Cuadro de texto: Publications      Back to my Home Page  C. Beltrán, Luis M. Pardo. "Smale’s 17th Problem: Average Polynomial Time to Compute Affine and projective Solutions”. Journal of the Amer. Math. Soc., 2008, PII S0894-0347-08-00630-9 (to appear in print). C. E. Borges, Luis M. Pardo. “On the probability Distribution of Data al Points in Real Complete Intersection Varieties”. Journal of Complexity vol. 24, No. 4 (2008) 492-523. C. Beltrán, Luis M. Pardo. "On Smale’s 17th Problem: A Positive Answer in Probabilistic Polynomial Time ". Found. Comput. Math. 8 (2008) 1-43. C. Beltrán, Luis M. Pardo. "On The Probability Distribution of Condition Numbers of Complete Intersection Varieties and The Average Radius of Convergece of Newton's Method in the Under-determined Case". Mathematics of Computation  76 (2007) 1393-1424. C. Beltrán, Luis M. Pardo. "On the Probability Distribution of Singular Varieties of Given Corank". Journal of Symbolic Computation  42  (2007) 4-29. C. Beltrán, Luis M. Pardo. "Estimates on the Probability Distribution of Condition Numbers of Singular Matrices". Found. Comput. Math.  7 (2007) 87-134. C. Beltrán, L.M. Pardo. "Upper bounds on the distribution of the condition number of singular matrices". Comptes Rendus Mathématique   340  (2005) 915-919. B. Bank, M. Giusti, J. Heintz, L.M. Pardo. "Generalized polar varieties: Geometry and algorithms".  J. of Complexity 21 (2005) 377-412. B. Bank, M. Giusti, J. Heintz, L.M. Pardo. "Generalized Polar Varieties and an Efficient Real Elimination Procedure". Kybernetika vol 40 (2004) 519-550. J. San Martín, L.M. Pardo. "Deformation Tehcniques that solve Generalised Pham Systems".   Theoret. Comput. Sci.  315 (2004) 593-625. D. Castro, M. Giusti, J. Heintz, G. Matera, L.M. Pardo. "The hardness of polynomial equation solving". Found. Comput. Math. 3 (2003) 347-420. D. Castro,  J. San Martín, L.M. Pardo. "Systems of rational polynomial equations have polynomial size approximate zeros on the average". J. Complexity 19 (2003), 161-209. D. Castro,  J. San Martín, J.L. Montaña, L.M. Pardo. "The distribution of condition numbers of rational data of bounded bit length". Found. Comput. Math. 2 (2002), 1-52. T. Krick, L.M. Pardo, M. Sombra. "Sharp estimates for the arithmetic Nullstellensatz". Duke Math. J. 109 (2001), 521--598. M. Aldaz,  G. Matera, J.L. Montaña, L.M. Pardo. "A new method to obtain lower bounds for polynomial evaluation". Theoret. Comput. Sci. 259 (2001), 577-596. D. Castro, K. Hägele, J.E. Morais, L.M. Pardo. "Kronecker's and Newton's approaches to solving: a first comparison". J. Complexity 17 (2001), 212-303. M. Aldaz,  J. Heintz, G. Matera, J.L. Montaña, L.M. Pardo. "Time-space tradeoffs in algebraic complexity theory".  J. Complexity 16 (2000),  2-49. K. Hägele, J.E. Morais, L.M. Pardo, M. Sombra. "On the intrinsic complexity of the arithmetic Nullstellensatz". J. Pure Appl. Algebra 146 (2000), 103--183. J. Heintz, G. Matera,  L.M. Pardo, R. Wachenchauzer. "The intrinsic complexity of parametric elimination methods". Electron. J. SADIO 1 (1998), 37--51. M. Aldaz,  J. Heintz, G. Matera, J.L. Montaña, L.M. Pardo." Time-space tradeoffs for polynomial evaluation". C. R. Acad. Sci. Paris Sér. I Math. 327 (1998), 907--912. J.L. Montaña, L.M. Pardo. "On Kolmogorov complexity in the real Turing machine setting". Inform. Process. Lett. 67 (1998), 81--86. M. Giusti, J. Heintz, J. Morgenstern, J.E. Morais,  L.M. Pardo. "Straight-line programs in geometric elimination theory". J. Pure Appl. Algebra 124 (1998),  101--146. M. Giusti, J. Heintz, J.E. Morais,  L.M. Pardo. "Le rôle des structures de données dans les problèmes d'élimination".  C. R. Acad. Sci. Paris Sér. I Math. 325 (1997), 1223--1228. M. Giusti, J. Heintz, K. Hägele, J.L. Montaña, J.E. Morais,  L.M. Pardo. "Lower bounds for Diophantine approximations".  J. Pure Appl. Algebra 117&118 (1997), 277--317. J.L. Montaña, J.E. Morais,  L.M. Pardo.  "Lower bounds for arithmetic networks II : Sum of Betti numbers". Appl. Algebra Engrg. Comm. Comput. 7 (1996),  41--51. J.L. Montaña, L.M. Pardo, T. Recio. "A note on Rabin's width of a complete proof". Comput. Complexity 4 (1994), 12--36. T. Krick, L.M. Pardo. "Une approche informatique pour l'approximation diophantienne".  C. R. Acad. Sci. Paris Sér. I Math. 318 (1994), 407--412. F. Cucker, J.L. Montaña, L.M. Pardo."A non-deterministic time hierarchy over the reals". Extracta Math. 8 (1993) 87--91. J.L. Montaña, L.M. Pardo, R. Ramanakoraisina."An extension of Warren's lower bounds for approximations. J. Pure Appl. Algebra 87 (1993) 251--258. J.L. Montaña, L.M. Pardo."Lower bounds for arithmetic networks". Appl. Algebra Engrg. Comm. Comput. 4 (1993)  1--24. F. Cucker, J.L. Montaña, L.M. Pardo."Time bounded computations over the reals". Internat. J. Algebra Comput. 2 (1992) 395--408. L.M. PardoVasallo. "The polynomial separation problem in Specr(A)". C. R. Math. Rep. Acad. Sci. Canada 9 (1987) 17--20. Research Articles in Conference Proceedings J.L. Montaña, L.M. Pardo, M. Callau. “VC Dimension Bounds for Analytic Algebraic Computations”. In Proc. CooCoon 2008, X. Hu, J. Wang eds., Lect. Notes in Comput. Sci. 5092, Springer, 2008,62-71 C. Beltrán, L.M. Pardo."On  the Complexity of Nonuniversal Polynomial Equation Solving: old and new results". In Foundations of Computational Mathematics 2005: Santander,  L.M. Pardo, A. Pinkus, E. Sülli, M.J. Todd (eds.), Cambridge University Press, (2006) 1-36. C.L. Alonso, J.L. Montaña, L.M. Pardo."On the Number of random digits required in Monte Carlo integration of definable functions". In Proc. MFCS'2005.,J. Jedrzejowicz, A. Szepietowski , eds. Lect. Notes in Comput. Sci. 3618 (2005) 83-94. L.M. Pardo. "Universal Elimination requires exponential running time". In  Actas EACA'2000, A. Montes ed.  UPC (2000) 25-50. M. Aldaz,  J. Heintz, G. Matera, J.L. Montaña, L.M. Pardo. "Combinatorial hardness proofs for polynomial evaluation (extended abstract)". In  Mathematical foundations of computer science, MFCS'98 (Brno), Lecture Notes in Computer Science  1450, Springer Verlag, Berlin  (1998) 167--175. T. Krick, L.M. Pardo. "A computational method for Diophantine approximation". In Algorithms in algebraic geometry and applications (Santander, 1994), Progr. Math., 143, Birkhäuser, Basel,  (1996) 193--253. F. Cucker, J.L. Montaña, L.M. Pardo. "Models for parallel computation with real numbers". In Number-theoretic and algebraic methods in computer science (Moscow, 1993),  World Sci. Publishing, River Edge, NJ, (1995) 53--63. L.M. Pardo."How lower and upper complexity bounds meet in elimination theory". In Applied algebra, algebraic algorithms and error-correcting codes (Paris, 1995),Lecture Notes in Comput. Sci., 948, SpringerVerlag , Berlin  (1995) 33--69. Noaï Fitchas (With the collaboration of  J. Heintz, L.M. Pardo, J. Sabia, P. Solernó) M. Giusti, F. Smietanski."Sur la complexité du théorème des zéros".In Approx. Optim., 8, Approximation and optimization in the Caribbean, II (Havana, 1993), Peter Lang Verlag,  Frankfurt am Main, (1995) 274--329. M. Giusti, J. Heintz, K. Hägele, J.L. Montaña, J.E. Morais,  L.M. Pardo. "When polynomial equation systems can be "solved" fast?". In Applied algebra, algebraic algorithms and error-correcting codes (Paris, 1995),Lecture Notes in Comput. Sci., 948, SpringerVerlag , Berlin  (1995)  205-231. J.L. Montaña, L.M. Pardo, T. Recio."The nonscalar model of complexity in computational geometry". Effective methods in algebraic geometry (Castiglioncello, 1990), 347--361, Progr. Math., 94, Birkhäuser Boston  (1991) 347--361. L.M. Pardo, T. Recio."Rabin's width of a complete proof and the width of a semialgebraic set". In Proc. EUROCAL '87 (Leipzig, 1987) Lecture Notes in Comput. Sci., 378, Springer, Berlin,(1989) 456--462. F. Cucker, L.M. Pardo, M. Raimondo, T. Recio, M.F. Roy."On the computation of the local and global analytic branches of a real algebraic curve". In Applied algebra, algebraic algorithms and error- correcting codes (Menorca, 1987) Lecture Notes in Comput. Sci., 356, Springer, Berlin  (1989) 161--181. Editing: M. Giusti, Luis M. Pardo (eds.). "ISSAC'2002".  Journal of Symbolic Computation vol.  36  Issues 3-4, (2003) 287-683. T. Lickteig, Luis M. Pardo (eds.). "Schonhage Festschrift". J. of Complexity 21, Issue 4 (2005). Luis M. Pardo, A. Pinkus, E. Sülli, M.J. Todd (eds.). "Foundations of Computational Mathematics 2005: Santander". Cambridge University Press (2006) Contributions to Books : M. Giusti , L.M. Pardo. "Arithmetic with polynomials, rational functions and power series". In Handbook of Computer Algebra. Grabmeier, Kaltofen & Weispfenning eds., Springer Verlag (2003) 13-17.. M. Giusti , L.M. Pardo, V. Weispfenning. "Algorithms of Commutative Algebra and Algebraic Geometry: Algorithms for polynomial ideals and their varieties". In Handbook of Computer Algebra. Grabmeier, Kaltofen & Weispfenning eds., Springer Verlag (2003) 51-54.