MPFI

Motivations for an arbitrary precision interval arithmetic and the MPFI library. This paper justifies why an arbitrary precision interval arithmetic is needed. To provide accurate results, interval computations require small input intervals; this explains why bisection is so often employed in interval algorithms. The MPFI library has been built in order to fulfill this need. Indeed, no existing library met the required specifications. The main features of this library are briefly given and a comparison with a fixed-precision interval arithmetic, on a specific problem, is presented. It shows that the overhead due to the multiple precision is completely acceptable. Eventually, some applications based on MPFI are given: robotics, isolation of polynomial real roots (by an algorithm combining symbolic and numerical computations) and approximation of real roots with arbitrary accuracy.


References in zbMATH (referenced in 38 articles )

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  1. Bouzidi, Yacine; Quadrat, Alban; Rouillier, Fabrice: Certified non-conservative tests for the structural stability of discrete multidimensional systems (2019)
  2. Gómez-Serrano, Javier: Computer-assisted proofs in PDE: a survey (2019)
  3. Bahsoun, Wael; Galatolo, Stefano; Nisoli, Isaia; Niu, Xiaolong: A rigorous computational approach to linear response (2018)
  4. Cable, Jacob; Süß, Hendrik: On the classification of Kähler-Ricci solitons on Gorenstein del Pezzo surfaces (2018)
  5. Caluza Machado, Fabrício; de Oliveira Filho, Fernando Mário: Improving the semidefinite programming bound for the kissing number by exploiting polynomial symmetry (2018)
  6. Muller, Jean-Michel; Brunie, Nicolas; de Dinechin, Florent; Jeannerod, Claude-Pierre; Joldes, Mioara; Lefèvre, Vincent; Melquiond, Guillaume; Revol, Nathalie; Torres, Serge: Handbook of floating-point arithmetic (2018)
  7. Cordero, Alicia; Hueso, José L.; Martínez, Eulalia; Torregrosa, Juan R.: Multistep high-order methods for nonlinear equations using Padé-like approximants (2017)
  8. Dostert, Maria; Guzmán, Cristóbal; de Oliveira Filho, Fernando Mário; Vallentin, Frank: New upper bounds for the density of translative packings of three-dimensional convex bodies with tetrahedral symmetry (2017)
  9. Figueras, J.-Ll.; Haro, A.; Luque, A.: Rigorous computer-assisted application of KAM theory: a modern approach (2017)
  10. Imbach, Rémi; Moroz, Guillaume; Pouget, Marc: A certified numerical algorithm for the topology of resultant and discriminant curves (2017)
  11. Beliakov, Gleb; Matiyasevich, Yuri: A parallel algorithm for calculation of determinants and minors using arbitrary precision arithmetic (2016)
  12. Platt, D. J.; Trudgian, T. S.: On the first sign change of (\theta(x) -x) (2016)
  13. Rusu, David; Santoprete, Manuele: Bifurcations of central configurations in the four-body problem with some equal masses (2016)
  14. Platt, David J.: Computing (\pi(x)) analytically (2015)
  15. Platt, D. J.; Trudgian, T. S.: Linnik’s approximation to Goldbach’s conjecture, and other problems (2015)
  16. Andreu, Carlos; Cambil, Noelia; Cordero, Alicia; Torregrosa, Juan R.: Preliminary orbit determination of artificial satellites: a vectorial sixth-order approach (2013)
  17. Cordero, Alicia; Torregrosa, Juan R.; Vassileva, María P.: New predictor-corrector methods with high efficiency for solving nonlinear systems (2012)
  18. De Maesschalck, Peter; Popović, Nikola: Gevrey properties of the asymptotic critical wave speed in a family of scalar reaction-diffusion equations (2012)
  19. Krämer, Walter: Multiple/arbitrary precision interval computations in C-XSC (2012)
  20. Spandl, Christoph: Computational complexity of iterated maps on the interval (2012)

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