A Norm Convergence Result on Random Products ofRelaxed Projections
نویسنده
چکیده
Suppose X is a Hilbert space and C
منابع مشابه
A Norm Convergence Result on Random Products of Relaxed Projections in Hilbert Space
Suppose A' is a Hilbert space and C\.Cjy are closed convex intersecting subsets with projections P\, ... , P^ ■ Suppose further r is a mapping from N onto {\, ... , N) that assumes every value infinitely often.We prove (a more general version of) the following result: If the TV-tuple (C\, ... , C#) is "innately boundedly regular", then the sequence (xn), defined by xo € X arbitrary, xn+i := Pr(...
متن کاملOn convergence of sample and population Hilbertian functional principal components
In this article we consider the sequences of sample and population covariance operators for a sequence of arrays of Hilbertian random elements. Then under the assumptions that sequences of the covariance operators norm are uniformly bounded and the sequences of the principal component scores are uniformly sumable, we prove that the convergence of the sequences of covariance operators would impl...
متن کاملProducts of Random Matrices: Dimension and Growth in Norm
Suppose that X1, . . . , Xn, . . . , are independent, identically-distributed, rotationally invariant N×N matrices. Let Πn = Xn . . . X1. It is known that n −1 log ‖Πn‖ converges to a non-random limit. We prove that under certain additional assumptions on matrices Xi the speed of convergence to this limit does not decrease when the size of matrices, N, grows.
متن کاملOn Compressive Ensemble Induced Regularisation: How Close is the Finite Ensemble Precision Matrix to the Infinite Ensemble?
Averaging ensembles of randomly oriented low-dimensional projections of a singular covariance represent a novel and attractive means to obtain a well-conditioned inverse, which only needs access to random projections of the data. However, theoretical analyses so far have only been done at convergence, implying good properties for ‘large-enough’ ensembles. But how large is ‘large enough’? Here w...
متن کاملOn The Mean Convergence of Biharmonic Functions
Let denote the unit circle in the complex plane. Given a function , one uses t usual (harmonic) Poisson kernel for the unit disk to define the Poisson integral of , namely . Here we consider the biharmonic Poisson kernel for the unit disk to define the notion of -integral of a given function ; this associated biharmonic function will be denoted by . We then consider the dilations ...
متن کامل