Maike Meier
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View article: Fast randomized least-squares solvers can be just as accurate and stable as classical direct solvers
Fast randomized least-squares solvers can be just as accurate and stable as classical direct solvers Open
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-squares problems. However, none of the existing algorithms is ba…
View article: Fast randomized numerical rank estimation for numerically low-rank matrices
Fast randomized numerical rank estimation for numerically low-rank matrices Open
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. However, estimating the rank has been done largely in an …
View article: Are sketch-and-precondition least squares solvers numerically stable?
Are sketch-and-precondition least squares solvers numerically stable? Open
Sketch-and-precondition techniques are efficient and popular for solving large least squares (LS) problems of the form $Ax=b$ with $A\in\mathbb{R}^{m\times n}$ and $m\gg n$. This is where $A$ is ``sketched" to a smaller matrix $SA$ with $S…
View article: Randomized algorithms for Tikhonov regularization in linear least squares
Randomized algorithms for Tikhonov regularization in linear least squares Open
We describe two algorithms to efficiently solve regularized linear least squares systems based on sketching. The algorithms compute preconditioners for $\min \|Ax-b\|^2_2 + λ\|x\|^2_2$, where $A\in\mathbb{R}^{m\times n}$ and $λ>0$ is a reg…
View article: Fast randomized numerical rank estimation for numerically low-rank matrices
Fast randomized numerical rank estimation for numerically low-rank matrices Open
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. However, estimating the rank has been done largely in an …