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2018 | OriginalPaper | Chapter

HomotopyContinuation.jl: A Package for Homotopy Continuation in Julia

Authors : Paul Breiding, Sascha Timme

Published in: Mathematical Software – ICMS 2018

Publisher: Springer International Publishing

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Abstract

We present the Julia package HomotopyContinuation.jl, which provides an algorithmic framework for solving polynomial systems by numerical homotopy continuation. We introduce the basic capabilities of the package and demonstrate the software on an illustrative example. We motivate our choice of Julia and how its features allow us to improve upon existing software packages with respect to usability, modularity and performance. Furthermore, we compare the performance of HomotopyContinuation.jl to the existing packages Bertini and PHCpack.

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Footnotes
2
The authors discovered the examples in the excellent database of Jan Verschelde available at http://​homepages.​math.​uic.​edu/​~jan/​.
 
Literature
1.
Alizadeh, F.: Interior point methods in semidefinite programming with applications to combinatorial optimization. SIAM J. Optim. 5(1), 13–51 (1995)MathSciNetCrossRef
2.
Bates, D.J., Hauenstein, J.D., Sommese, A.J., Wampler, C.W.: Adaptive multiprecision path tracking. SIAM J. Numer. Anal. 46(2), 722–746 (2008)MathSciNetCrossRef
3.
4.
Bezanson, J., Edelman, A., Karpinski, S., Shah, V.B.: Julia: a fresh approach to numerical computing. SIAM Rev. 59(1), 65–98 (2017)MathSciNetCrossRef
5.
Björck, G., Fröberg, R.: A faster way to count the solutions of inhomogeneous systems of algebraic equations, with applications to cyclic n-roots. J. Symbolic Comput. 12(3), 329–336 (1991)MathSciNetCrossRef
6.
Cayley, A.: A memoir on quartic surfaces. Proc. London Math. Soc. 3, 19–69 (1869/1871). (Collected Papers, VII, 133–181; see also the sequels on pages 256–260, 264–297)
7.
Degtyarev, A., Itenberg, I.: On real determinantal quartics. In: Proceedings of the Gökova Geometry Topology Conference 2010 (2011)
8.
Huber, B., Verschelde, J.: Polyhedral end games for polynomial continuation. Numer. Algorithms 18(1), 91–108 (1998)MathSciNetCrossRef
9.
Katsura, S.: Spin glass problem by the method of integral equation of the effective field. In: New Trends in Magnetism, pp. 110–121 (1990)
10.
Knuth, D.E.: The Art of Computer Programming, 3rd edn. Seminumerical Algorithms, vol. 2. Addison-Wesley Longman Publishing Co. (1997)
11.
Nelson, C.V., Hodgkin, B.C.: Determination of magnitudes, directions, and locations of two independent dipoles in a circular conducting region from boundary potential measurements. IEEE Trans. Biomed. Eng. 12, 817–823 (1981)CrossRef
12.
13.
14.
15.
Verschelde, J.: Algorithm 795: PHCpack: a general-purpose solver for polynomial systems by homotopy continuation. ACM Trans. Math. Software (TOMS) 25(2), 251–276 (1999)CrossRef
16.
17.
Wampler, C., Morgan, A.: Solving the 6R inverse position problem using a generic-case solution methodology. Mech. Mach. Theory 26(1), 91–106 (1991)CrossRef
18.
Wampler, I.C.W.: The Numerical Solution of Systems of Polynomials Arising in Engineering and Science. World Scientific (2005)
Metadata
Title
HomotopyContinuation.jl: A Package for Homotopy Continuation in Julia
Authors
Paul Breiding
Sascha Timme
Copyright Year
2018
Book
Mathematical Software – ICMS 2018

Print ISBN: 978-3-319-96417-1

Electronic ISBN: 978-3-319-96418-8

Copyright Year: 2018

DOI
https://doi.org/10.1007/978-3-319-96418-8_54

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