MultRoot swMATH ID: 604 Software Authors: Zheng, Zhonggang Description: Algorithm 835: MultRoot - a Matlab package for computing polynomial roots and multiplicities. MultRoot is a collection of Matlab modules for accurate computation of polynomial roots, especially roots with non-trivial multiplicities. As a blackbox-type software, MultRoot requires the polynomial coefficients as the only input, and outputs the computed roots, multiplicities, backward error, estimated forward error, and the structure-preserving condition number. The most significant features of MultRoot are the multiplicity identification capability and high accuracy on multiple roots without using multiprecision arithmetic, even if the polynomial coefficients are inexact. A comprehensive test suite of polynomials that are collected from the literature is included for numerical experiments and performance comparison. Homepage: http://www.neiu.edu/~zzeng/ Dependencies: Matlab Related Software: Matlab; PHCpack; ApaTools; mctoolbox; Maple; GPGCD; Bertini; na20; SINGULAR; SNAP; NACLab; UTV; alphaCertified; HOM4PS; BPOLY; CASA; LAPACK; Algorithm 931; gfun; NewtonLib Cited in: 100 Publications Standard Articles 1 Publication describing the Software, including 1 Publication in zbMATH Year Algorithm 835: MultRoot - -a Matlab package for computing polynomial roots and multiplicities. Zbl 1070.65542Zheng, Zhonggang 2004 all top 5 Cited by 130 Authors 12 Winkler, Joab R. 12 Zeng, Zhonggang 6 Zhi, Lihong 5 Szántó, Ágnes 4 Bourne, Martin 4 Frauendiener, Jörg 4 Klein, Christian 4 Terui, Akira 3 Christou, Dimitrios 3 Corless, Robert Malcolm 3 Kaltofen, Erich L. 3 Karcanias, Nicos 3 Lao, Xin 3 Li, Tien-Yien 3 Luo, Zhongxuan 3 Mitrouli, Marilena 3 Su, Yi 2 Belhaj, Skander 2 Boito, Paola 2 Chang, Feng Cheng 2 Cheng, Jinsan 2 Dayton, Barry H. 2 Dou, Xiaojie 2 Feng, Erbao 2 Galligo, André 2 Giesbrecht, Mark W. 2 Guglielmi, Nicola 2 Haraldson, Joseph 2 Hasan, Madina 2 Hodorog, Mădălina 2 Lee, Tsung-Lin 2 Li, Bingyu 2 Liu, Zhuojun 2 Markovsky, Ivan 2 May, John P. 2 Mourrain, Bernard 2 Pan, Victor Yakovlevich 2 Peterson, Chris 2 Schicho, Josef 2 Sommese, Andrew John 2 Verschelde, Jan 2 Yakoubsohn, Jean-Claude 2 Yang, Zhengfeng 2 Zidna, Ahmed 1 Abbott, John A. 1 Adrovic, Danko 1 Allan, John D. 1 Aris, Nor’aini 1 Batenkov, Dmitry 1 Bates, Dan 1 Bates, Daniel J. 1 Beltrán, Carlos 1 Ben Kahla, Haithem 1 Bini, Dario Andrea 1 Busé, Laurent 1 Chèze, Guillaume 1 D’Andrea, Carlos 1 Díaz-Toca, Gema María 1 Dridi, Marwa 1 Elkadi, Mohamed 1 Emiris, Ioannis Z. 1 Fazzi, Antonio 1 Fillion, Nicolas 1 Galántai, Aurél 1 Gao, Shuhong 1 Giusti, Marc 1 Gonzalez-Vega, Laureano 1 Habib, H. M. 1 Halawani, Hanan 1 Hao, Wenrui 1 Hauenstein, Jonathan D. 1 Hegedus, Csaba J. 1 Henrion, Didier 1 Hu, Wenyu 1 Janovitz-Freireich, Itnuit 1 Kako, Fujio 1 Konstantinov, Mikhail Mikhajlov 1 Krick, Teresa 1 Labahn, George 1 Laub, Alan J. 1 Le Thi, Hoai An 1 Lecerf, Grégoire 1 Lee, Hwangrae 1 Leykin, Anton 1 Li, Zhe 1 Li, Zijia 1 Lichtblau, Daniel A. 1 Liu, Qi 1 Luo, Xingjun 1 Michel, Dominique 1 Mir, Nazir Ahmad 1 Moakher, Maher 1 Nagasaka, Kosaku 1 Ouanes, Mohand 1 Pardo, Luis Miguel 1 Pérez-Díaz, Sonia 1 Petkov, Petko Hr. 1 Petković, Ljiljana D. 1 Petković, Miodrag S. 1 Pope, Scott R. ...and 30 more Authors all top 5 Cited in 36 Serials 12 Journal of Computational and Applied Mathematics 9 Theoretical Computer Science 9 Journal of Symbolic Computation 5 Foundations of Computational Mathematics 4 Numerical Algorithms 3 Applied Mathematics and Computation 3 Linear Algebra and its Applications 2 Mathematics of Computation 2 Journal of Algebra 2 Mathematics and Computers in Simulation 2 Applied Numerical Mathematics 2 Journal of Complexity 2 SIAM Journal on Matrix Analysis and Applications 2 Mathematics in Computer Science 1 Computers & Mathematics with Applications 1 Inverse Problems 1 Letters in Mathematical Physics 1 Nonlinearity 1 ACM Transactions on Mathematical Software 1 Calcolo 1 Journal of Pure and Applied Algebra 1 SIAM Journal on Numerical Analysis 1 Computer Aided Geometric Design 1 Journal of Scientific Computing 1 Signal Processing 1 Journal of Mathematical Imaging and Vision 1 SIAM Journal on Scientific Computing 1 Applied Mathematics. Series B (English Edition) 1 Discrete Dynamics in Nature and Society 1 Applied Mathematics E-Notes 1 Journal of Applied Mathematics 1 Computational Methods and Function Theory 1 Tesi. Scuola Normale Superiore di Pisa (Nuova Serie) 1 ISRN Applied Mathematics 1 ISRN Computational Mathematics 1 Mathematics all top 5 Cited in 21 Fields 77 Numerical analysis (65-XX) 36 Computer science (68-XX) 30 Field theory and polynomials (12-XX) 23 Commutative algebra (13-XX) 13 Algebraic geometry (14-XX) 11 Linear and multilinear algebra; matrix theory (15-XX) 10 Number theory (11-XX) 7 Functions of a complex variable (30-XX) 6 Real functions (26-XX) 6 Information and communication theory, circuits (94-XX) 3 Special functions (33-XX) 2 Operator theory (47-XX) 2 Operations research, mathematical programming (90-XX) 1 General and overarching topics; collections (00-XX) 1 Ordinary differential equations (34-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Approximations and expansions (41-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Manifolds and cell complexes (57-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Systems theory; control (93-XX) Citations by Year