18 citations · 25 across the 12 of their papers we have counts for
22 papers
Eigenvalue avoidance of structured matrices depending smoothly on a real parameter
Yuji Nakatsukasa, Vanni Noferini
We explore the concept of eigenvalue avoidance, which is well understood for real symmetric and Hermitian matrices, for other classes of structured matrices. We adopt a differentia…
A Structure-Preserving Divide-and-Conquer Method for Pseudosymmetric Matrices
Peter Benner, Yuji Nakatsukasa, Carolin Penke
We devise a spectral divide-and-conquer scheme for matrices that are self-adjoint with respect to a given indefinite scalar product (i.e. pseudosymmetic matrices). The pseudosymmet…
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\|^…
Stochastic diagonal estimation: probabilistic bounds and an improved algorithm
Robert A. Baston, Yuji Nakatsukasa
We study the problem of estimating the diagonal of an implicitly given matrix . For such a matrix we have access to an oracle that allows us to evaluate the matrix vector produc…
Least-squares spectral methods for ODE eigenvalue problems
Behnam Hashemi, Yuji Nakatsukasa
We develop spectral methods for ODEs and operator eigenvalue problems that are based on a least-squares formulation of the problem. The key tool is a method for rectangular general…
Full operator preconditioning and the accuracy of solving linear systems
Stephan Mohr, Yuji Nakatsukasa, Carolina Urzúa-Torres
Unless special conditions apply, the attempt to solve ill-conditioned systems of linear equations with standard numerical methods leads to uncontrollably high numerical error. Ofte…