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Improved Fixed-Rank Nyström Approximation via QR Decomposition: Practical and Theoretical Aspects
Farhad Pourkamali-Anaraki, Stephen Becker
The Nystrom method is a popular technique that uses a small number of landmark points to compute a fixed-rank approximation of large kernel matrices that arise in machine learning…
Efficient Adjoint Computation for Wavelet and Convolution Operators
James Folberth, Stephen Becker
First-order optimization algorithms, often preferred for large problems, require the gradient of the differentiable terms in the objective function. These gradients often involve l…
URV Factorization with Random Orthogonal System Mixing
Stephen Becker, James Folberth, Laura Grigori
The unpivoted and pivoted Householder QR factorizations are ubiquitous in numerical linear algebra. A difficulty with pivoted Householder QR is the communication bottleneck introdu…
Adapting Regularized Low Rank Models for Parallel Architectures
Derek Driggs, Stephen Becker, Aleksandr Aravkin
We introduce a reformulation of regularized low-rank recovery models to take advantage of GPU, multiple CPU, and hybridized architectures. Low-rank recovery often involves nuclear-…