Classification, Approximation by Multipliers and Algorithms
نویسنده
چکیده
In this paper we deal with the connection of frames with the class of Hilbert Schmidt operators. First we give an easy criteria for operators being in this class using frames. It is the equivalent to the criteria using orthonormal bases. Then we construct Bessel sequences frames and Riesz bases for the class of Hilbert Schmidt operators using the tensor product of such sequences in the original Hilbert space. We investigate how the Hilbert Schmidt inner product of an arbitrary operator and such a rank one operator can be calculated in an efficient way. Finally we give an algorithm to find the best approximation, in the Hilbert Schmidt sense, of arbitrary matrices by operators called frame multipliers, which multiply the analysis coefficents by a fixed symbol followed by a synthesis.
منابع مشابه
Random Multipliers Numerically Stabilize Gaussian and Block Gaussian Elimination: Proofs and an Extension to Low-rank Approximation
We study two applications of standard Gaussian random multipliers. At first we prove that with a probability close to 1 such a multiplier is expected to numerically stabilize Gaussian elimination with no pivoting as well as block Gaussian elimination. Then, by extending our analysis, we prove that such a multiplier is also expected to support low-rank approximation of a matrix without customary...
متن کاملCharacterization of finite $p$-groups by the order of their Schur multipliers ($t(G)=7$)
Let $G$ be a finite $p$-group of order $p^n$ and $|{mathcal M}(G)|=p^{frac{1}{2}n(n-1)-t(G)}$, where ${mathcal M}(G)$ is the Schur multiplier of $G$ and $t(G)$ is a nonnegative integer. The classification of such groups $G$ is already known for $t(G)leq 6$. This paper extends the classification to $t(G)=7$.
متن کاملRepresentation of Operators in the Time-Frequency Domain and Generalzed Gabor Multipliers
Starting from a general operator representation in the time-frequency domain, this paper addresses the problem of approximating linear operators by operators that are diagonal or band-diagonal with respect to Gabor frames. A characterization of operators that can be realized as Gabor multipliers is given and necessary conditions for the existence of (Hilbert-Schmidt) optimal Gabor multiplier ap...
متن کاملGDOP Classification and Approximation by Implementation of Time Delay Neural Network Method for Low-Cost GPS Receivers
Geometric Dilution of Precision (GDOP) is a coefficient for constellations of Global Positioning System (GPS) satellites. These satellites are organized geometrically. Traditionally, GPS GDOP computation is based on the inversion matrix with complicated measurement equations. A new strategy for calculation of GPS GDOP is construction of time series problem; it employs machine learning and artif...
متن کاملTR-2014008: Supporting GENP and Low-Rank Approximation with Random Multipliers
We prove that standard Gaussian random multipliers are expected to stabilize numerically both Gaussian elimination with no pivoting and block Gaussian elimination and that they also are expected to support the celebrated randomized algorithm for low-rank approximation of a matrix even without customary oversampling. Our tests show similar results where we apply random circulant and Toeplitz mul...
متن کامل