SLRA

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 22 articles , 1 standard article )

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  1. Golyandina, Nina; Zhigljavsky, Anatoly: Blind deconvolution of covariance matrix inverses for autoregressive processes (2020)
  2. Liu, Xifu; Luo, Le: Minimum rank positive semidefinite solution to the matrix approximation problem in the spectral norm (2020)
  3. Fazzi, Antonio; Guglielmi, Nicola; Markovsky, Ivan: An ODE-based method for computing the approximate greatest common divisor of polynomials (2019)
  4. Liu, Xifu: Minimum rank Hermitian solution to the matrix approximation problem in the spectral norm and its application (2019)
  5. Zhang, Ran; Plonka, Gerlind: Optimal approximation with exponential sums by a maximum likelihood modification of Prony’s method (2019)
  6. Golyandina, Nina; Korobeynikov, Anton; Zhigljavsky, Anatoly: Singular spectrum analysis with R (2018)
  7. Guglielmi, Nicola; Markovsky, Ivan: An ODE-based method for computing the distance of coprime polynomials to common divisibility (2017)
  8. Liu, Xifu; Li, Wen; Wang, Hongxing: Rank constrained matrix best approximation problem with respect to (skew) Hermitian matrices (2017)
  9. Sun, Chuangchuang; Dai, Ran: Rank-constrained optimization and its applications (2017)
  10. Usevich, Konstantin; Markovsky, Ivan: Variable projection methods for approximate (greatest) common divisor computations (2017)
  11. Condat, Laurent; Hirabayashi, Akira: Cadzow denoising upgraded: a new projection method for the recovery of Dirac pulses from noisy linear measurements (2015)
  12. Gillard, J. W.; Zhigljavsky, A. A.: Stochastic algorithms for solving structured low-rank matrix approximation problems (2015)
  13. Wang, Hongxing: Rank constrained matrix best approximation problem (2015)
  14. Balajewicz, Maciej; Farhat, Charbel: Reduction of nonlinear embedded boundary models for problems with evolving interfaces (2014)
  15. Ishteva, Mariya; Usevich, Konstantin; Markovsky, Ivan: Factorization approach to structured low-rank approximation with applications (2014)
  16. Markovsky, Ivan; Goos, Jan; Usevich, Konstantin; Pintelon, Rik: Realization and identification of autonomous linear periodically time-varying systems (2014)
  17. Markovsky, Ivan; Usevich, Konstantin: Software for weighted structured low-rank approximation (2014)
  18. Usevich, Konstantin; Markovsky, Ivan: Variable projection for affinely structured low-rank approximation in weighted (2)-norms (2014)
  19. Usevich, Konstantin; Markovsky, Ivan: Optimization on a Grassmann manifold with application to system identification (2014)
  20. Markovsky, Ivan; Usevich, Konstantin: Structured low-rank approximation with missing data (2013)

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