Bates, Daniel J.; Newell, Andrew J.; Niemerg, Matthew BertiniLab: a MATLAB interface for solving systems of polynomial equations. (English) Zbl 1333.65054 Numer. Algorithms 71, No. 1, 229-244 (2016). Summary: A MATLAB interface to the numerical homotopy continuation package Bertini is described. Bertini solves systems of polynomial equations. BertiniLab can be used to create input files for Bertini, run Bertini and process the solutions. All features of Bertini 1.5 are supported. The user can define the system of equations using a MATLAB numerical function, and vector and matrix operations are allowed. An object-oriented design allows the user to separate the statement of the problem from the details of the solution; the user can create subclasses to provide shortcuts or to tailor BertiniLab to a specific kind of problem. A complete example of an application to ferromagnetism is presented. Cited in 3 Documents MSC: 65H10 Numerical computation of solutions to systems of equations 65H04 Numerical computation of roots of polynomial equations 65H20 Global methods, including homotopy approaches to the numerical solution of nonlinear equations Keywords:polynomial system; numerical algebraic geometry; Matlab; algorithm; numerical homotopy continuation package Bertini Software:Paramotopy; Bertini; HOM4PS; PHCpack; PHClab; Matlab; BertiniLab PDFBibTeX XMLCite \textit{D. J. Bates} et al., Numer. Algorithms 71, No. 1, 229--244 (2016; Zbl 1333.65054) Full Text: DOI References: [1] Bates, D.J., Brake, D.A., Niemerg, M.E.: Paramotopy: Parameter homotopies in parallel (2015) · Zbl 1396.65179 [2] Bates, D.J., Davis, B., Eklund, D., Hanson, E., Peterson, C.: Perturbed homotopies for finding all isolated solutions of polynomial systems. Appl. Math. Comput. 247, 301-311 (2014) · Zbl 1338.13046 [3] Bates, D.J., Hauenstein, J.D., Sommese, A.J., Wampler, C.W.: Bertini: Software for numerical algebraic geometry. Available at http://www.nd.edu/ sommese/bertini (2010) [4] Bates, D.J., Hauenstein, J.D., Sommese, A.J., Wampler, C.W.: Bertini: Software for numerical algebraic geometry. Web page. http://www.bertini.nd.edu/ (2010) · Zbl 1338.13046 [5] Bates, D.J., Hauenstein, J.D., Sommese, A.J., Wampler, C.W.: Numerically Solving Polynomial Systems with Bertin. SIAM (2013) · Zbl 1295.65057 [6] Guan, Y., Verschelde, J.: PHClab: A MATLAB/Octave interface to PHCpack. In: Software for Algebraic Geometry, The IMA Volumes in Mathematics and its Applications, vol. 148, pp. 15-32. Springer, New York (2008). doi:10.1007/978-0-387-78133-4_2 · Zbl 1148.68578 [7] Hao, W., Hauenstein, J.D., Hu, B., McCoy, T., Sommese, A.J.: Computing steady-state solutions for a free boundary problem modeling tumor growth by stokes equation. J. Comput. Appl. Math. 237(1), 326-334 (2013) · Zbl 1303.92044 [8] Hauenstein, J., Sommese, A., Wampler, C.: Regeneration homotopies for solving systems of polynomials. Math. Comput. 80(273), 345-377 (2011) · Zbl 1221.65121 [9] Lee, T., Li, T., Tsai, C.: Hom4ps-2.0: Homotopy method for solving polynomial systems. Web page. http://www.math.nsysu.edu.tw/leetsung/works/HOM4PS_soft.htm (2008) · Zbl 1167.65366 [10] Nam, K.M., Gyori, B.M., Brake, D., Bates, D.J., Gunawardena, J.: The parameter geography of multistability in protein post-translational modification (2014) · Zbl 1221.65121 [11] Newell, A.J.: Superparamagnetic relaxation times for mixed anisotropy and high energy barriers with intermediate to high damping: I. Uniaxial axis in a <001> direction. Geochem. Geophys. Geosyst. 7(3), Q03,016 (2006). doi:10.1029/2005GC001146 [12] Newell, A.J.: Transition to superparamagnetism in chains of magnetosome crystals. Geochem. Geophys. Geosyst. 10(Q11Z08) (2009). doi:10.1029/2009GC002538 [13] Rostalski, P., Fotiou, I.A., Bates, D.J., Beccuti, A.G., Morari, M.: Numerical algebraic geometry for optimal control applications. SIAM J. Optim. 21(2), 417-437 (2011) · Zbl 1228.49018 [14] Sommese, A.J., Wampler II, C.W.: The Numerical Solution of Systems of Polynomials Arising in Engineering and Science. World Scientific, 401 (2005) · Zbl 1091.65049 [15] Verschelde, J.: Algorithm 795: PHCpack: a general-purpose solver for polynomial systems by homotopy continuation. ACM Trans. Math. Softw. 25(2), 251-276 (1999). doi:10.1145/317275.317286 · Zbl 0961.65047 [16] Wampler, C.W., Sommese, A.J.: Numerical algebraic geometry and algebraic kinematics. Acta Numerica 20, 469-567 (2011) · Zbl 1254.13031 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.