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. Recent results: normalization, division and sqrt , . Goals: formally proven algorithms, elementary functions implementation. Some talks: [ASAP14] [Henon13][SMC14]
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; efficient computations of supremum norms of approximation errors ; formally proven Taylor Models . 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:
 Sylvain Chevillard, John Harrison, Mioara Joldeş, and Christoph Lauter. Efficient and accurate computation of upper bounds of approximation errors. Theoretical Computer Science, 16(412):1523–1543, 2011. 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.
 Mioara Joldes, Olivier Marty, Jean-Michel Muller, and Valentina Popescu. Arithmetic algorithms for extended precision using floating-point expansions. IEEE Transactions on Computers, 2015. In print, doi: 10.1109/TC.2015.2441714, 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, 2015. Preliminary version.
 Alexandre Benoit, Mioara Joldes, and Marc Mezzarobba. Rigorous uniform approximation of D-finite functions using Chebyshev expansions. Accepted for publication to Mathematics of Computation, 2015. 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.
 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. Thesis, École Normale Supérieure de Lyon - ENS LYON, September 2011. https://tel.archives-ouvertes.fr/tel-00657843.
 Romain Serra, Denis Arzelier, Mioara Joldes, and Aude Rondepierre. Probability of collision between spherical space objects for short-term space encounters. Technical report, LAAS-CNRS No. 14154, Mars 2014. Astrium Funding for PhD.
 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. Submitted. Preliminary version