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When Are Quasi-Monte Carlo Algorithms Efficient for High Dimensional Integrals?
This paper presents a partial answer to why quasi-Monte Carlo algorithms can work well for arbitrarily larged. 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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Explicit Cost Bounds of Algorithms for Multivariate Tensor Product Problems
We study multivariate tenser product problems in the worst case and average case settings. Expand
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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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Estimating the Largest Eigenvalue by the Power and Lanczos Algorithms with a Random Start
This paper addresses the problem of computing an approximation to the largest eigenvalue of an $n \times n$ large symmetric positive definite matrix with relative error at most $\varepsilon $. Expand
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A general theory of optimal algorithms
By reading, you can know the knowledge and things more, not only about what you get from people to people. Expand
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Information-based complexity
Information-based complexity seeks to develop general results about the intrinsic difficulty of solving problems where available information is partial or approximate and to apply these results to specific problems. Expand
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Convergence and Complexity of Newton Iteration for Operator Equations
An optimal convergence condition for Newton iteration in a Banach space is established. Expand
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Average case complexity of multivariate integration
We study the average case complexity of multivariate integration for the class of continuous functions of d variables equipped with the classical Wiener sheet measure. To derive the average caseExpand
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