📚 Bibliography¶
Daniel J. Bates, Jonathan D. Hauenstein, Andrew J. Sommese, and Charles W. Wampler. Numerically Solving Polynomial Systems with Bertini. SIAM, first edition, 2013. ISBN 978-1-611972-69-6.
Göran Björck and Ralf Fröberg. A faster way to count the solutions of inhomogeneous systems of algebraic equations, with applications to cyclic n-roots. Journal of Symbolic Computation, 12(3):329–336, 1991.
Yang Dai, Sunyoung Kim, and Masakazu Kojima. Computing all nonsingular solutions of cyclic-n polynomial using polyhedral homotopy continuation methods. Journal of Computational and Applied Mathematics, 152(1):83–97, 2003.
Andreas Griewank and Michael R Osborne. Analysis of newton’s method at irregular singularities. SIAM Journal on Numerical Analysis, 20(4):747–773, 1983.
Jonathan D Hauenstein. Numerically computing real points on algebraic sets. Acta applicandae mathematicae, 125(1):105–119, 2013.
Alexander Morgan and Andrew Sommese. A homotopy for solving general polynomial systems that respects m-homogeneous structures. Applied Mathematics and Computation, 24(2):101–113, 1987.
Alexander P Morgan, Andrew J Sommese, and Charles W Wampler. Computing singular solutions to nonlinear analytic systems. Numerische Mathematik, 58(1):669–684, 1990.
Alexander P Morgan, Andrew J Sommese, and Charles W Wampler. A power series method for computing singular solutions to nonlinear analytic systems. Numerische Mathematik, 63(1):391–409, 1992.
Alexander P Morgan, Andrew J Sommese, and Charles W Wampler. Computing singular solutions to polynomial systems. Advances in Applied Mathematics, 13(3):305–327, 1992.
Melissa Vellela and Hong Qian. Stochastic dynamics and non-equilibrium thermodynamics of a bistable chemical system: the schlögl model revisited. Journal of The Royal Society Interface, 6(39):925, 2008.