NumGfun: a package for numerical and analytic computation with D-finite functions. (English) Zbl 1321.65202
Watt, Stephen M. (ed.), Proceedings of the 35th international symposium on symbolic and algebraic computation, ISSAC 2010, Munich, Germany, July 25–28, 2010. New York, NY: Association for Computing Machinery (ACM) (ISBN 978-1-4503-0150-3). 139-145 (2010).
MSC:
| 65Y15 | Packaged methods for numerical algorithms |
| 65L05 | Numerical methods for initial value problems involving ordinary differential equations |
Keywords:
\(D\)-finite functions; Maple; bounds; certified numerical computation; linear differential equationsReferences:
| [1] | J. Abad, F. J. Gómez, and J. Sesma. An algorithm to obtain global solutions of the double confluent Heun equation. Numer. Algorithms, 49(1-4):33-51, 2008. · Zbl 1162.65041 |
| [2] | M. Beeler, R. W. Gosper, and R. Schroeppel. Hakmem. AI Memo 239, MIT Artificial Intelligence Laboratory, 1972. |
| [3] | F. Bellard. Computation of 2700 billion decimal digits of Pi using a Desktop Computer. 2010. http://bellard.org/pi/pi2700e9/ |
| [4] | D. J. Bernstein. Fast multiplication and its applications. In J. Buhler and P. Stevenhagen, editors, Algorithmic Number Theory, pages 325-384. Cambridge University Press, 2008. · Zbl 1208.68239 |
| [5] | A. Bostan, T. Cluzeau, and B. Salvy. Fast algorithms for polynomial solutions of linear differential equations. In ISSAC’05, pages 45-52. ACM press, 2005. 10.1145/1073884.1073893 · Zbl 1360.68920 |
| [6] | R. P. Brent. The complexity of multiple-precision arithmetic. In R. S. Anderssen and R. P. Brent, editors, The Complexity of Computational Problem Solving, pages 126-165, 1976. |
| [7] | R. P. Brent. A Fortran multiple-precision arithmetic package. ACM Trans. Math. Softw., 4(1):57-70, 1978. 10.1145/355769.355775 |
| [8] | R. P. Brent and P. Zimmermann. Modern Computer Arithmetic. Version 0.4. 2009. |
| [9] | P. Bürgisser, M. Clausen, and M. A. Shokrollahi. Algebraic complexity theory. Springer Verlag, 1997. · Zbl 1087.68568 |
| [10] | H. Cheng, G. Hanrot, E. Thomé, E. Zima, and P. Zimmermann. Time- and space-efficient evaluation of some hypergeometric constants. In ISSAC’07. ACM press, 2007. 10.1145/1277548.1277561 |
| [11] | D. V. Chudnovsky and G. V. Chudnovsky. On expansion of algebraic functions in power and Puiseux series (I, II). J. Complexity, 2(4):271-294, 1986; 3(1):1-25, 1987. 10.1016/0885-064X(87)90002-1 |
| [12] | D. V. Chudnovsky and G. V. Chudnovsky. Computer algebra in the service of mathematical physics and number theory. In Computers in mathematics (Stanford, CA, 1986), pages 109-232. 1990. · Zbl 0712.11078 |
| [13] | R. Dupont. Moyenne arithmético-géométrique, suites de Borchardt et applications. Thèse de doctorat, École polytechnique, Palaiseau, 2006. |
| [14] | P. Falloon, P. Abbott, and J. Wang. Theory and computation of spheroidal wavefunctions. J. Phys. A, 36:5477-5495, 2003. · Zbl 1064.33019 |
| [15] | P. Flajolet and R. Sedgewick. Analytic Combinatorics. Cambridge University Press, 2009. · Zbl 1165.05001 |
| [16] | L. Fousse, G. Hanrot, V. Lefèvre, P. Pélissier, and P. Zimmermann. MPFR: A multiple-precision binary floating-point library with correct rounding. ACM Trans. Math. Softw., 33(2):13:1-13:15, 2007. 10.1145/1236463.1236468 · Zbl 1365.65302 |
| [17] | X. Gourdon and P. Sebah. Binary splitting method, 2001. http://numbers.computation.free.fr/ |
| [18] | T. Granlund. GMP. http://gmplib.org/ |
| [19] | B. Haible and R. B. Kreckel. CLN. http://www.ginac.de/CLN/ |
| [20] | http://ddmf.msr-inria.inria.fr/ |
| [21] | B. Haible and T. Papanikolaou. Fast multiprecision evaluation of series of rational numbers, 1997. |
| [22] | L. Heffter. Einleitung in die Theorie der linearen Differentialgleichungen. Teubner, Leipzig, 1894. |
| [23] | E. Jeandel. Évaluation rapide de fonctions hypergéométriques. Rapport technique RT-0242, INRIA-ENS Lyon, 2000. |
| [24] | O. M. Makarov. An algorithm for multiplying 3 x 3 matrices. Comput. Math. Math. Phys., 26(1):179-180, 1987. 10.1016/0041-5553(86)90203-X · Zbl 0614.65036 |
| [25] | L. Meunier and B. Salvy. ESF: an automatically generated encyclopedia of special functions. In ISSAC’03, pages 199-206. ACM Press, 2003. http://algo.inria.fr/esf/ 10.1145/860854.860898 · Zbl 1072.68687 |
| [26] | M. Mezzarobba. Génération automatique de procédures numériques pour les fonctions D-finies. Rapport de stage, Master parisien de recherche en informatique, 2007. |
| [27] | M. Mezzarobba and B. Salvy. Effective bounds for P-recursive sequences. J. Symbolic Comput., to appear. arXiv:0904.2452v2. 10.1016/j.jsc.2010.06.024 · Zbl 1201.65219 |
| [28] | E. G. C. Poole. Introduction to the theory of linear differential equations. The Clarendon Press, Oxford, 1936. · Zbl 0014.05801 |
| [29] | B. Salvy and P. Zimmermann. Gfun: A Maple package for the manipulation of generating and holonomic functions in one variable. ACM Trans. Math. Softw., 20(2):163-177, 1994. http://algo.inria.fr/libraries/papers/gfun.html 10.1145/178365.178368 · Zbl 0888.65010 |
| [30] | R. P. Stanley. Enumerative combinatorics, volume 2. Cambridge University Press, 1999. · Zbl 0928.05001 |
| [31] | É. Tournier. Solutions formelles d’équations différentielles. Thèse de doctorat, Université de Grenoble, 1987. |
| [32] | J. van der Hoeven. Fast evaluation of holonomic functions. Theoret. Comput. Sci., 210(1):199-216, 1999. 10.1016/S0304-3975(98)00102-9 · Zbl 0912.68081 |
| [33] | J. van der Hoeven. Fast evaluation of holonomic functions near and in regular singularities. J. Symbolic Comput., 31(6):717-743, 2001. 10.1006/jsco.2000.0474 · Zbl 0982.65024 |
| [34] | J. van der Hoeven. Majorants for formal power series. Technical Report 2003-15, Université Paris-Sud, 2003. |
| [35] | J. van der Hoeven. Efficient accelero-summation of holonomic functions. J. Symbolic Comput., 42(4):389-428, 2007. 10.1016/j.jsc.2006.12.005 · Zbl 1125.34072 |
| [36] | J. van der Hoeven. On effective analytic continuation. Mathematics in Computer Science, 1(1):111-175, 2007. · Zbl 1154.68574 |
| [37] | J. van der Hoeven. Transséries et analyse complexe effective. Mémoire d’habilitation, Université Paris-Sud, 2007. |
| [38] | A. Waksman. On Winograd’s algorithm for inner products. IEEE Trans. Comput., C-19(4):360-361, 1970. 10.1109/T-C.1970.222926 · Zbl 0196.17104 |
| [39] | P. Zimmermann. The bit-burst algorithm. Slides of a talk at the workshop “Computing by the Numbers: Algorithms, Precision, and Complexity” for R. Brent 60th birthday, 2006. |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
