MPFI swMATH ID: 597 Software Authors: Revol, Nathalie; Rouillier, Fabrice Description: 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. Homepage: http://perso.ens-lyon.fr/nathalie.revol/software.html Programming Languages: C Keywords: Multiple Precision Floating-point Reliable Arithmetic Libraryarithmetic library Related Software: MPFR; C-XSC 2.0; gmp; ISOLATE; Arb; INTLAB; mctoolbox; Algorithm 524; SageMath; PROFIL/BIAS; filib++; C-XSC; kepler98; INTOPT_90; PNM; intpakX; Boost Interval Arithmetic; iRRAM; SHRAD; XBLAS Cited in: 50 Documents all top 5 Cited by 101 Authors 5 Revol, Nathalie 5 Rouillier, Fabrice 3 Cordero, Alicia 3 Melquiond, Guillaume 3 Platt, David John 3 Torregrosa Sanchez, Juan Ramón 2 Bouzidi, Yacine 2 de Oliveira Filho, Fernando Mário 2 Farjudian, Amin 2 Figueras, Jordi-Lluís 2 Galatolo, Stefano 2 Haro, Àlex 2 Jaulin, Luc 2 Jeannerod, Claude-Pierre 2 Krämer, Walter 2 Li, Yiran 2 Luque, Alejandro 2 Muller, Jean-Michel 2 Nisoli, Isaia 2 Trudgian, Timothy S. 1 Andreu, Carlos 1 Bahsoun, Wael 1 Beliakov, Gleb 1 Benet, Luis 1 Boldo, Sylvie 1 Bréhard, Florent 1 Brönnimann, Hervé 1 Brunie, Nicolas 1 Cable, Jacob 1 Caluza Machado, Fabrício 1 Cambil, Noelia 1 Chabert, Gilles 1 Daney, David 1 de Dinechin, Florent 1 De Maesschalck, Peter 1 Dostert, Maria 1 Edalat, Abbas 1 Ferranti, Luca 1 Gómez-Serrano, Javier 1 Graillat, Stef 1 Granvilliers, Laurent 1 Grimmer, Markus 1 Gu, Nong 1 Guzmán, Cristóbal 1 Hales, Thomas Callister 1 Hormann, Kai 1 Hueso, José Luis 1 Imbach, Rémi 1 Jézéquel, Fabienne 1 Joldeş, Mioara 1 Kreinovich, Vladik Yakovlevich 1 Kuliamin, Victor V. 1 Lasserre, Jean-Bernard 1 Laurent, Monique 1 Lazard, Daniel 1 Lebbah, Yahia 1 Lefèvre, Vincent 1 Macoveiciuc, Elisei 1 Mahboubi, Assia 1 Martel, Matthieu 1 Martínez, Eulalia 1 Matiyasevich, Yuriĭ Vladimirovich 1 McLaughlin, Sean 1 Merlet, Jean-Pierre 1 Michel, Claude 1 Monge, Maurizio 1 Moore, Ramon E. 1 Moroz, Guillaume 1 Nipkow, Tobias 1 Niu, Xiaolong 1 Obua, Steven 1 Petras, Knut 1 Pion, Sylvain 1 Popović, Nikola 1 Pouget, Marc 1 Pous, Damien 1 Quadrat, Alban 1 Reißig, Gunther 1 Rohou, Simon 1 Rostalski, Philipp 1 Rueher, Michel 1 Rump, Siegfried Michael 1 Rusu, David 1 Santoprete, Manuele 1 Saouter, Yannick 1 Shaikh, Razin A. 1 Spandl, Christoph 1 Süss, Hendrik 1 Torres, Serge 1 Vallentin, Frank 1 van der Hoeven, Joris 1 Vassileva, María P. 1 Wang, Shiyue 1 Weber, Alexander 1 Xiang, Yong 1 Yap, Chee-Keng 1 Zhang, Ya Shi 1 Zhilin, Sergei I. 1 Zhou, Can 1 Zhu, Yuxiang ...and 1 more Authors all top 5 Cited in 30 Serials 3 Mathematics of Computation 3 Reliable Computing 2 Nonlinearity 2 Theoretical Computer Science 2 Discrete & Computational Geometry 2 Foundations of Computational Mathematics 2 Mathematics in Computer Science 1 Journal of Mathematical Analysis and Applications 1 BIT 1 Computing 1 Journal of Computational and Applied Mathematics 1 Journal of Number Theory 1 Mathematics and Computers in Simulation 1 Programming and Computer Software 1 SIAM Journal on Numerical Analysis 1 Systems & Control Letters 1 Journal of Symbolic Computation 1 Multidimensional Systems and Signal Processing 1 Mathematical Structures in Computer Science 1 Experimental Mathematics 1 Abstract and Applied Analysis 1 Discrete Dynamics in Nature and Society 1 Communications in Nonlinear Science and Numerical Simulation 1 Journal of Applied Mathematics 1 SIAM Journal on Applied Dynamical Systems 1 Acta Numerica 1 SIAM Studies in Applied Mathematics 1 Albanian Journal of Mathematics 1 S\(\vec{\text{e}}\)MA Journal 1 European Journal of Mathematics all top 5 Cited in 16 Fields 29 Numerical analysis (65-XX) 13 Computer science (68-XX) 6 Dynamical systems and ergodic theory (37-XX) 5 Number theory (11-XX) 4 Algebraic geometry (14-XX) 4 Operations research, mathematical programming (90-XX) 4 Systems theory; control (93-XX) 3 Commutative algebra (13-XX) 3 Convex and discrete geometry (52-XX) 2 Partial differential equations (35-XX) 2 Mechanics of particles and systems (70-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Difference and functional equations (39-XX) 1 Approximations and expansions (41-XX) 1 Biology and other natural sciences (92-XX) 1 Information and communication theory, circuits (94-XX) Citations by Year