13 papers
Nyström method for symmetric indefinite matrices
Yijia Chen, Yuji Nakatsukasa, Anjali Narendran +1
The Nyström method approximates , where is a column subset ma…
A multilevel sketch-and-solve method for overdetermined least squares problems
Irina-Beatrice Haas, Michael B. Giles, Yuji Nakatsukasa
Sketch-and-solve (SAS) is a very successful method to efficiently estimate the solution of heavily overdetermined large linear least squares problems. It uses random sketching to r…
Finding accurate eigenvalues and eigenvectors of positive semi-definite matrices given a subspace
Yuji Nakatsukasa, Zheng Tang
We revisit a classical problem in numerical linear algebra: given an -dimensional subspace that approximates the leading eigenspace of an positive semi…
Approximating Sparse Matrices and their Functions using Matrix-vector products
Taejun Park, Yuji Nakatsukasa
The computation of a matrix function is an important task in scientific computing appearing in machine learning, network analysis and the solution of partial differential eq…
Matrix Perturbation Theory in the Tangent Space of Isospectral Matrices
Francesco Hrobat, Yuji Nakatsukasa
Eigenvalue and eigenvector perturbation theory is a fundamental topic in several disciplines, including numerical linear algebra, quantum physics, and related fields. The central p…
Fast, High-Accuracy, Randomized Nullspace Computations for Tall Matrices
Ethan N. Epperly, Taejun Park, Yuji Nakatsukasa
In this paper, we develop RLOBPCG, an efficient method for computing a small number of singular triplets corresponding to the smallest singular values of large, tall matrices. The…