U. Bauer, M. Kerber, and J. Reininghaus, PHAT (Persistent Homology Algorithm Toolbox)
DOI : 10.1007/978-3-662-44199-2_24

P. Bendich, H. Edelsbrunner, and M. Kerber, Computing robustness and persistence for images, IEEE Transactions on Visualization and Computer Graphics, vol.16, issue.6, pp.1251-1260, 2010.
DOI : 10.1109/tvcg.2010.139

URL : http://www.mpi-sb.mpg.de/%7Emkerber/bek-crpi-2010.pdf

P. Bendich, H. Edelsbrunner, M. Kerber, and A. Patel, Persistent homology under non-uniform error, Mathematical Foundations of Computer Science, vol.6281, pp.12-23, 2010.
DOI : 10.1007/978-3-642-15155-2_2

URL : http://www.mpi-sb.mpg.de/%7Emkerber/BEKP_MFCS_10.pdf

P. Bubenik and P. Lotko, A persistence landscapes toolbox for topological statistics, Journal of Symbolic Computations
DOI : 10.1016/j.jsc.2016.03.009

URL : https://hal.archives-ouvertes.fr/hal-01258875

G. Carlsson and A. Zomorodian, The theory of multidimensional persistence, Discrete & Computational Geometry, vol.42, issue.1, pp.71-93, 2009.
DOI : 10.1145/1247069.1247105

URL : http://www.cs.dartmouth.edu/~afra/papers/socg07/multid.ps.gz

A. Cerri and C. Landi, Hausdorff stability of persistence spaces, Foundations of Computational Mathematics, vol.16, issue.2, pp.343-367, 2016.

A. Cerri, B. Di-fabio, M. Ferri, P. Frosini, and C. Landi, Betti numbers in multidimensional persistent homology are stable functions, Mathematical Methods in the Applied Sciences, vol.36, issue.12, pp.1543-1557, 2013.

F. Chazal, D. Cohen-steiner, M. Glisse, L. J. Guibas, and S. Oudot, Proximity of persistence modules and their diagrams, Proceedings of the Twenty-Fifth Annual Symposium on Computational Geometry, ACM SCG '09, pp.237-246, 2009.
URL : https://hal.archives-ouvertes.fr/inria-00292566

F. Chazal, V. Silva, M. Glisse, and S. Oudot, The Structure and Stability of Persistence Modules, SpringerBriefs in Mathematics, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01107617

B. Chazelle, An optimal convex hull algorithm in any fixed dimension, Discrete & Computational Geometry, vol.10, issue.4, pp.377-409, 1993.

G. S. Cochran, T. Wanner, and P. Lotko, A randomized subdivision algorithm for determining the topology of nodal sets, SIAM Journal on Scientific Computing, vol.35, issue.5, pp.1034-1054, 2013.

D. Cohen-steiner, H. Edelsbrunner, and J. Harer, Stability of persistence diagrams, Discrete & Computational Geometry, vol.37, issue.1, pp.103-120, 2007.

S. Day, W. D. Kalies, and T. Wanner, Verified homology computations for nodal domains, SIAM Journal on Multiscale Modeling & Simulation, vol.7, issue.4, pp.1695-1726, 2009.

S. Day, R. Vandervorst, and T. Wanner, Topology in dynamics, differential equations, and data, vol.334, pp.1-3, 2016.

, GUDHI: User and Reference Manual

P. Dd-lotko, T. Kaczynski, M. Mrozek, and T. Wanner, Coreduction Homology Algorithm for Regular CW-Complexes, Discrete & Computational Geometry, vol.46, issue.2, pp.361-388, 2011.

P. Dd-lotko and T. Wanner, Topological microstructure analysis using persistence landscapes, Physica D, vol.334, issue.1, pp.60-81, 2016.

H. Edelsbrunner, J. Harer, and C. Topology, , 2010.

H. Edelsbrunner, D. Letscher, and A. Zomorodian, Topological persistence and simplification, Discrete & Computational Geometry, vol.29, issue.4, pp.511-533, 2002.

L. H. De-figueiredo and J. Stolfi, Affine arithmetic: Concepts and applications, vol.37, pp.147-158, 2004.

E. R. Hansen, A generalized interval arithmetic, Interval Mathematics, volume 29 of the series Lecture Notes in Computer Science, pp.7-18, 2005.

J. Jaquette and M. Kramar, Rigorous computation of persistent homology, accepted to Mathematics of Computation, 2016.

W. S. Massey, A Basic Course in Algebraic Topology, 1991.

K. Mischaikow and V. Nanda, Morse theory for filtrations and efficient computation of persistent homology, Discrete & Computational Geometry, vol.50, issue.2, pp.330-353, 2013.

R. E. Moore, R. B. Kearfott, and M. J. Cloud, Introduction to Interval Analysis, 2009.

D. Morozov and D. ,

M. Mrozek and T. Wanner, Coreduction homology algorithm for inclusions and persistent homology, vol.60, pp.2812-2833, 2010.

V. Nanda, Perseus, the Persistent Homology Software

A. Neumaier, Interval Methods for Systems of Equations, 1990.

T. Wanner, Topological analysis of the diblock copolymer equation, Mathematical Challenges in a New Phase of Materials Science, pp.27-51, 2016.

S. Wylie and P. J. Hilton, Homology Theory. An Introduction to Algebraic Topology, 1994.