Publications      Back to my Home Page

Referred Articles

  1. B. Bank, M. Giusti, J. Heintz, Luis M. Pardo, Algorithms of Intrinsic Complexity for Point Searching in Compact Real Singular Hypersurfaces. Foundations of Computational Mathematics 12 (2012), 75-122.
  2. C. Beltrán, Luis M. Pardo, Fast Linear Homotopy to Find Approximate Zeros of Polynomial Systems. Foundations of Computational Mathematics 11 (2011), 95-129.
  3. C. Beltrán, Luis M. Pardo, Efficient Polynomial System Solving by Numerical Methods, in  "Randomization, Relaxation, and Complexity in Polynomial Equation Solving", L. Gurvits, P. Pebay, J.M. Rojas, D. Thompson, eds., Contemporary
    Mathematics, vol. 556, American Mathematical Society, 2011, 1-35.
  4. C. Beltrán, Luis M. Pardo, Smale's 17th Problem: Average Polynomial Time to Compute Affine and Projective Solutions. Journal of the American Mathematical Society 22 (2009), 363-385.
  5. C. Beltrán, Luis M. Pardo, Efficient polynomial system-solving by numerical methods. J. Fixed Point Theory and Applications 6 (2009), 65-85.
  6. J.L. Montaña, Luis M. Pardo, On the Vapnik-Chervonenkis dimension of computer programs which use transcendental elementary operations. Annals of Mathematics in Arti cial Intelligence 56 (2009), 371-388.
  7. B. Bank, M. Giusti, J. Heintz, Luis M. Pardo, On the intrinsic complexity of point finding in real singular hypersurfaces. Information Processing Letters 109 (2009), 1141-1144.
  8. C. Beltrán, Luis M. Pardo, On Smale's 17th Problem: A probabilistic positive solution. Foundations of Computational Mathematics 8 (2008) 1-43.
  9. C. E. Borges, Luis M. Pardo, On the probability distribution of data at points in real complete intersection varieties. Journal of Complexity 24 (2008) 492-523.
  10. M. Callau, J.L. Montaña, Luis M. Pardo, VC Dimension Bounds for Analytic Algebraic Computations, in  Lecture Notes in Computer Science 5092, X. Hu & J. Wang eds., Springer Verlag, 2008, 62-71.
  11. C. Beltrán, Luis M. Pardo, Estimates on the distribution of the condition number of singular matrices. Foundations of Computational Mathematics 7 (2007), 87-134.
  12. C. Beltrán, Luis M. Pardo, On the probability distribution of singular varieties of given co-rank, Journal of Symbolic Computation 42 (2007), 4-29.
  13. C. Beltrán, Luis M. Pardo, On the Complexity of Non Universal Polynomial Equation Solving: Old and New Results, in "Foundations of Computational Mathematics, Santander 2005", L.M. Pardo, A. Pinkus, E. Sülli & M. Todd eds., London Mathematical Society Lecture Notes Series 331, Cambridge University Press, 2006, 1-35.
  14. C. Beltrán, Luis M. Pardo, On The Probability Distribution of Condition Numbers of Complete Intersection Varieties and The Average Radius of Convergence of Newton's Method in the Under-determined Case. Mathematics of Computation  76 (2007) 1393-1424.
  15. C.L. Alonso, J.L. Montaña, Luis M. Pardo, On the number of random digits required in MonteCarlo integration of definable functions, in Lecture Notes in Computer Science 3618 (2005), 83-94.
  16. C. Beltrán, Luis M. Pardo, Upper Bounds on the distribution of the condition number of singular matrices. Comptes Rendues Acad. Sci. Paris, Série I, Mathématiques 340 (2005), 915-919.
  17. B. Bank, M. Giusti, J. Heintz, Luis M. Pardo, Generalized polar varieties: geometry and algorithms. Journal of Complexity 21 (2004), 377-412.
  18. B. Bank, M. Giusti, J. Heintz, L.M. Pardo, Generalized Polar Varieties and an Efficient Real Elimination Procedure. Kybernetika  40 (2004), 519-550.
  19.  J. San Martín, L.M. Pardo, Deformation Tehcniques that solve Generalised Pham Systems. Theoretical Computer Science  315 (2004), 593-625.
  20. D. Castro, M. Giusti, J. Heintz, G. Matera, Luis M. Pardo, The Hardness of Polynomial Equation Solving. Foundations of Computational Mathematics 3 (2003), 347-420.
  21.  D. Castro,  J. San Martín, Luis M. Pardo, Systems of rational polynomial equations have polynomial size approximate zeros on the average. Journal of Complexity 19 (2003), 161-209.
  22. D. Castro, J.L. Montaña, J. San Martín, Luis M. Pardo, The distribution of condition numbers of rational data of bounded bit length. Foundations of Computational Mathematics 2 (2002), 1-52.
  23.  T. Krick, Luis M. Pardo, M. Sombra, Sharp estimates for the arithmetic Nullstellensatz. Duke Mathematical Journal 109 (2001), 521-598.
  24. D. Castro, K. Haegele, J.E. Morais, Luis M. Pardo, Kronecker's and Newton's approaches to solving: a fi rst comparison. Journal of Complexity 17 (2001), 212-303.
  25. M. Aldaz,  G. Matera, J.L. Montaña, Luis M. Pardo, A new method to obtain lower bounds for polynomial evaluation. Theoret. Comput. Sci. 259 (2001), 577-596.
  26. M. Aldaz,  J. Heintz, G. Matera, J.L. Montaña, Luis M. Pardo, Time-space tradeoffs in algebraic complexity theory.  Journal of Complexity 16 (2000),  2-49.
  27. K. Hägele, J.E. Morais, L.M. Pardo, M. Sombra, The intrinsic complexity of the arithmetic Nullstellensatz. Journal of Pure & Applied Algebra 146 (2000), 103--183.
  28. J. Heintz, G. Matera,  L.M. Pardo, R. Wachenchauzer. "The intrinsic complexity of parametric elimination methods". Electron. J. SADIO 1 (1998), 37--51.
  29. M. Aldaz,  J. Heintz, G. Matera, J.L. Montaña, Luis M. Pardo, Time-space tradeoffs for polynomial evaluation. Comptes Rendues Acad. Sci. Paris, Série I, Mathématiques 327 (1998), 907--912.
  30. M. Giusti, J. Heintz, J. Morgenstern, J.E. Morais,  Luis M. Pardo, Straight-line programs in geometric elimination theory. Journal of Pure & Applied Algebra 124 (1998),  101--146.
  31. J.L. Montaña, Luis M. Pardo, On Kolmogorov complexity in the real Turing machine setting. Information Processing Letters 67 (1998), 81--86.
  32. M. Aldaz, J. Heintz, G. Matera, J.L. Montaña, Luis M. Pardo, Combinatorial Hardness Proofs for Polynomial Evaluation, in Lecture Notes in Computer Science 1450, J. Gruska, J. Zlatuska eds, Springer Verlag, 1998, 167-175.
  33. M. Giusti, J. Heintz, J.E. Morais,  Luis M. Pardo, Le rôle des structures de données dans les problèmes  d'élimination. Comptes Rendues Acad. Sci. Paris, Série I, Mathématiques 325 (1997), 1223--1228.
  34. M. Giusti, K. Haegele, J. Heintz, J.E. Morais, J.L. Montaña, Luis M- Pardo, Lower bounds for diophantine approximations. Journal of Pure and Applied Algebra 117 (1997), 277-317.
  35.  J.L. Montaña, J.E. Morais,  Luis M. Pardo, Lower bounds for arithmetic networks II : Sum of Betti numbers. Applicable Algebra in Engineering Communications &  Computing  7 (1996),  41--51.
  36. T. Krick, Luis M. Pardo, A computational method for Diophantine approximation, in Algorithms in Algebraic Geometry, Progress in Mathematics 143, L. González Vega & T. Recio eds., Birkhauser Verlag, 1996, 193-253.
  37. Lui M. Pardo, How lower and upper complexity bounds meet in elimination theory, in Lecture Notes in Computer Science 948, G. Cohen, M. Giusti & T. Mora, eds., Springer Verlag, 1995, 33-69.
  38. M. Giusti, J. Heintz, J.E. Morais, Luis M. Pardo, When polynomial equation systems can be "solved" fast?, Lecture Notes in Computer Science 948, G. Cohen, M. Giusti & T. Mora, eds., Springer Verlag, 1995, 205-231.
  39. F. Cucker, J.L. Montaña, Luis M. Pardo, Models for Parallel Computation with real Numbers, in "Number Theoretic and Algebraic Methods in Computer Science (Moscow, 1993)", A.J. van der Poorten, I. Shparlinski & H.G. Zimmer eds.,
    World Scienti c, 1995, 53-63.
  40. M. Giusti, N. Fitchas (L. M. Pardo, J. Heintz,  J. Sabia, P. Solerno), F. Smietansky, Sur la Complexité du Théorème des Zéros, in Approximation and Optimization 8, J. Guddat et al. eds., Peter Lange Verlag, 1995, 274-329.
  41. J.L. Montaña, Luis M. Pardo, T. Recio,  A Note on Rabin's Width of a Complete Proof. Computational Complexity 4 (1994), 12-36.
  42. T. Krick, L.M. Pardo, Une approche informatique pour l'approximation diophantienne.  Comptes Rendues Acad. Sci. Paris, Série I, Mathématiques 318 (1994), 407-412.
  43.  J.L. Montaña, Luis M. Pardo, Lower bounds for arithmetic networks. Applicable Algebra in Engineering Communications &  Computing  4 (1993),  1-24.
  44. J.L. Montaña, Luis M. Pardo, R. Ramanakoraisina, An extension of Warren's lower bounds for approximations. Journal of Pure and Applied Algebra 87 (1993), 251-258.
  45. F. Cucker, J.L. Montaña, Luis M. Pardo, Time bounded computations over the reals. International Journal of Algebra & Computation 2 (1992), 395--408.
  46. J.L. Montaña, Luis M. Pardo, T. Recio, The Non-Scalar Model of Complexity in Computational Geometry, Progress in Mathematics 94, T. Mora & C. Traverso eds., Birkhauser Verlag, 1991, 347-361.
  47. T. Recio, Luis M. Pardo, Rabin's Width of a Complete Proof and the Width of a Semi-Algebraic Set, in Lecture Notes in Computer Science 378, J.H. Davenport ed., 1989, 456-462.
  48. F. Cucker, Luis 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 Lecture Notes in Computer Science 356, L. Huguet & A. Poli eds., 1989, 161-181.
  49. L.M. PardoVasallo, The polynomial separation problem in Specr(A). Comptes Rendus Mathématiques  Acad. Sci. Canada 9 (1987) 17--20.


Other Publications:

  1. B.Bank, M. Giusti, J. Heintz, Luis M. Pardo,  Bipolar varieties and real solving of a singular polynomial equation, Jaen Journal on Approximation 2 (2010), 65-77.5).
  2. M. Giusti , Luis M. Pardo. Arithmetic with polynomials, rational functions and power series, in "Computer Algebra Handbook", Grabmeier, Kaltofen & Weispfenning eds., Springer Verlag, 2003, 13-17.
  3. M. Giusti, Luis M. Pardo, V. Weispfenning, Algorithms of Commutative Algebra and Algebraic Geometry: Algorithms for polynomial ideals and their varieties, in "Computer Algebra Handbook", Grabmeier, Kaltofen & Weispfenning eds., Springer Verlag, 2003, 51-54.
  4. T. Recio, Luis M. Pardo, El Profesor Abellanas y la falsa moneda, Revista de la Sociedad Puig-Adams 58 (2001), 78.94.
  5. L.M. Pardo, Universal Elimination requires exponential running time. In  "Actas EACA'2000", A. Montes ed.,  UPC, 2000, 25-50.
  6. M. Aldaz, J.E. Morais, J.L. Montaña, Luis M. Pardo, Lower Bounds for the complexity of arithmetic problems with integer inputs, in "The Bulletin of the Workshop on Model Theory and Complexity", Kronos, 1997, 3-8.
  7. F. Cucker, J.L. Montaña, Luis M. Pardo, A non-deterministic time hierarchy over the reals. Extracta Math. 8 (1993), 87--91