5 papers
SuperPCA: subspace analysis and an efficient algorithm for high-dimensional PCA
Irina-Beatrice Haas, Maike Meier, Yuji Nakatsukasa +1
Principal component analysis (PCA) is a fundamental tool to reduce the dimensionality of the data in many applications. PCA finds a few signal directions that contain most of the v…
Fast randomized least-squares solvers can be just as accurate and stable as classical direct solvers
Ethan N. Epperly, Maike Meier, Yuji Nakatsukasa
One of the greatest success stories of randomized algorithms for linear algebra has been the development of fast, randomized algorithms for highly overdetermined linear least-squar…
Are sketch-and-precondition least squares solvers numerically stable?
Maike Meier, Yuji Nakatsukasa, Alex Townsend +1
Sketch-and-precondition techniques are efficient and popular for solving large least squares (LS) problems of the form with and . This i…
Randomized algorithms for Tikhonov regularization in linear least squares
Maike Meier, Yuji Nakatsukasa
We describe two algorithms to efficiently solve regularized linear least squares systems based on sketching. The algorithms compute preconditioners for $\min \|Ax-b\|^2_2 + λ\|x\|^…
Fast randomized numerical rank estimation for numerically low-rank matrices
Maike Meier, Yuji Nakatsukasa
Matrices with low-rank structure are ubiquitous in scientific computing. Choosing an appropriate rank is a key step in many computational algorithms that exploit low-rank structure…