The Experts below are selected from a list of 3615 Experts worldwide ranked by ideXlab platform
Lihong Zhi - One of the best experts on this subject based on the ideXlab platform.
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fast low rank approximation of a sylvester matrix by structured total least norm
Jouranl of Japan Society for Symboric and Algebraic Computation, 2005Co-Authors: Zhengfeng Yang, Lihong ZhiAbstract:The problem of approximating the Greatest Common Divisor(GCD) for polynomials with inexact coefficients can be formulated as a low rank approximation problem with a Sylvester matrix. In this paper, we present an algorithm based on fast Structured Total Least Norm(STLN) for constructing a Sylvester matrix of given lower rank and obtaining the nearest perturbed polynomials with exact GCD of given degree.
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qr factoring to compute the gcd of univariate approximate polynomials
IEEE Transactions on Signal Processing, 2004Co-Authors: Robert M Corless, Stephen M Watt, Lihong ZhiAbstract:We present a stable and practical algorithm that uses QR factors of the Sylvester matrix to compute the Greatest Common Divisor (GCD) of univariate approximate polynomials over /spl Ropf/[x] or /spl Copf/[x]. An approximate polynomial is a polynomial with coefficients that are not known with certainty. The algorithm of this paper improves over previously published algorithms by handling the case when Common roots are near to or outside the unit circle, by splitting and reversal if necessary. The algorithm has been tested on thousands of examples, including pairs of polynomials of up to degree 1000, and is now distributed as the program QRGCD in the SNAP package of Maple 9.
Robert M Corless - One of the best experts on this subject based on the ideXlab platform.
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approximate gcd in bernstein basis
ACM Communications in Computer Algebra, 2019Co-Authors: Robert M Corless, Leili Rafiee SevyeriAbstract:In general, finding the Greatest Common Divisor (GCD) of two exactly-known univariate polynomials is a well understood problem. However, it is also known that the GCD problem for noisy polynomials (polynomials with errors in their coefficients) is ill-posed. More precisely, a small error in coefficients of polynomials P and Q with a non-trivial GCD generically leads to a constant GCD. We note that the choice of basis makes no difference to this difficulty.
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qr factoring to compute the gcd of univariate approximate polynomials
IEEE Transactions on Signal Processing, 2004Co-Authors: Robert M Corless, Stephen M Watt, Lihong ZhiAbstract:We present a stable and practical algorithm that uses QR factors of the Sylvester matrix to compute the Greatest Common Divisor (GCD) of univariate approximate polynomials over /spl Ropf/[x] or /spl Copf/[x]. An approximate polynomial is a polynomial with coefficients that are not known with certainty. The algorithm of this paper improves over previously published algorithms by handling the case when Common roots are near to or outside the unit circle, by splitting and reversal if necessary. The algorithm has been tested on thousands of examples, including pairs of polynomials of up to degree 1000, and is now distributed as the program QRGCD in the SNAP package of Maple 9.
Marilena Mitrouli - One of the best experts on this subject based on the ideXlab platform.
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A matrix pencil based numerical method for the computation of the GCD of polynomials
[1992] Proceedings of the 31st IEEE Conference on Decision and Control, 1992Co-Authors: Nicos Karcanias, Marilena MitrouliAbstract:The authors present a novel numerical method for the computation of the Greatest Common Divisor (GCD) of an m-set of polynomials of R(s), P/sub m,d/, of maximal degree d. It is based on a procedure that characterizes the GCD of P/sub m,d/ as the output decoupling zero polynomial of a linear system that may be associated with P/sub m,d/. The computation of the GCD is thus reduced to finding the finite zeros of a certain pencil. An error analysis proving the stability of the described procedures is given. Three numerical results that demonstrate the effectiveness of the method are presented.
Barry H Dayton - One of the best experts on this subject based on the ideXlab platform.
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the approximate gcd of inexact polynomials
International Symposium on Symbolic and Algebraic Computation, 2004Co-Authors: Zhonggang Zeng, Barry H DaytonAbstract:This paper presents an algorithm and its implementation for computing the approximate GCD (Greatest Common Divisor) of multivariate polynomials whose coefficients may be inexact. The method and the companion software appear to be the first practical package with such capabilities. The most significant features of the algorithm are its robustness and accuracy as demonstrated in computational experiments. In addition, two variations of a squarefree factorization method for multivariate polynomials are proposed as an application of the GCD algorithm.
Sumaia Saad Eddin - One of the best experts on this subject based on the ideXlab platform.
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sums of weighted averages of gcd sum functions
International Journal of Number Theory, 2018Co-Authors: Isao Kiuchi, Sumaia Saad EddinAbstract:Let gcd(j,k) be the Greatest Common Divisor of the integers j and k. In this paper, we give several interesting asymptotic formulas for weighted averages of the gcd-sum function f(gcd(j,k)) and the...
