Variable projection methods for approximate GCD computations. This paper presents optimization methods and software for the approximate GCD problem of multiple univariate polynomials in the weighted 2-norm. Backward error minimization and Sylvester low-rank approximation formulations of the problem are solved by the variable projection method. Optimization methods are implemented in publicly available C++ software package with an interface to MATLAB. Results on computational complexity are presented.

References in zbMATH (referenced in 15 articles , 1 standard article )

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  1. Guglielmi, Nicola; Markovsky, Ivan: An ODE-based method for computing the distance of coprime polynomials to common divisibility (2017)
  2. Sun, Chuangchuang; Dai, Ran: Rank-constrained optimization and its applications (2017)
  3. Usevich, Konstantin; Markovsky, Ivan: Variable projection methods for approximate (greatest) common divisor computations (2017)
  4. Condat, Laurent; Hirabayashi, Akira: Cadzow denoising upgraded: a new projection method for the recovery of Dirac pulses from noisy linear measurements (2015)
  5. Gillard, J.W.; Zhigljavsky, A.A.: Stochastic algorithms for solving structured low-rank matrix approximation problems (2015)
  6. Wang, Hongxing: Rank constrained matrix best approximation problem (2015)
  7. Balajewicz, Maciej; Farhat, Charbel: Reduction of nonlinear embedded boundary models for problems with evolving interfaces (2014)
  8. Ishteva, Mariya; Usevich, Konstantin; Markovsky, Ivan: Factorization approach to structured low-rank approximation with applications (2014)
  9. Markovsky, Ivan; Goos, Jan; Usevich, Konstantin; Pintelon, Rik: Realization and identification of autonomous linear periodically time-varying systems (2014)
  10. Markovsky, Ivan; Usevich, Konstantin: Software for weighted structured low-rank approximation (2014)
  11. Usevich, Konstantin; Markovsky, Ivan: Variable projection for affinely structured low-rank approximation in weighted $2$-norms (2014)
  12. Usevich, Konstantin; Markovsky, Ivan: Optimization on a Grassmann manifold with application to system identification (2014)
  13. Markovsky, Ivan; Usevich, Konstantin: Structured low-rank approximation with missing data (2013)
  14. Markovsky, Ivan: Low rank approximation. Algorithms, implementation, applications (2012)
  15. Usevich, Konstantin; Markovsky, Ivan: Variable projection methods for approximate GCD computations (2012) ioport