SLRA swMATH ID: 11262 Software Authors: Usevich, Konstantin; Markovsky, Ivan Description: 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. Homepage: https://github.com/slra/slra Source Code: https://github.com/slra/slra Related Software: GPGCD; Daisy; MultRoot; TSDL; IDENT; GSL; Matlab; Noweb; SDPLR; TEASER++; SE-Sync; CVX; BioSSA; svd; Rssa; devtools; raster; forecast; FFTW; R Cited in: 23 Publications Standard Articles 1 Publication describing the Software Year Variable projection methods for approximate GCD computations Usevich, Konstantin; Markovsky, Ivan 2012 all top 5 Cited by 25 Authors 11 Markovsky, Ivan 7 Usevich, Konstantin 3 Liu, Xifu 3 Zhigljavsky, Anatoly A. 2 Golyandina, Nina 2 Guglielmi, Nicola 2 Wang, Hongxing 1 Balajewicz, Maciej J. 1 Cifuentes, Diego 1 Condat, Laurent 1 Dai, Ran 1 Farhat, Charbel H. 1 Fazzi, Antonio 1 Gillard, Jonathan W. 1 Goos, Jan 1 Hirabayashi, Akira 1 Ishteva, Mariya 1 Korobeynikov, Anton 1 Liu, Tianxiang 1 Luo, Le 1 Pintelon, Rik 1 Plonka, Gerlind 1 Pong, Ting Kei 1 Sun, Chuangchuang 1 Takeda, Akiko all top 5 Cited in 14 Serials 4 SIAM Journal on Matrix Analysis and Applications 3 Automatica 3 Journal of Computational and Applied Mathematics 3 Applied Mathematics Letters 1 Journal of Computational Physics 1 SIAM Journal on Numerical Analysis 1 Theoretical Computer Science 1 Numerical Algorithms 1 Linear Algebra and its Applications 1 Advances in Computational Mathematics 1 Communications in Nonlinear Science and Numerical Simulation 1 Sampling Theory in Signal and Image Processing 1 Use R! 1 Communications and Control Engineering all top 5 Cited in 11 Fields 15 Linear and multilinear algebra; matrix theory (15-XX) 14 Numerical analysis (65-XX) 6 Operations research, mathematical programming (90-XX) 5 Systems theory; control (93-XX) 4 Statistics (62-XX) 3 Number theory (11-XX) 3 Approximations and expansions (41-XX) 2 Information and communication theory, circuits (94-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Operator theory (47-XX) 1 Calculus of variations and optimal control; optimization (49-XX) Citations by Year