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High dimensional polynomial interpolation on sparse grids
We study polynomial interpolation on a d-dimensional cube, where d is large. Expand
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Tractability of Multivariate Problems
Multivariate problems occur in many applications. These problems are defined on spaces of d-variate functions and d can be huge – in the hundreds or even in the thousands. Some high-dimensionalExpand
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Deterministic and Stochastic Error Bounds in Numerical Analysis
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The inverse of the star-discrepancy depends linearly on the dimension
We study bounds on the classical ∗-discrepancy and on its inverse. Let n∞(d, e) be the inverse of the ∗-discrepancy, i.e., the minimal number of points in dimension d with the ∗-discrepancy at mostExpand
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Special issue
“Criminal Justice Drug Abuse Treatment Studies” (CJ- DATS) supports much of our corrections-based treatment research as part of the TCU CJ-DATS Project. Expand
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High dimensional integration of smooth functions over cubes
Summary.We construct a new algorithm for the numerical integration of functions that are defined on a $d$-dimensional cube. It is based on the Clenshaw-Curtis rule for $d=1$ and on Smolyak'sExpand
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Quantum Complexity of Integration
  • E. Novak
  • Computer Science, Physics
  • J. Complex.
  • 29 August 2000
It is known that quantum computers yield a speed-up for certain discrete problems. Here we want to know whether quantum computers are useful for continuous problems. We study the computation of theExpand
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Simple Cubature Formulas with High Polynomial Exactness
Abstract. We study cubature formulas for d -dimensional integrals with arbitrary weight function of tensor product form. We present a construction that yields a high polynomial exactness: for fixedExpand
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Global Optimization Using Hyperbolic Cross Points
We propose a new numerical method for finding the global minimum of a real-valued function defined on a d-dimensional box. Expand
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