Mioara JoldesLAAS-CNRS 7 Avenue du Colonel Roche, 31077 Toulouse, Cedex 4 France phone:(+33) (0)5 61 33 69 26 email: joldes AT laas DOT fr
Rigorous computing (validated computing): use numerical computations, but provide mathematical
statements about the obtained result, such as sure, yet reasonably tight, error bounds. Build efficient
symbolic-numeric objects, algorithms and software tools with direct applications in control of dynamical
systems and in particular in the aerospace domain. Use and develop expertise and ideas from Computer Arithmetic and Computer Algebra.
A. Towards Fast and Certified Multiple Precision Arithmetic Libraries: develop a multiple precision arithmetic library tuned for Graphics Processing Units (GPUs). Targets high-performance computing problems which require multiple precision e.g., the study of strange attractors such as the Hénon attractor . Use floating-point expansions that is, extended precision is represented as the unevaluated sum of standard machine floating-point numbers. Valentina Popescu defended her PhD thesis, co-supervised with Jean-Michel Muller, on 6th of July 2017. Some recent related articles are , , , , , . Other goals: formally proven algorithms, elementary functions implementation. Some talks: [ASAP14] [Henon13][SMC14][ICMS16]
B. Rigorous Polynomial Approximation (RPA): a polynomial approximation together with rigorous error bounds. Use Taylor Models [1, 14, 15, 9] and Chebyshev polynomial interpolation/series Models , [19, Chap. 4]. Adapt to rigorous computations many numerical algorithms based on Chebyshev/Taylor Series for solving ordinary differential equations, quadrature, etc. Recent results: compute rigorous uniform approximations based on Chebyshev Series for D-finite functions, i.e. solutions of ordinary differential equations with polynomial coefficients  e.g., erf, exp, sin, Bessel, Airy functions.
With Florent Bréhard and Nicolas Brisebarre, we developed a validated numerics method for the solution of linear ordinary differential equations (LODEs). A theoretical and practical complexity analysis of a so-called a posteriori quasi-Newton validation method is given in .
Objectives: efficient implementation of operations with Chebyshev Models, extensions to multivariate functions; efficient finite precision evaluation of power series. Some talks: [RPA] [TAMADI][SeaMac]
C. Applications to Optimal Control and Aerospace:
 Alexandre Benoit, Mioara Joldes, and Marc Mezzarobba. Rigorous uniform approximation of d-finite functions using chebyshev expansions. Math. Comput., 86(305):1303–1341, 2017. Preliminary version.
 Romain Serra, Denis Arzelier, Mioara Joldes, Jean-Bernard Lasserre, Aude Rondepierre, and Bruno Salvy. Fast and accurate computation of orbital collision probability for short-term encounters. Journal of Guidance, Control, and Dynamics, 39(5):1009–1021, 2016. Preliminary version.
 Mioara Joldes, Olivier Marty, Jean-Michel Muller, and Valentina Popescu. Arithmetic algorithms for extended precision using floating-point expansions. IEEE Transactions on Computers, 65(4):1197–1210, Apr 2016. Preliminary version.
 Mioara Joldes, Jean-Michel Muller, and Valentina Popescu. Tight and rigourous error bounds for basic building blocks of double-word arithmetic. Accepted for publication in ACM Transactions on Math. Software, July 2016. Preliminary version.
 Mioara Joldes, Valentina Popescu, and Warwick Tucker. Searching for sinks for the Hénon map using a multipleprecision GPU arithmetic library. SIGARCH Comput. Archit. News, 42(4):63–68, December 2014.Preliminary version.
 Sylvain Chevillard, John Harrison, Mioara Joldes, and Christoph Lauter. Efficient and accurate computation of upper bounds of approximation errors. Theoretical Comp. Science, 16(412):1523–1543, 2011.Preliminary version.
 Mioara Joldes, Jean-Michel Muller, and Valentina Popescu. Implementation and performance evaluation of an extended precision floating-point arithmetic library for high-accuracy semidefinite programming. In Proceedings of IEEE Symposium on Computer Arithmetic (Arith24), London, United Kingdom, July 2017. Preliminary version.
 Sylvie Boldo, Mioara Joldes, Jean-Michel Muller, and Valentina Popescu. Formal Verification of a Floating-Point Expansion Renormalization Algorithm. In Proceedings of ITP2017: 8th International Conference on Interactive Theorem Proving, Brasilia, Brasil, 2017. Preliminary version
 Paulo Ricardo Arantes Gilz, Mioara Joldes, Christophe Louembet, and Frédéric Camps. Model predictive control for rendezvous hovering phases based on a novel description of constrained trajectories. In Proceedings of IFAC 2017: The 20th World Congress of the International Federation of Automatic Control, 9-14 July 2017, Toulouse, France, July 2017. Preliminary version
 Denis Arzelier, Florent Bréhard, Norbert Deak, Mioara Joldes, Christophe Louembet, Aude Rondepierre, and Romain Serra. Linearized impulsive fixed-time fuel-optimal space rendezvous: A new numerical approach. In Proceedings of 20th IFAC Symposium on Automatic Control in Aerospace, 21-25 Aug, 2016, Sherbrooke, Canada. Preliminary version
 Sylvain Collange, Mioara Joldes, Jean-Michel Muller, and Valentina Popescu. Parallel floating-point expansions for extended-precision GPU computations. In Proceedings of ASAP 2016: 27th IEEE International Conference on Application-specific Systems, Architectures and Processors, 6-8 July 2016, London, England. Preliminary version
 Florent Bréhard, Nicolas Brisebarre, and Mioara Joldes. A New Efficient Algorithm for Computing Validated Chebyshev Approximations Solutions of Linear Differential Equations . In SCAN2016: 17th International Symposium on Scientific Computing,Computer Arithmetic and Verified Numerics, Uppsala, Sweden, Sept. 2016, pages 41–43, 2016.
 Mioara Joldes, Jean-Michel Muller, Valentina Popescu, and Warwick Tucker. Campary: Cuda multiple precision arithmetic library and applications. In Gert-Martin Greuel, Thorsten Koch, Peter Paule, and Andrew Sommese, editors, Mathematical Software – ICMS 2016: 5th International Conference, Berlin, Germany, July 11-14, 2016, Proceedings, pages 232–240, Cham, 2016. Springer International Publishing. Preliminary version
 Romain Serra, Denis Arzelier, Mioara Joldes, Jean-Bernard Lasserre, Aude Rondepierre, and Bruno Salvy. A new method to compute the probability of collision for short-term space encounters. In Astrodynamics Specialist Conference, pages 1–7, Aug 2014.
 Romain Serra, Denis Arzelier, Mioara Joldes, and Aude Rondepierre. Probabilistic collision avoidance for long-term space encouters via risk selection. In 3rd CEAS European Aerospace Guidance, Navigation and Control (EuroGNC) Conference, pages –21, Dec 2014.
 Mioara Joldes, Jean-Michel Muller, and Valentina Popescu. On the computation of the reciprocal of floating point expansions using an adapted Newton-Raphson iteration. In IEEE 25th International Conference on Application-Specific Systems, Architectures and Processors, ASAP 2014, Zurich, Switzerland, June 18-20, 2014, pages 63–67. IEEE, 2014. Preliminary version.
 Nicolas Brisebarre, Mioara Joldes, Érik Martin-Dorel, Micaela Mayero, Jean-Michel Muller, Ioana Pasca, Laurence Rideau, and Laurent Théry. Rigorous polynomial approximation using Taylor Models in Coq. In Alwyn Goodloe and Suzette Person, editors, NASA Formal Methods - 4th International Symposium, NFM 2012, Norfolk, VA, USA, April 3-5, 2012. Proceedings, volume 7226 of Lecture Notes in Computer Science, pages 85–99. Springer, 2012. Preliminary version
 Nicolas Brisebarre, Mioara Joldes, Peter Kornerup, Érik Martin-Dorel, and Jean-Michel Muller. Augmented precision square roots and 2-d norms, and discussion on correctly rounding sqrt(x^2+y^2). In Elisardo Antelo, David Hough, and Paolo Ienne, editors, 20th IEEE Symposium on Computer Arithmetic, ARITH 2011, Tübingen, Germany, 25-27 July 2011, pages 23–30. IEEE Computer Society, 2011. Preliminary version
 Nicolas Brisebarre and Mioara Joldes. Chebyshev interpolation polynomial-based tools for rigorous computing. In Wolfram Koepf, editor, Symbolic and Algebraic Computation, International Symposium, ISSAC 2010, Munich, Germany, July 25-28, 2010, Proceedings, pages 147–154. ACM, 2010.Preliminary version.
 Florent de Dinechin, Mioara Joldes, and Bogdan Pasca. Automatic generation of polynomial-based hardware architectures for function evaluation. In François Charot, Frank Hannig, Jürgen Teich, and Christophe Wolinski, editors, 21st IEEE International Conference on Application-specific Systems Architectures and Processors, ASAP 2010, Rennes, France, 7-9 July 2010, pages 216–222. IEEE, 2010. Preliminary version.
 Florent de Dinechin, Mioara Joldes, Bogdan Pasca, and Guillaume Revy. Multiplicative square root algorithms for FPGAs. In International Conference on Field Programmable Logic and Applications, FPL 2010, August 31 2010 - September 2, 2010, Milano, Italy, pages 574–577. IEEE, 2010. Preliminary version
 Sylvain Chevillard, Mioara Joldes, and Christoph Quirin Lauter. Sollya: An environment for the development of numerical codes. In Komei Fukuda, Joris van der Hoeven, Michael Joswig, and Nobuki Takayama, editors, Mathematical Software - ICMS 2010, Third International Congress on Mathematical Software, Kobe, Japan, September 13-17, 2010. Proceedings, volume 6327 of Lecture Notes in Computer Science, pages 28–31. Springer, 2010.
 Sylvain Chevillard, Mioara Joldes, and Christoph Quirin Lauter. Certified and fast computation of supremum norms of approximation errors. In Javier D. Bruguera, Marius Cornea, Debjit Das Sarma, and John Harrison, editors, 19th IEEE Symposium on Computer Arithmetic, ARITH 2009, Portland, Oregon, USA, 9-10 June 2009, pages 169–176. IEEE Computer Society, 2009.
 Mioara Joldes, Valentina Popescu, and Warwick Tucker. Searching for sinks of Hénon map using a multiple-precision GPU arithmetic library. In Forum des Jeunes Mathématicien-ne-s, pages –6, Nov 2013.
 Florent de Dinechin, Mioara Joldes, Bogdan Pasca, and Guillaume Revy. Racines carrées multiplicatives sur FPGA. In SYMPosium en Architectures nouvelles de machines (SYMPA), Toulouse, September 2009.
 Mioara Joldes. Rigorous Polynomial Approximations and Applications. Theses, École Normale Supérieure de Lyon - ENS LYON, September 2011. https://tel.archives-ouvertes.fr/tel-00657843.
 Florent Bréhard, Nicolas Brisebarre, and Mioara Joldes. Validated and numerically efficient Chebyshev spectral methods for linear ordinary differential equations. Submitted to ACM Trans. Math. Software, July 2017. Preliminary version.