Lattice Rules for Multivariate Approximation in the Worst Case Setting

[1]  Henryk Wozniakowski,et al.  When Are Quasi-Monte Carlo Algorithms Efficient for High Dimensional Integrals? , 1998, J. Complex..

[2]  Henryk Wozniakowski,et al.  Liberating the weights , 2004, J. Complex..

[3]  E. Novak,et al.  Tractability of Approximation for Weighted Korobov Spaces on Classical and Quantum Computers , 2002, Found. Comput. Math..

[4]  Fred J. Hickernell,et al.  Error Analysis of Splines for Periodic Problems Using Lattice Designs , 2006 .

[5]  Josef Dick.  On the convergence rate of the component-by-component construction of good lattice rules , 2004, J. Complex..

[6]  Henryk Wozniakowski,et al.  Information-based complexity , 1987, Nature.

[7]  F. J. Hickernell,et al.  Tractability of Multivariate Integration for Periodic Functions , 2001, J. Complex..

[8]  Ian H. Sloan,et al.  Component-by-component construction of good lattice rules , 2002, Math. Comput..

[9]  Frances Y. Kuo,et al.  Reducing the construction cost of the component-by-component construction of good lattice rules , 2004, Math. Comput..

[10]  Dirk Nuyens,et al.  Fast algorithms for component-by-component construction of rank-1 lattice rules in shift-invariant reproducing kernel Hilbert spaces , 2006, Math. Comput..

[11]  Frances Y. Kuo,et al.  Component-by-component constructions achieve the optimal rate of convergence for multivariate integration in weighted Korobov and Sobolev spaces , 2003, J. Complex..

[12]  Frances Y. Kuo,et al.  Component-by-Component Construction of Good Lattice Rules with a Composite Number of Points , 2002, J. Complex..

[13]  Frances Y. Kuo,et al.  Constructing Good Lattice Rules with Millions of Points , 2004 .

[14]  I. Sloan.  Lattice Methods for Multiple Integration , 1994 .

[15]  I. H. SLOAN,et al.  Constructing Randomly Shifted Lattice Rules in Weighted Sobolev Spaces , 2002, SIAM J. Numer. Anal..

[16]  H. Woxniakowski.  Information-Based Complexity , 1988 .

[17]  Henryk Wozniakowski,et al.  On the Power of Standard Information for Weighted Approximation , 2001, Found. Comput. Math..

[18]  Владимир Николаевич Темляков,et al.  О восстановлении пер иодических функций н ескольких переменных по значен иям в узлах теоретико числовых сеток , 1986 .

[19]  Vladimir N. Temlyakov,et al.  On Approximate Recovery of Functions with Bounded Mixed Derivative , 1993, J. Complex..

[20]  S. Y. Cheng,et al.  Recent advances in scientific computing and partial differential equations : international conference on the occasion of Stanley Osher's 60th birthday, December 12-15, 2002, Hong Kong Baptist University, Hong Kong , 2003 .

[21]  Henryk Wozniakowski,et al.  Weighted Tensor Product Algorithms for Linear Multivariate Problems , 1999, J. Complex..

[22]  Frances Y. Kuo,et al.  On the step-by-step construction of quasi-Monte Carlo integration rules that achieve strong tractability error bounds in weighted Sobolev spaces , 2002, Math. Comput..

[23]  Henryk Wozniakowski,et al.  Tractability of Multivariate Integration for Weighted Korobov Classes , 2001, J. Complex..

[24]  Frances Y. Kuo,et al.  Component-By-Component Construction of Good Intermediate-Rank Lattice Rules , 2003, SIAM J. Numer. Anal..

[25]  Vladimir Temlyakov,et al.  APPROXIMATE RECOVERY OF PERIODIC FUNCTIONS OF SEVERAL VARIABLES , 1987 .