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Results 1 - 10
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2,993
Norm Convergence of Realistic Projection and Reflection Methods
, 2014
"... We provide sufficient conditions for norm convergence of various projection and reflection methods, as well as giving limiting examples regarding convergence rates. ..."
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We provide sufficient conditions for norm convergence of various projection and reflection methods, as well as giving limiting examples regarding convergence rates.
Norm convergence of nilpotent ergodic averages
, 2012
"... Abstract We show that multiple polynomial ergodic averages arising from nilpotent groups of measure preserving transformations of a probability space always converge in the L 2 norm. ..."
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Cited by 12 (0 self)
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Abstract We show that multiple polynomial ergodic averages arising from nilpotent groups of measure preserving transformations of a probability space always converge in the L 2 norm.
Norm convergence of multiple ergodic averages for commuting transformations
, 2007
"... Let T1,..., Tl: X → X be commuting measure-preserving transformations on a probability space (X, X, µ). We show that the multiple ergodic averages 1 PN−1 N n=0 f1(T n 1 x)... fl(T n l x) are convergent in L2 (X, X, µ) as N → ∞ for all f1,..., fl ∈ L ∞ (X, X, µ); this was previously established fo ..."
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Cited by 81 (4 self)
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Let T1,..., Tl: X → X be commuting measure-preserving transformations on a probability space (X, X, µ). We show that the multiple ergodic averages 1 PN−1 N n=0 f1(T n 1 x)... fl(T n l x) are convergent in L2 (X, X, µ) as N → ∞ for all f1,..., fl ∈ L ∞ (X, X, µ); this was previously established
Sobolev Norm Convergence of Stationary Subdivision Schemes
- In Surface and multiresolution methods
, 1997
"... . We show that Sobolev norm convergence of a stationary subdivision scheme is equivalent to standard norm convergence of the stationary subdivision scheme to a limit function in the Sobolev space. x1. Introduction Stationary subdivision is an iterative method for the generation of refinable functio ..."
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. We show that Sobolev norm convergence of a stationary subdivision scheme is equivalent to standard norm convergence of the stationary subdivision scheme to a limit function in the Sobolev space. x1. Introduction Stationary subdivision is an iterative method for the generation of refinable
A remark on operator-norm convergence of Trotter-Kato product formula
- Integral Equations Operator Theory
"... An example is given which clarifies the present situation of the operator norm convergence of Trotter-Kato product formula. It shows that the rate of convergence of the formula with respect to the operator norm obtained in [NZ2] is best possible. It also yields a counter-example of the operator norm ..."
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Cited by 5 (3 self)
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An example is given which clarifies the present situation of the operator norm convergence of Trotter-Kato product formula. It shows that the rate of convergence of the formula with respect to the operator norm obtained in [NZ2] is best possible. It also yields a counter-example of the operator
Sufficient Conditions For Norm Convergence Of The EM Algorithm
"... this paper we provide sufficient conditions for convergence of a general class of alternating estimationmaximization (EM) type continuous-parameter estimation algorithms with respect to a given norm. This class includes EM, penalized EM, Peter Green's OSL-EM, and other approximate EM algorithms ..."
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this paper we provide sufficient conditions for convergence of a general class of alternating estimationmaximization (EM) type continuous-parameter estimation algorithms with respect to a given norm. This class includes EM, penalized EM, Peter Green's OSL-EM, and other approximate EM
Operator Norm Convergence of Spectral Clustering on Level Sets
"... Following Hartigan (1975), a cluster is defined as a connected component of the t-level set of the underlying density, that is, the set of points for which the density is greater than t. A clustering algorithm which combines a density estimate with spectral clustering techniques is proposed. Our alg ..."
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Cited by 2 (1 self)
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the almost sure convergence in operator norm of the empirical graph Laplacian operator associated with the algorithm. Furthermore, we give the typical behavior of the representation of the data set into the feature space, which establishes the strong consistency of our proposed algorithm.
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