Fast Spectral Low Rank Matrix Approximation
Haishan Ye, Zhihua Zhang
TL;DR
This paper introduces new fast algorithms for spectral norm matrix approximation, including spectral norm-based matrix multiplication, generalized linear regression, and singular value decomposition, enhancing efficiency and accuracy.
Contribution
It extends approximate matrix multiplication results to the spectral norm and develops fast algorithms for spectral norm-based regression and SVD.
Findings
Extended approximate matrix multiplication to spectral norm
Developed fast spectral norm-based regression algorithms
Provided efficient approximate SVD methods
Abstract
First, we extend the results of approximate matrix multiplication from the Frobenius norm to the spectral norm. Second, We develop a class of fast approximate generalized linear regression algorithms with respect to the spectral norm. Finally, We give a fast approximate SVD.
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Taxonomy
TopicsSparse and Compressive Sensing Techniques · Stochastic Gradient Optimization Techniques · Matrix Theory and Algorithms