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A High Performance GPU CountSketch Implementation and Its Application to Multisketching and Least Squares Problems
Andrew J. Higgins, Erik G. Boman, Ichitaro Yamazaki
Random sketching is a dimensionality reduction technique that approximately preserves norms and singular values up to some distortion factor with high probability. The most…
Random-sketching Techniques to Enhance the Numerical Stability of Block Orthogonalization Algorithms for s-step GMRES
Ichitaro Yamazaki, Andrew J. Higgins, Erik G. Boman +1
We integrate random sketching techniques into block orthogonalization schemes needed for s-step GMRES. The resulting block orthogonalization schemes generate the basis vectors whos…
Two-Stage Block Orthogonalization to Improve Performance of -step GMRES
Ichitaro Yamazaki, Andrew J. Higgins, Erik G. Boman +1
On current computer architectures, GMRES' performance can be limited by its communication cost to generate orthonormal basis vectors of the Krylov subspace. To address this perform…
Analysis of Randomized Householder-Cholesky QR Factorization with Multisketching
Andrew J. Higgins, Daniel B. Szyld, Erik G. Boman +1
CholeskyQR2 and shifted CholeskyQR3 are two state-of-the-art algorithms for computing tall-and-skinny QR factorizations since they attain high performance on current computer archi…