Stochastic dynamical low-rank approximation method
نویسندگان
چکیده
منابع مشابه
Dynamical low-rank approximation
In low-rank approximation, separation of variables is used to reduce the amount of data in computations with high-dimensional functions. Such techniques have proved their value, e.g., in quantum mechanics and recommendation algorithms. It is also possible to fold a low-dimensional grid into a high-dimensional object, and use low-rank techniques to compress the data. Here, we consider low-rank t...
متن کاملDynamical Low-Rank Approximation
For the low rank approximation of time-dependent data matrices and of solutions to matrix differential equations, an increment-based computational approach is proposed and analyzed. In this method, the derivative is projected onto the tangent space of the manifold of rank-r matrices at the current approximation. With an appropriate decomposition of rank-r matrices and their tangent matrices, th...
متن کاملSchur method for low-rank matrix approximation
The usual way to compute a low-rank approximant of a matrix H is to take its truncated SVD. However, the SVD is computationally expensive. This paper describes a much simpler generalized Schur-type algorithm to compute similar low-rank approximants. For a given matrix H which has d singular values larger than ε, we find all rank d approximants Ĥ such that H − Ĥ has 2-norm less than ε. The set o...
متن کاملStochastic algorithms for solving structured low-rank matrix approximation problems
In this paper, we investigate the complexity of the numerical construction of the Hankel structured low-rank approximation (HSLRA) problem, and develop a family of algorithms to solve this problem. Briefly, HSLRA is the problem of finding the closest (in some pre-defined norm) rank r approximation of a given Hankel matrix, which is also of Hankel structure. We demonstrate that finding optimal s...
متن کاملLow-rank Tensor Approximation
Approximating a tensor by another of lower rank is in general an ill posed problem. Yet, this kind of approximation is mandatory in the presence of measurement errors or noise. We show how tools recently developed in compressed sensing can be used to solve this problem. More precisely, a minimal angle between the columns of loading matrices allows to restore both existence and uniqueness of the...
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: Journal of Computational Physics
سال: 2018
ISSN: 0021-9991
DOI: 10.1016/j.jcp.2018.06.058