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International Journal of Control Volume 58, 1993 - Issue 1
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Original Articles

Computation of the GCD of polynomials using gaussian transformations and shifting

MARILENA MITROULI Control Engineering Centre, Department of Electrical, Electronic and Information Engineering, City University, Northampton Square, London, EC1V OHB, U.K.
&
NICOS KARCANIAS Control Engineering Centre, Department of Electrical, Electronic and Information Engineering, City University, Northampton Square, London, EC1V OHB, U.K.
Pages 211-228 | Received 14 Jun 1991, Published online: 15 Mar 2007

Citations (31)

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Nicos Karcanias, Olga Limantseva & George Halikias. (2022) The feedback invariant measures of distance to uncontrollability and unobservability. International Journal of Control 95:5, pages 1218-1227.
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N. Karcanias, M. Mitrouli & D. Triantafyllou. (2006) Matrix pencil methodologies for computing the greatest common divisor of polynomials: hybrid algorithms and their performance. International Journal of Control 79:11, pages 1447-1461.
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Articles from other publishers (29)

Olga Limantseva, George Halikias & Nicos Karcanias. (2020) Nearest common root of a set of polynomials: A structured singular value approach. Linear Algebra and its Applications 584, pages 233-256.
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O. Limantseva, G. Halikias & N. Karcanias. (2020) An alternating projection algorithm for the “approximate” GCD calculation. IFAC-PapersOnLine 53:2, pages 5837-5842.
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Dimitrios Christou, Marilena Mitrouli & Dimitrios Triantafyllou. (2017) Structured Matrix Methods Computing the Greatest Common Divisor of Polynomials. Special Matrices 5:1, pages 202-224.
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Dimitrios Christou, Nicos Karcanias & Marilena Mitrouli. (2016) Approximate least common multiple of several polynomials using the ERES division algorithm. Linear Algebra and its Applications 511, pages 141-175.
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Thomas Berger, George Halikias & Nicos Karcanias. (2013) Effects of dynamic and non‐dynamic element changes in RC and RL networks. International Journal of Circuit Theory and Applications 43:1, pages 36-59.
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Nicos Karcanias, John Leventides & Maria Livada. (2014) Multi-parameter structural transformations of passive electrical networks and natural frequency assignment. Multi-parameter structural transformations of passive electrical networks and natural frequency assignment.
D. Christou, N. Karcanias & M. Mitrouli. (2014) Matrix representation of the shifting operation and numerical properties of the ERES method for computing the greatest common divisor of sets of many polynomials. Journal of Computational and Applied Mathematics 260, pages 54-67.
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Nicos Karcanias & George Halikias. (2013) Approximate zero polynomials of polynomial matrices and linear systems. Linear Algebra and its Applications 439:4, pages 1091-1103.
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Mohsen Zamani, Brian D.O. Anderson, Uwe Helmke & Weitian Chen. (2013) On the zeros of blocked time-invariant systems. Systems & Control Letters 62:7, pages 597-603.
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Nicos Karcanias. (2013) Properties and classification of Generalized Resultants and polynomial combinants. Properties and classification of Generalized Resultants and polynomial combinants.
Stavros Fatouros, Nicos Karcanias, Dimitrios Christou & Pericles Papadopoulos. (2013) Approximate Greatest Common Divisor of Many Polynomials and Pseudo-Spectrum. IFAC Proceedings Volumes 46:2, pages 623-628.
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Masaru Sanuki. (2012) Challenge to fast and stable computation of approximate univariate GCD, based on displacement structures. Challenge to fast and stable computation of approximate univariate GCD, based on displacement structures.
Kosaku Nagasaka. (2011) Approximate polynomial GCD over integers. Journal of Symbolic Computation 46:12, pages 1306-1317.
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Nicos Karcanias. (2011) The Minimal Design Problem on Dynamic Polynomial Combinants. IFAC Proceedings Volumes 44:1, pages 3333-3340.
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Dimitrios Christou, Nicos Karcanias, Marilena Mitrouli & Dimitrios Triantafyllou. 2011. Numerical Linear Algebra in Signals, Systems and Control. Numerical Linear Algebra in Signals, Systems and Control 123 144 .
D. Christou, N. Karcanias & M. Mitrouli. (2010) The ERES method for computing the approximate GCD of several polynomials. Applied Numerical Mathematics 60:1-2, pages 94-114.
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Christos Kravvaritis & Marilena Mitrouli. (2008) Compound matrices: properties, numerical issues and analytical computations. Numerical Algorithms 50:2, pages 155-177.
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Panagiotis Tzekis, Nicholas Karampetakis & Haralambos Terzidis. (2007) On the Computation of the GCD of 2-D Polynomials. International Journal of Applied Mathematics and Computer Science 17:4, pages 463-470.
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N. Karcanias, S. Fatouros, M. Mitrouli & G.H. Halikias. (2006) Approximate greatest common divisor of many polynomials, generalised resultants, and strength of approximation. Computers & Mathematics with Applications 51:12, pages 1817-1830.
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Nicos Karcanias, Marilena Mitrouli & Dimitrios Triantafyllou. 2006. Computational Science – ICCS 2006. Computational Science – ICCS 2006 399 406 .
Dimitrios Christou & Marilena Mitrouli. (2005) Estimation of the Greatest Common Divisor of many polynomials using hybrid computations performed by the ERES method. Applied Numerical Analysis & Computational Mathematics 2:3, pages 293-305.
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Nicos Karcanias & Marilena Mitrouli. (2004) System theoretic based characterisation and computation of the least common multiple of a set of polynomials. Linear Algebra and its Applications 381, pages 1-23.
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N. Karcanias, S. Fatouros, M. Mitrouli & G. Halikias. (2003) Approximate greatest common divisor of many polynomials and generalised resultants. Approximate greatest common divisor of many polynomials and generalised resultants.
N Karcanias & M Mitrouli. (2003) Normal factorisation of polynomials and computational issues. Computers & Mathematics with Applications 45:1-3, pages 229-245.
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N. Karcanias, M. Mitrouli & S. Fatouros. (2001) Computation of Normal Factorisation of Polynomials Using Resultant Sets. IFAC Proceedings Volumes 34:13, pages 107-112.
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N. Karcanias & K.G. Vafiadis. (2001) Effective Transfer Function Models by Input, Output Variables Reduction. IFAC Proceedings Volumes 34:13, pages 59-64.
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M. Mitrouli, N. Karcanias & C. Koukouvinos. (1996) Numerical performance of the matrix pencil algorithm computing the greatest common divisor of polynomials and comparison with other matrix-based methodologies. Journal of Computational and Applied Mathematics 76:1-2, pages 89-112.
Crossref
M. Mitrouli & G. Kalogeropoulos. (1994) A compound matrix algorithm for the computation of the Smith form of a polynomial matrix. Numerical Algorithms 7:2, pages 145-159.
Crossref
N. Karcanias & M. Mitrouli. (1994) A matrix pencil based numerical method for the computation of the GCD of polynomials. IEEE Transactions on Automatic Control 39:5, pages 977-981.
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