6 citations · 16 across the 18 of their papers we have counts for
19 papers
Solving a sequence of eigenvalue problems using snapshot and row subsampling
Francesco Hrobat, Yuji Nakatsukasa
A sequence of eigenvalue problems requires solving where , and (usually) is the largest or smallest eigenvalue o…
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…
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…
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…
Numerical Stability of the Nyström Method
Alberto Bucci, Yuji Nakatsukasa, Taejun Park
The Nyström method is a widely used technique for improving the scalability of kernel-based algorithms, including kernel ridge regression, spectral clustering, and Gaussian process…
IterativeCUR: Large Rank-Adaptive Approximation From a Small Recycled Sketch
Nathaniel Pritchard, Taejun Park, Yuji Nakatsukasa +1
The computation of accurate low-rank matrix approximations is central to improving the scalability of various techniques in machine learning, uncertainty quantification, and contro…
Sharp error bounds for approximate eigenvalues and singular values from subspace methods
Irina-Beatrice Haas, Yuji Nakatsukasa
Subspace methods are commonly used for finding approximate eigenvalues and singular values of large-scale matrices. Once a subspace is found, the Rayleigh-Ritz method (for symmetri…
Polynomial approximation of noisy functions
Takeru Matsuda, Yuji Nakatsukasa
Approximating a univariate function on the interval with a polynomial is among the most classical problems in numerical analysis. When the function evaluations come with n…
Matrix perturbation analysis of methods for extracting singular values from approximate singular subspaces
Lorenzo Lazzarino, Hussam Al Daas, Yuji Nakatsukasa
Given (orthonormal) approximations and to the left and right subspaces spanned by the leading singular vectors of a matrix , we discuss methods to approx…
Low-rank approximation of parameter-dependent matrices via CUR decomposition
Taejun Park, Yuji Nakatsukasa
A low-rank approximation of a parameter-dependent matrix is an important task in the computational sciences appearing for example in dynamical systems and compression of a s…
A Sherman--Morrison--Woodbury approach to solving least squares problems with low-rank updates
Stefan Güttel, Yuji Nakatsukasa, Marcus Webb +1
We present a simple formula to update the pseudoinverse of a full-rank rectangular matrix that undergoes a low-rank modification, and demonstrate its utility for solving least squa…
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…
Accuracy and Stability of CUR decompositions with Oversampling
Taejun Park, Yuji Nakatsukasa
This work investigates the accuracy and numerical stability of CUR decompositions with oversampling. The CUR decomposition approximates a matrix using a subset of columns and rows…
The first five years of the AAA algorithm
Yuji Nakatsukasa, Olivier Sete, Lloyd N. Trefethen
The AAA algorithm, introduced in 2018, computes best or near-best rational approximations to functions or data on subsets of the real line or the complex plane. It is much faster a…
RTSMS: Randomized Tucker with single-mode sketching
Behnam Hashemi, Yuji Nakatsukasa
We propose RTSMS (Randomized Tucker via Single-Mode-Sketching), a randomized algorithm for approximately computing a low-rank Tucker decomposition of a given tensor. It uses sketch…
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…