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170,579
On the Hardness of Approximate Multivariate Integration
 Proc. of APPROX
, 2003
"... We show that it is NPhard to 2nkapproximate the integral of a positive, smooth, polynomialtime computable nvariate function, for any fixed integer k. 1 ..."
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Cited by 2 (0 self)
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We show that it is NPhard to 2nkapproximate the integral of a positive, smooth, polynomialtime computable nvariate function, for any fixed integer k. 1
Tractability of Multivariate Integration for Periodic Functions
 J. Complexity
, 2000
"... We study multivariate integration in the worst case setting for weighted Korobov spaces of smooth periodic functions of d variables. We wish to reduce the initial error by a factor # for functions from the unit ball of the weighted Korobov space. Tractability means that the minimal number of functio ..."
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Cited by 14 (2 self)
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We study multivariate integration in the worst case setting for weighted Korobov spaces of smooth periodic functions of d variables. We wish to reduce the initial error by a factor # for functions from the unit ball of the weighted Korobov space. Tractability means that the minimal number
L2 discrepancy and multivariate integration
 IN “ANALYTIC NUMBER THEORY – ESSAYS IN HONOR OF KLAUS ROTH,” CAMBRIDGE UNIVERSITY PRESS, TO APPEAR. GRZEGORZ W. WASILKOWSKI AND HENRYK WO´ZNIAKOWSKI
"... We study the L2 discrepancy of measurable subsets B(t) of Rd for t ∈ D with D ⊆ Rτ(d) for some integer τ(d). We assume that t is distributed according to the density ρ, R D ρ(t) dt = 1. For specific cases of B(t), we obtain various discrepancies including probably the most celebrated discrepancy an ..."
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Cited by 1 (1 self)
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anchored at zero studied by Roth, or its analogue anchored at α, the quadrant discrepancy anchored at α, the unanchored discrepancy, and the periodic ball discrepancy. We show that the L2 discrepancy for sets B(t) corresponds to multivariate integration for the Hilbert space with some reproducing kernel Kd
Multivariable Integrated Model Predictive Control of Nuclear
"... Abstract. This paper presents the method of multivariable integrated model predictive control for the nuclear power plant, including designing controller and building the modeling of turbine and oncethrough steam generator. The simulation results show that the rotate speed of turbine and outlet pre ..."
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Cited by 1 (0 self)
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Abstract. This paper presents the method of multivariable integrated model predictive control for the nuclear power plant, including designing controller and building the modeling of turbine and oncethrough steam generator. The simulation results show that the rotate speed of turbine and outlet
Multivariate Integration On Hypercubic And Mesh Networks
, 1998
"... We analyze a class of adaptive algorithms for integration over Ndimensional hyperrectangular or simplical regions, on distributed systems. An adaptive algorithm attempts to achieve the requested accuracy by refining the subdivision of the integration region, thus allowing for a concentration of s ..."
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Cited by 8 (5 self)
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We analyze a class of adaptive algorithms for integration over Ndimensional hyperrectangular or simplical regions, on distributed systems. An adaptive algorithm attempts to achieve the requested accuracy by refining the subdivision of the integration region, thus allowing for a concentration
On strong tractability of weighted multivariate integration
, 2004
"... . We prove that for every dimension s and every number n of points, there exists a pointset Pn,s whose weighted unanchored L ∞ discrepancy is bounded from above by C(b)/n1/2−b independently of s provided that the sequence = {γk} has � ∞ k=1 γa k < ∞ for some (even arbitrarily large) a. Here ..."
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Cited by 7 (2 self)
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b is a positive number that could be chosen arbitrarily close to zero and C(b) depends on b but not on s or n. This result yields strong tractability of the corresponding integration problems including approximation of weighted integrals � D f(x) ρ(x) dx over unbounded domains such as D = Rs
Adaptive Multivariate Integration using MPI
, 1997
"... We describe a coarse grain parallel algorithm for multivariate adaptive integration using MPI. The algorithm is asynchronous in nature and allows for load balancing. Timing results show good speedups obtained on a network of workstations for a class of integrals from Bayesian statistics. 1 Introduc ..."
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We describe a coarse grain parallel algorithm for multivariate adaptive integration using MPI. The algorithm is asynchronous in nature and allows for load balancing. Timing results show good speedups obtained on a network of workstations for a class of integrals from Bayesian statistics. 1
Statistical Analysis of Cointegrated Vectors
 Journal of Economic Dynamics and Control
, 1988
"... We consider a nonstationary vector autoregressive process which is integrated of order 1, and generated by i.i.d. Gaussian errors. We then derive the maximum likelihood estimator of the space of cointegration vectors and the likelihood ratio test of the hypothesis that it has a given number of dimen ..."
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Cited by 2735 (12 self)
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We consider a nonstationary vector autoregressive process which is integrated of order 1, and generated by i.i.d. Gaussian errors. We then derive the maximum likelihood estimator of the space of cointegration vectors and the likelihood ratio test of the hypothesis that it has a given number
Modeling and Forecasting Realized Volatility
, 2002
"... this paper is built. First, although raw returns are clearly leptokurtic, returns standardized by realized volatilities are approximately Gaussian. Second, although the distributions of realized volatilities are clearly rightskewed, the distributions of the logarithms of realized volatilities are a ..."
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Cited by 547 (50 self)
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are approximately Gaussian. Third, the longrun dynamics of realized logarithmic volatilities are well approximated by a fractionallyintegrated longmemory process. Motivated by the three ABDL empirical regularities, we proceed to estimate and evaluate a multivariate model for the logarithmic realized volatilities
Exponential Convergence and Tractability of Multivariate Integration for Korobov Spaces
, 2010
"... In this paper we study multivariate integration for a weighted Korobov space for which the Fourier coefficients of the functions decay exponentially fast. This implies that the functions of this space are infinitely times differentiable. Weights of the Korobov space monitor the influence of each var ..."
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Cited by 7 (4 self)
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In this paper we study multivariate integration for a weighted Korobov space for which the Fourier coefficients of the functions decay exponentially fast. This implies that the functions of this space are infinitely times differentiable. Weights of the Korobov space monitor the influence of each
Results 1  10
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170,579