Lattice Builder Manual Software Package for Constructing Rank-1 Lattices

- Main Page
- Related Pages
- Modules
- Namespaces
- Classes
- Files
- Examples

All Classes Namespaces Files Functions Variables Typedefs Enumerations Friends Modules Pages
Bibliography

[1]

  L. Afflerbach and H. Grothe. Calculation of Minkowski-reduced lattice bases. Computing, 35:269–276, 1985.

[2]

  Henri Cohen. A course in computational algebraic number theory, volume 138. Springer, 1993.

[3]

  J. H. Conway and N. J. A. Sloane. Sphere Packings, Lattices and Groups. Grundlehren der Mathematischen Wissenschaften 290. Springer-Verlag, New York, 3rd edition, 1999.

[4]

  R. Cools, F. Y. Kuo, and D. Nuyens. Constructing embedded lattice rules for multivariate integration. SIAM Journal on Scientific Computing, 28(16):2162–2188, 2006.

[5]

  J. Dick, F. Pillichshammer, and B. J. Waterhouse. The construction of good extensible rank-1 lattices. Mathematics of Computation, 77(264):2345–2373, 2008.

[6]

  U. Dieter. How to calculate shortest vectors in a lattice. Mathematics of Computation, 29(131):827–833, 1975.

[7]

  G. S. Fishman. Multiplicative congruential random number generators with modulus 2^eta: An exhaustive analysis for eta=32 and a partial analysis for eta=48. Mathematics of Computation, 54(189):331–344, Jan 1990.

[8]

  S. Joe and I. H. Sloan. On computing the lattice rule criterion R. Mathematics of Computation, 59:557–568, 1992.

[9]

  D. E. Knuth. The Art of Computer Programming, Volume 2: Seminumerical Algorithms. Addison-Wesley, Reading, MA, second edition, 1981.

[10]

  D. E. Knuth. The Art of Computer Programming, Volume 2: Seminumerical Algorithms. Addison-Wesley, Reading, MA, third edition, 1998.

[11]

  P. L'Ecuyer and R. Couture. An implementation of the lattice and spectral tests for multiple recursive linear random number generators. INFORMS Journal on Computing, 9(2):206–217, 1997.

[12]

  P. L'Ecuyer and R. Couture. An implementation of the lattice and spectral tests for multiple recursive linear random number generators. INFORMS Journal on Computing, 9(2):206–217, 1997.

[13]

  P. L'Ecuyer. Random numbers for simulation. Communications of the ACM, 33(10):85–97, 1990.

[14]

  P. L'Ecuyer. Tables of maximally equidistributed combined LFSR generators. Mathematics of Computation, 68(225):261–269, 1999.

[15]

  A. K. Lenstra, H. W. Lenstra, and L. Lovász. Factoring polynomials with rational coefficients. Math. Ann., 261:515–534, 1982.

[16]

  G. Marsaglia. Random numbers fall mainly in the planes. Proceedings of the National Academy of Sciences of the United States of America, 60:25–28, 1968.

[17]

  V. Sinescu and S. Joe. Good lattice rules with a composite number of points based on the product weighted star discrepancy. In A. Keller, S. Heinrich, and H. Niederreiter, editors, Monte Carlo and Quasi-Monte Carlo Methods 2006, pages 645–658. Springer, 2008.

[18]

  V. Sinescu and P. L'Ecuyer. Existence and contruction of shifted lattice rules with an arbitrary number of points and bounded worst-case error for general weights. Journal of Complexity, 27(5):449–465, 2011.