منابع مشابه
Interpolative Butterfly Factorization
This paper introduces the interpolative butterfly factorization for nearly optimal implementation of several transforms in harmonic analysis, when their explicit formulas satisfy certain analytic properties and the matrix representations of these transforms satisfy a complementary low-rank property. A preliminary interpolative butterfly factorization is constructed based on interpolative low-ra...
متن کاملDistributed-memory Hierarchical Interpolative Factorization
The hierarchical interpolative factorization (HIF) offers an efficient way for solving or preconditioning elliptic partial differential equations. By exploiting locality and low-rank properties of the operators, the HIF achieves quasi-linear complexity for factorizing the discrete positive definite elliptic operator and linear complexity for solving the associated linear system. In this paper, ...
متن کاملButterfly Factorization
The paper introduces the butterfly factorization as a data-sparse approximation for the matrices that satisfy a complementary low-rank property. The factorization can be constructed efficiently if either fast algorithms for applying the matrix and its adjoint are available or the entries of the matrix can be sampled individually. For an N ×N matrix, the resulting factorization is a product of O...
متن کاملMultidimensional butterfly factorization
This paper introduces the multidimensional butterfly factorization as a data-sparse representation of multidimensional kernel matrices that satisfy the complementary low-rank property. This factorization approximates such a kernel matrix of size N ×N with a product of O(logN) sparse matrices, each of which contains O(N) nonzero entries. We also propose efficient algorithms for constructing this...
متن کاملA CUR Factorization Algorithm based on the Interpolative Decomposition
An algorithm for the efficient computation of the CUR decomposition is presented. The method is based on simple modifications to the classical truncated pivoted QR decomposition, which means that highly optimized library codes can be utilized for its implementation. Numerical experiments demonstrate advantageous performance compared to existing techniques for computing CUR factorizations.
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: SIAM Journal on Scientific Computing
سال: 2017
ISSN: 1064-8275,1095-7197
DOI: 10.1137/16m1074941