7 citations · 23 across the 12 of their papers we have counts for
13 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…
Randomized Jacobi-Davidson method
Laura Grigori, Taejun Park, Igor Simunec
The Jacobi-Davidson method is a widely used subspace method for computing a few eigenpairs of a large, sparse, non-Hermitian matrix closest to a target. Like other subspace methods…
Randomized Block Davidson Eigensolvers for Plane-Wave Density-Functional Theory
Moritz Gubler, Taejun Park, Augustin Bussy +4
Iterative diagonalization is the dominant cost of plane-wave density-functional theory (DFT), with search-space orthogonalization scaling particularly quickly with problem size and…
Nyström method for symmetric indefinite matrices
Yijia Chen, Yuji Nakatsukasa, Anjali Narendran +1
The Nyström method approximates , where is a column subset ma…
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…
Rewarding How Models Think Pedagogically: Integrating Pedagogical Reasoning and Thinking Rewards for LLMs in Education
Unggi Lee, Jiyeong Bae, Jaehyeon Park +7
Large language models (LLMs) are increasingly deployed as intelligent tutoring systems, yet research on optimizing LLMs specifically for educational contexts remains limited. Recen…
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…
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…
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…
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…
Randomized low-rank approximation for symmetric indefinite matrices
Taejun Park, Yuji Nakatsukasa
The Nyström method is a popular choice for finding a low-rank approximation to a symmetric positive semi-definite matrix. The method can fail when applied to symmetric indefinite m…
A Fast Randomized Algorithm for Computing an Approximate Null Space
Yuji Nakatsukasa, Taejun Park
Randomized algorithms in numerical linear algebra can be fast, scalable and robust. This paper examines the effect of sketching on the right singular vectors corresponding to the s…