
Rational Krylov and ADI iteration for infinite size quasiToeplitz matrix equations
We consider a class of linear matrix equations involving semiinfinite m...
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Statistical Meaning of Mean Functions
The basic properties of the Fisher information allow to reveal the stati...
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Uniform approximation by multivariate quasiprojection operators
Approximation properties of quasiprojection operators Q_j(f,φ, φ) are s...
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Approximate Joint Diagonalization and Geometric Mean of Symmetric Positive Definite Matrices
We explore the connection between two problems that have arisen independ...
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Krylov Iterative Methods for the Geometric Mean of Two Matrices Times a Vector
In this work, we are presenting an efficient way to compute the geometri...
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Nonparametric regression estimation for quasiassociated Hilbertian processes
We establish the asymptotic normality of the kernel type estimator for t...
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A computational framework for twodimensional random walks with restarts
The treatment of twodimensional random walks in the quarter plane leads...
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Geometric means of quasiToeplitz matrices
We study means of geometric type of quasiToeplitz matrices, that are semiinfinite matrices A=(a_i,j)_i,j=1,2,… of the form A=T(a)+E, where E represents a compact operator, and T(a) is a semiinfinite Toeplitz matrix associated with the function a, with Fourier series ∑_ℓ=∞^∞ a_ℓ e^𝔦ℓ t, in the sense that (T(a))_i,j=a_ji. If a is and essentially bounded, then these matrices represent bounded selfadjoint operators on ℓ^2. We consider the case where a is a continuous function, where quasiToeplitz matrices coincide with a classical Toeplitz algebra, and the case where a is in the Wiener algebra, that is, has absolutely convergent Fourier series. We prove that if a_1,…,a_p are continuous and positive functions, or are in the Wiener algebra with some further conditions, then means of geometric type, such as the ALM, the NBMP and the Karcher mean of quasiToeplitz positive definite matrices associated with a_1,…,a_p, are quasiToeplitz matrices associated with the geometric mean (a_1⋯ a_p)^1/p, which differ only by the compact correction. We show by numerical tests that these operator means can be practically approximated.
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