Dokl. 17 1160 1164 1976
    • (1976) Sov. Math Dokl. , vol.17 , pp. 1160-1164
    • Suslin, A.A.1
  • 91
    • 0001277020 scopus 로고
    • On B. Buchberger's method for solving systems of algebraic equations
    • W. Trinks On B. Buchberger's method for solving systems of algebraic equations J. Number Theory 10 475 488 1978
    • (1978) J. Number Theory , vol.10 , pp. 475-488
    • Trinks, W.1
  • 92
    • 0033881842 scopus 로고    scopus 로고
    • A contribution to the analysis of flexible link systems
    • F. Ubertini A contribution to the analysis of flexible link systems Int. J. Solids Structures 37 7 969 990 2000
    • (2000) Int. J. Solids Structures , vol.37 , Issue.7 , pp. 969-990
    • Ubertini, F.1
  • 93
    • 33947698298 scopus 로고    scopus 로고
    • Signal reconstruction from multiple unregistered sets of samples using Groebner bases
    • P. Vandewalle L. Sbaiz M. Vetterli Signal reconstruction from multiple unregistered sets of samples using Groebner bases Proc. ICASSP III 604 607 Proc. ICASSP Tuluse France 2006
    • (2006) , vol.III , pp. 604-607
    • Vandewalle, P.1    Sbaiz, L.2    Vetterli, M.3
  • 94
    • 0004257127 scopus 로고    scopus 로고
    • Modern Computer Algebra
    • Cambridge Univ. Press U.K., Cambridge
    • J. von zur Gathen J. Gerhard Modern Computer Algebra 2003 Cambridge Univ. Press U.K., Cambridge
    • (2003)
    • von zur Gathen, J.1    Gerhard, J.2
  • 95
    • 85177138089 scopus 로고
    • Johannes Kepler Univ. Austria, Linz
    • B. Wall Computation of syzygies, solution of linear systems over a multivariate polynomial ring 1988 Johannes Kepler Univ. Austria, Linz
    • (1988)
    • Wall, B.1
  • 96
    • 0035307308 scopus 로고    scopus 로고
    • On the computation of switching surfaces in optimal control: A Gröbner basis approach
    • U. Walther T. T. Georgiou A. Tannenbaum On the computation of switching surfaces in optimal control: A Gröbner basis approach IEEE Trans. Autom. Control 46 4 534 540 Apr. 2001
    • (2001) IEEE Trans. Autom. Control , vol.46 , Issue.4 , pp. 534-540
    • Walther, U.1    Georgiou, T.T.2    Tannenbaum, A.3
  • 97
  • 98
    • 27244451010 scopus 로고    scopus 로고
    • On multivariate polynomial matrix factorization problems
    • M. Wang C. P. Kwong On multivariate polynomial matrix factorization problems Math. Control Signals Syst. 17 4 297 311 2005
    • (2005) Math. Control Signals Syst. , vol.17 , Issue.4 , pp. 297-311
    • Wang, M.1    Kwong, C.P.2
  • 99
    • 85177138084 scopus 로고    scopus 로고
    • Optimal minimax control solution using rate feedback
    • C. Charoenlarpnopparut Optimal minimax control solution using rate feedback Proc. ICICS 6 9 Proc. ICICS Bangkok Thailand 2005-Dec.
    • (2005) , pp. 6-9
    • Charoenlarpnopparut, C.1
  • 100
    • 0003611980 scopus 로고
    • An Introduction to Grbner Bases
    • Amer. Math. Soc. RI, Providence
    • W. W. Adams P. Loustaunau An Introduction to Grbner Bases 3 1994 Amer. Math. Soc. RI, Providence
    • (1994) , vol.3
    • Adams, W.W.1    Loustaunau, P.2
  • 101
    • 0004199603 scopus 로고    scopus 로고
    • Numerical Methods for Scientists and Engineers
    • Birkhauser New York
    • H. M. Antia Numerical Methods for Scientists and Engineers 2002 Birkhauser New York
    • (2002)
    • Antia, H.M.1
  • 102
    • 0032209984 scopus 로고    scopus 로고
    • Multidimensional filter banks and wavelets—A system theoretic perspective
    • S. Basu Multidimensional filter banks and wavelets—A system theoretic perspective J. Franklin Inst. 335B 8 1367 1409 1998
    • (1998) J. Franklin Inst. , vol.335B , Issue.8 , pp. 1367-1409
    • Basu, S.1
  • 103
    • 0036600851 scopus 로고    scopus 로고
    • Multidimensional causal, stable, perfect reconstruction filter banks
    • S. Basu Multidimensional causal, stable, perfect reconstruction filter banks IEEE Trans. Circuits Syst. I, Fundam. Theory Appl. 49 6 832 842 Jun. 2002
    • (2002) IEEE Trans. Circuits Syst. I, Fundam. Theory Appl. , vol.49 , Issue.6 , pp. 832-842
    • Basu, S.1
  • 105
    • 79251599436 scopus 로고
    • Grbner Bases
    • Springer-Verlag Germany, Berlin
    • T. Becker V. Weisfenning Grbner Bases 1993 Springer-Verlag Germany, Berlin
    • (1993)
    • Becker, T.1    Weisfenning, V.2
  • 106
    • 0022958982 scopus 로고
    • Causal 2-D compensators: Stabilization algorithms for multivariable 2-D systems
    • M. Bisiacco E. Fornasini G. Marchesini Causal 2-D compensators: Stabilization algorithms for multivariable 2-D systems Proc. 25th Conf. Decision Control 2171 2174 Proc. 25th Conf. Decision Control 1986
    • (1986) , pp. 2171-2174
    • Bisiacco, M.1    Fornasini, E.2    Marchesini, G.3
  • 107
    • 18744414812 scopus 로고    scopus 로고
    • Numerical Analysis in Engineering
    • Alpha Sci. U.K., Pangbourne
    • R. B. Bhat S. Chakraverty Numerical Analysis in Engineering 2004 Alpha Sci. U.K., Pangbourne
    • (2004)
    • Bhat, R.B.1    Chakraverty, S.2
  • 108
    • 0003754331 scopus 로고
    • Applied Multidimensional Systems Theory
    • Van Nostrand Reinhold New York
    • N. K. Bose Applied Multidimensional Systems Theory 1982 Van Nostrand Reinhold New York
    • (1982)
    • Bose, N.K.1
  • 109
    • 0347807014 scopus 로고    scopus 로고
    • Multivariate matrix factorization: New results
    • N. K. Bose C. Charoenlarpnopparut Multivariate matrix factorization: New results Proc. MTNS 97 100 Proc. MTNS Padova Italy 1998-Jul.
    • (1998) , pp. 97-100
    • Bose, N.K.1    Charoenlarpnopparut, C.2
  • 111
    • 0003913372 scopus 로고    scopus 로고
    • Multidimensional Systems Theory and Applications
    • Kluwer The Netherlands, Dordrecht
    • N. K. Bose B. Buchberger J. P. Guiver Multidimensional Systems Theory and Applications 2003 Kluwer The Netherlands, Dordrecht
    • (2003)
    • Bose, N.K.1    Buchberger, B.2    Guiver, J.P.3
  • 112
    • 85177140118 scopus 로고    scopus 로고
    • Two decades (1985–2005) of Gröbner bases in multidimensional systems
    • N. K. Bose Two decades (1985–2005) of Gröbner bases in multidimensional systems Proc. Workshop on GB in Contr. Theory Signal Process. Proc. Workshop on GB in Contr. Theory Signal Process. Linz Austria 2006-May
    • (2006)
    • Bose, N.K.1
  • 113
    • 0004055894 scopus 로고    scopus 로고
    • Convex Optimization
    • Cambridge Univ. Press U.K., Cambridge
    • S. Boyd L. Vandenberghe Convex Optimization 2004 Cambridge Univ. Press U.K., Cambridge
    • (2004)
    • Boyd, S.1    Vandenberghe, L.2
  • 114
    • 85177136392 scopus 로고
    • Univ. of Innsbruck Austria, Innsbruck
    • B. Buchberger An algorithm for finding the basis elements of the residue class ring modulo a zero-dimensional polynomial ideal (German) 1965 Univ. of Innsbruck Austria, Innsbruck
    • (1965)
    • Buchberger, B.1
  • 115
    • 33646925446 scopus 로고
    • An algorithmic criterion for the solvability of algebraic systems of equations (German)
    • B. Buchberger An algorithmic criterion for the solvability of algebraic systems of equations (German) Aequationes Mathematicae 4 3 374 383 1970
    • (1970) Aequationes Mathematicae , vol.4 , Issue.3 , pp. 374-383
    • Buchberger, B.1
  • 116
    • 0002803133 scopus 로고
    • Multidimensional Systems Theory: Progress, Directions and Open Problems
    • Grbner bases: An algorithmic method in polynomial ideal theory Reidel The Netherlands, Dordrecht
    • B. Buchberger Multidimensional Systems Theory: Progress, Directions and Open Problems 184 232 1985 Reidel The Netherlands, Dordrecht Grbner bases: An algorithmic method in polynomial ideal theory
    • (1985) , pp. 184-232
    • Buchberger, B.1
  • 117
    • 0012744412 scopus 로고    scopus 로고
    • Grbbner Bases and Applications
    • Cambridge Univ. Press U.K., Cambridge
    • Grbbner Bases and Applications London Mathematical Society Series 457 1998 Cambridge Univ. Press U.K., Cambridge
    • (1998)
  • 119
    • 0036495441 scopus 로고    scopus 로고
    • Hamming metric decoding of alternant codes over Galois rings
    • E. Byrne P. Fitzpatrick Hamming metric decoding of alternant codes over Galois rings IEEE Trans. Inf. Theory 48 3 683 694 Mar. 2002
    • (2002) IEEE Trans. Inf. Theory , vol.48 , Issue.3 , pp. 683-694
    • Byrne, E.1    Fitzpatrick, P.2
  • 120
    • 0036539221 scopus 로고    scopus 로고
    • Decoding a class of Lee metric codes over a Galois ring
    • E. Byrne Decoding a class of Lee metric codes over a Galois ring IEEE Trans. Inf. Theory 48 4 966 975 Apr. 2002
    • (2002) IEEE Trans. Inf. Theory , vol.48 , Issue.4 , pp. 966-975
    • Byrne, E.1
  • 121
    • 42949102090 scopus 로고    scopus 로고
    • Testability evaluation for analog linear circuits via transfer function analysis
    • B. Cannas A. Fanni A. Montisci Testability evaluation for analog linear circuits via transfer function analysis Proc. ISCAS 992 995 Proc. ISCAS Kobe Japan 2005-May
    • (2005) , pp. 992-995
    • Cannas, B.1    Fanni, A.2    Montisci, A.3
  • 122
    • 34547533045 scopus 로고    scopus 로고
    • Exact inversion of MIMO nonlinear polynomial mixtures
    • HI
    • M. Castella Exact inversion of MIMO nonlinear polynomial mixtures Proc. ICASSP III 1429 1432 Proc. ICASSP Honolulu HI 2007
    • (2007) , vol.III , pp. 1429-1432
    • Castella, M.1
  • 125
    • 0037744792 scopus 로고    scopus 로고
    • Multidimensional convolutional code: Progresses and bottlenecks
    • C. Charoenlarpnopparut S. Tantaratana Multidimensional convolutional code: Progresses and bottlenecks Proc. ISCAS III 686 689 Proc. ISCAS Bangkok Thailand 2003-May
    • (2003) , vol.III , pp. 686-689
    • Charoenlarpnopparut, C.1    Tantaratana, S.2
  • 126
    • 11144281886 scopus 로고    scopus 로고
    • Algebraic approach to reduce the number of delay elements in the realization of multidimensional convolutional code
    • C. Charoenlarpnopparut S. Tantaratana Algebraic approach to reduce the number of delay elements in the realization of multidimensional convolutional code Proc. MWSCAS II-529 II-532 Proc. MWSCAS Hiroshima Japan 2004-Jul.
    • (2004) , pp. II-529-II-532
    • Charoenlarpnopparut, C.1    Tantaratana, S.2
  • 127
    • 34250795617 scopus 로고    scopus 로고
    • On factor prime factorizations for $n$ -D polynomial matries
    • M. Wang On factor prime factorizations for $n$ -D polynomial matries IEEE Trans. Circuits Syst. I, Reg. Papers 54 6 1398 1405 Jun. 2007
    • (2007) IEEE Trans. Circuits Syst. I, Reg. Papers , vol.54 , Issue.6 , pp. 1398-1405
    • Wang, M.1
  • 128
    • 85177112582 scopus 로고    scopus 로고
    • Notre Dame Univ. IN, South Bend
    • P. A. Weiner Multidimensional convolutional codes 1998 Notre Dame Univ. IN, South Bend
    • (1998)
    • Weiner, P.A.1
  • 129
    • 0003925015 scopus 로고    scopus 로고
    • Polynomial Algorithms in Computer Algebra
    • Springer-Verlag New York
    • F. Winkler Polynomial Algorithms in Computer Algebra 1996 Springer-Verlag New York
    • (1996)
    • Winkler, F.1
  • 131
    • 0343297703 scopus 로고    scopus 로고
    • Minimum lag descriptions and minimal Gröbner bases
    • J. Wood E. Rogers D. Owens Minimum lag descriptions and minimal Gröbner bases Syst. Control Lett. 34 5 289 293 1998
    • (1998) Syst. Control Lett. , vol.34 , Issue.5 , pp. 289-293
    • Wood, J.1    Rogers, E.2    Owens, D.3
  • 132
  • 133
    • 34548836291 scopus 로고    scopus 로고
    • Multi-valued model checking via Gröbner basis approach
    • J. Wu L. Zhao Multi-valued model checking via Gröbner basis approach Proc. IEEE/IFIP Theoretical Aspects of Software Engineering 35 44 Proc. IEEE/IFIP Theoretical Aspects of Software Engineering 2007-Jun.-68
    • (2007) , pp. 35-44
    • Wu, J.1    Zhao, L.2
  • 134
    • 2342422634 scopus 로고    scopus 로고
    • Feedback stabilization for a class of MIMO $n$D systems by Gröbner basis approach
    • L. Xu J. Q. Ying O. Saito Feedback stabilization for a class of MIMO $n$D systems by Gröbner basis approach Abstract 1st Int. Workshop Multidimensional Syst. 88 90 Abstract 1st Int. Workshop Multidimensional Syst. Lagow Poland 1998-Jul.
    • (1998) , pp. 88-90
    • Xu, L.1    Ying, J.Q.2    Saito, O.3
  • 135
    • 0028259472 scopus 로고
    • Output feedback stabilizability and stabilization algorithms for 2-D systems
    • L. Xu O. Saito K. Abe Output feedback stabilizability and stabilization algorithms for 2-D systems Multidimensional Syst. Signal Process. 5 41 60 1994
    • (1994) Multidimensional Syst. Signal Process. , vol.5 , pp. 41-60
    • Xu, L.1    Saito, O.2    Abe, K.3
  • 136
    • 85177117861 scopus 로고    scopus 로고
    • Minimal realization for a class of $n$D filters by Grobner basis approach
    • L. Xu Z. Lin Y. Anazawa Minimal realization for a class of $n$D filters by Grobner basis approach Proc. Asian Symp. Comput. Math. 185 188 Proc. Asian Symp. Comput. Math. Seoul Korea 2005-Dec.
    • (2005) , pp. 185-188
    • Xu, L.1    Lin, Z.2    Anazawa, Y.3
  • 137
    • 85177131087 scopus 로고    scopus 로고
    • Applications of Gröbner bases in synthesis of multidimensional control systems
    • L. Xu Applications of Gröbner bases in synthesis of multidimensional control systems Proc. Workshop on GB in Contr. Theory Signal Process. Proc. Workshop on GB in Contr. Theory Signal Process. Linz Austria 2006-May
    • (2006)
    • Xu, L.1
  • 138
    • 42949089052 scopus 로고    scopus 로고
    • Algebraic representation of error bounds for describing function using Groebner base
    • M. Yagi T. Hisakado K. Okumura Algebraic representation of error bounds for describing function using Groebner base Proc. ISCAS 2831 2834 Proc. ISCAS Kobe Japan 2005-May
    • (2005) , pp. 2831-2834
    • Yagi, M.1    Hisakado, T.2    Okumura, K.3
  • 139
    • 0001496305 scopus 로고    scopus 로고
    • A computational method for determining strong stabilizability of $n$-D systems
    • J. Q. Ying L. Xu Z. Lin A computational method for determining strong stabilizability of $n$-D systems J. Symbol. Computat. 27 479 499 1999
    • (1999) J. Symbol. Computat. , vol.27 , pp. 479-499
    • Ying, J.Q.1    Xu, L.2    Lin, Z.3
  • 140
    • 0018434354 scopus 로고
    • Notes on $n$-dimensional system theory
    • D. C. Youla G. Gnavi Notes on $n$-dimensional system theory IEEE Trans. Circuits Syst. CAS-26 2 105 111 Feb. 1979
    • (1979) IEEE Trans. Circuits Syst. , vol.CAS-26 , Issue.2 , pp. 105-111
    • Youla, D.C.1    Gnavi, G.2
  • 141
    • 0021442133 scopus 로고
    • The Quillen-Suslin theorem and the structure of $n$-dimensional elementary polynomial matrices
    • D. C. Youla P. F. Pickel The Quillen-Suslin theorem and the structure of $n$-dimensional elementary polynomial matrices IEEE Trans. Circuits Syst. CAS-31 4 513 518 Apr. 1984
    • (1984) IEEE Trans. Circuits Syst. , vol.CAS-31 , Issue.4 , pp. 513-518
    • Youla, D.C.1    Pickel, P.F.2
  • 142
    • 85177131356 scopus 로고
    • MIT Cambridge
    • G. Zacharias Generalized Grbner basis in commutative polynomial rings 1978 MIT Cambridge
    • (1978)
    • Zacharias, G.1
  • 143
    • 0030284047 scopus 로고    scopus 로고
    • Primeness of multivariate polynomial matrices
    • E. Zerz Primeness of multivariate polynomial matrices Syst. Control Lett. 29 139 145 1996
    • (1996) Syst. Control Lett. , vol.29 , pp. 139-145
    • Zerz, E.1
  • 144
    • 0005647486 scopus 로고    scopus 로고
    • Topics in Multidimensional Linear Systems Theory
    • Springer-Verlag London Ltd. U.K., London
    • E. Zerz Topics in Multidimensional Linear Systems Theory 256 2000 Springer-Verlag London Ltd. U.K., London
    • (2000) , vol.256
    • Zerz, E.1
  • 145
    • 0035385820 scopus 로고    scopus 로고
    • Extension modules in behavioral linear systems theory
    • E. Zerz Extension modules in behavioral linear systems theory Multidimensional Syst. Signal Process. 12 309 327 2001
    • (2001) Multidimensional Syst. Signal Process. , vol.12 , pp. 309-327
    • Zerz, E.1
  • 146
    • 0036338047 scopus 로고    scopus 로고
    • A constructive solution to interconnection and decomposition problems with multidimensional behaviors
    • E. Zerz V. Lomadze A constructive solution to interconnection and decomposition problems with multidimensional behaviors SIAM J. Control Optim. 40 4 1072 1086 2001
    • (2001) SIAM J. Control Optim. , vol.40 , Issue.4 , pp. 1072-1086
    • Zerz, E.1    Lomadze, V.2
  • 147
    • 33847672255 scopus 로고    scopus 로고
    • Two-dimensional antisymmetric linear phase filter bank construction using symmetric completion
    • L. Zhang A. Makur Two-dimensional antisymmetric linear phase filter bank construction using symmetric completion IEEE Trans. Circuits Syst. II, Exp. Briefs 54 1 57 60 Jan. 2007
    • (2007) IEEE Trans. Circuits Syst. II, Exp. Briefs , vol.54 , Issue.1 , pp. 57-60
    • Zhang, L.1    Makur, A.2
  • 148
    • 33749174108 scopus 로고    scopus 로고
    • Multidimensional multichannel FIR deconvolution using Gröbner bases
    • J. Zhou M. N. Do Multidimensional multichannel FIR deconvolution using Gröbner bases IEEE Trans. Image Process. 15 10 2998 3007 Oct. 2006
    • (2006) IEEE Trans. Image Process. , vol.15 , Issue.10 , pp. 2998-3007
    • Zhou, J.1    Do, M.N.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.