Geometric multiscale decompositions of dynamic low-rank matrices
نویسندگان
چکیده
منابع مشابه
Geometric multiscale decompositions of dynamic low-rank matrices
The present paper is concerned with the study of manifold-valued multiscale transforms with a focus on the Stiefel manifold. For this specific geometry we derive several formulas and algorithms for the computation of geometric means which will later enable us to construct multiscale transforms of wavelet type. As an application we study compression of piecewise smooth families of low-rank matri...
متن کاملRegularized Computation of Approximate Pseudoinverse of Large Matrices Using Low-Rank Tensor Train Decompositions
We propose a new method for low-rank approximation of Moore-Penrose pseudoinverses (MPPs) of large-scale matrices using tensor networks. The computed pseudoinverses can be useful for solving or preconditioning large-scale overdetermined or underdetermined systems of linear equations. The computation is performed efficiently and stably based on the modified alternating least squares (MALS) schem...
متن کاملDiagonal and Low-Rank Matrix Decompositions, Correlation Matrices, and Ellipsoid Fitting
In this paper we establish links between, and new results for, three problems that are not usually considered together. The first is a matrix decomposition problem that arises in areas such as statistical modeling and signal processing: given a matrix X formed as the sum of an unknown diagonal matrix and an unknown low rank positive semidefinite matrix, decompose X into these constituents. The ...
متن کاملVector Spaces of Matrices of Low Rank
In this paper we study vector spaces of matrices, all of whose elements have rank at most a given number. The problem of classifying such spaces is roughly equivalent to the problem of classifying certain torsion-free sheaves on projective spaces. We solve this problem in case the sheaf in question has first Chern class equal to 1; the characterization of the vector spaces of matrices of rank d...
متن کاملLow-Rank and Low-Order Decompositions for Local System Identification
As distributed systems increase in size, the need for scalable algorithms becomes more and more important. We argue that in the context of system identification, an essential building block of any scalable algorithm is the ability to estimate local dynamics within a large interconnected system. We show that in what we term the “full interconnection measurement” setting, this task is easily solv...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Computer Aided Geometric Design
سال: 2013
ISSN: 0167-8396
DOI: 10.1016/j.cagd.2013.07.002