12,305 research outputs found
Randomized methods for matrix computations
The purpose of this text is to provide an accessible introduction to a set of
recently developed algorithms for factorizing matrices. These new algorithms
attain high practical speed by reducing the dimensionality of intermediate
computations using randomized projections. The algorithms are particularly
powerful for computing low-rank approximations to very large matrices, but they
can also be used to accelerate algorithms for computing full factorizations of
matrices. A key competitive advantage of the algorithms described is that they
require less communication than traditional deterministic methods
Efficient Algorithms for CUR and Interpolative Matrix Decompositions
The manuscript describes efficient algorithms for the computation of the CUR
and ID decompositions. The methods used are based on simple modifications to
the classical truncated pivoted QR decomposition, which means that highly
optimized library codes can be utilized for implementation. For certain
applications, further acceleration can be attained by incorporating techniques
based on randomized projections. Numerical experiments demonstrate advantageous
performance compared to existing techniques for computing CUR factorizations
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