Optimizing Halley's Iteration for Computing the Matrix Polar Decomposition. - Yuji Nakatsukasa; Zhaojun Bai; François Gygi (SIAM J. Matrix Anal. Appl., 2010)

Gerschgorin's theorem for generalized eigenvalue problems in the Euclidean metric. - Yuji Nakatsukasa (Math. Comput., 2011)

Perturbation of Partitioned Hermitian Definite Generalized Eigenvalue Problems. - Ren-Cang Li; Yuji Nakatsukasa; Ninoslav Truhar; Shufang Xu (SIAM J. Matrix Anal. Appl., 2011)

On the condition numbers of a multiple eigenvalue of a generalized eigenvalue problem. - Yuji Nakatsukasa (Numerische Mathematik, 2012)

dqds with Aggressive Early Deflation. - Yuji Nakatsukasa; Kensuke Aishima; Ichitaro Yamazaki (SIAM J. Matrix Anal. Appl., 2012)

Backward Stability of Iterations for Computing the Polar Decomposition. - Yuji Nakatsukasa; Nicholas J. Higham (SIAM J. Matrix Anal. Appl., 2012)

Erratum: Perturbation of Partitioned Hermitian Definite Generalized Eigenvalue Problems. - Ren-Cang Li; Yuji Nakatsukasa; Ninoslav Truhar; Shufang Xu (SIAM J. Matrix Anal. Appl., 2013)

Stable and Efficient Spectral Divide and Conquer Algorithms for the Symmetric Eigenvalue Decomposition and the SVD. - Yuji Nakatsukasa; Nicholas J. Higham (SIAM J. Sci. Comput., 2013)

Global Optimization Methods for Extended Fisher Discriminant Analysis. - Satoru Iwata 001; Yuji Nakatsukasa; Akiko Takeda (AISTATS, 2014)

CholeskyQR2: a simple and communication-avoiding algorithm for computing a tall-skinny QR factorization on a large-scale parallel system. - Takeshi Fukaya; Yuji Nakatsukasa; Yuka Yanagisawa; Yusaku Yamamoto (ScalA@SC, 2014)

A Logarithmic Minimization Property of the Unitary Polar Factor in the Spectral and Frobenius Norms. - Patrizio Neff; Yuji Nakatsukasa; Andreas Fischle (SIAM J. Matrix Anal. Appl., 2014)

Computing the common zeros of two bivariate functions via Bézout resultants. - Yuji Nakatsukasa; Vanni Noferini; Alex Townsend (Numerische Mathematik, 2015)

Computing the Signed Distance Between Overlapping Ellipsoids. - Satoru Iwata 001; Yuji Nakatsukasa; Akiko Takeda (SIAM J. Optim., 2015)

Roundoff error analysis of the CholeskyQR2 algorithm in an oblique inner product. - Yusaku Yamamoto; Yuji Nakatsukasa; Yuka Yanagisawa; Takeshi Fukaya (JSIAM Lett., 2016)

On the stability of computing polynomial roots via confederate linearizations. - Yuji Nakatsukasa; Vanni Noferini (Math. Comput., 2016)

Solving Generalized CDT Problems via Two-Parameter Eigenvalues. - Shinsaku Sakaue; Yuji Nakatsukasa; Akiko Takeda; Satoru Iwata 001 (SIAM J. Optim., 2016)

Scaled and Squared Subdiagonal Padé Approximation for the Matrix Exponential. - Stefan Güttel; Yuji Nakatsukasa (SIAM J. Matrix Anal. Appl., 2016)

Computing Fundamental Matrix Decompositions Accurately via the Matrix Sign Function in Two Iterations: The Power of Zolotarev's Functions. - Yuji Nakatsukasa; Roland W. Freund (SIAM Rev., 2016)

Finding a low-rank basis in a matrix subspace. - Yuji Nakatsukasa; Tasuku Soma; André Uschmajew (Math. Program., 2017)

Solving the Trust-Region Subproblem By a Generalized Eigenvalue Problem. - Satoru Adachi; Satoru Iwata 001; Yuji Nakatsukasa; Akiko Takeda (SIAM J. Optim., 2017)

Vector Spaces of Linearizations for Matrix Polynomials: A Bivariate Polynomial Approach. - Yuji Nakatsukasa; Vanni Noferini; Alex Townsend (SIAM J. Matrix Anal. Appl., 2017)

Stable polefinding and rational least-squares fitting via eigenvalues. - Shinji Ito; Yuji Nakatsukasa (Numerische Mathematik, 2018)

A Backward Stable Algorithm for Computing the CS Decomposition via the Polar Decomposition. - Evan S. Gawlik; Yuji Nakatsukasa; Brian D. Sutton (SIAM J. Matrix Anal. Appl., 2018)

On Orthogonal Tensors and Best Rank-One Approximation Ratio. - Zhening Li; Yuji Nakatsukasa; Tasuku Soma; André Uschmajew (SIAM J. Matrix Anal. Appl., 2018)

Reduction of Matrix Polynomials to Simpler Forms. - Yuji Nakatsukasa; Leo Taslaman; Françoise Tisseur; Ion Zaballa (SIAM J. Matrix Anal. Appl., 2018)

Rational Minimax Approximation via Adaptive Barycentric Representations. - Silviu-Ioan Filip; Yuji Nakatsukasa; Lloyd N. Trefethen; Bernhard Beckermann (SIAM J. Sci. Comput., 2018)

Fourth-Order Time-Stepping For Stiff PDEs On The Sphere. - Hadrien Montanelli; Yuji Nakatsukasa (SIAM J. Sci. Comput., 2018)

The AAA Algorithm for Rational Approximation. - Yuji Nakatsukasa; Olivier Sète; Lloyd N. Trefethen (SIAM J. Sci. Comput., 2018)

Accuracy of approximate projection to the semidefinite cone. - Paul J. Goulart; Yuji Nakatsukasa; Nikitas Rontsis (CoRR, 2019)

Classification of chaotic time series with deep learning. - Nicolas Boullé; Vassilios Dallas; Yuji Nakatsukasa; D. Samaddar (CoRR, 2019)

Weighted Monte Carlo with least squares and randomized extended Kaczmarz for option pricing. - Damir Filipovic; Kathrin Glau; Yuji Nakatsukasa; Francesco Statti (CoRR, 2019)

Eigenvalue-based algorithm and analysis for nonconvex QCQP with one constraint. - Satoru Adachi; Yuji Nakatsukasa (Math. Program., 2019)

Massively Parallel Polar Decomposition on Distributed-memory Systems. - Hatem Ltaief; Dalal Sukkari; Aniello Esposito; Yuji Nakatsukasa; David E. Keyes (ACM Trans. Parallel Comput., 2019)

Rational neural networks. - Nicolas Boullé; Yuji Nakatsukasa; Alex Townsend (NeurIPS, 2020)

Solving two-parameter eigenvalue problems using an alternating method. - Henrik Eisenmann; Yuji Nakatsukasa (CoRR, 2020)

Fast and stable randomized low-rank matrix approximation. - Yuji Nakatsukasa (CoRR, 2020)

Zolotarev's fifth and sixth problems. - Evan S. Gawlik; Yuji Nakatsukasa (CoRR, 2020)

Sharp error bounds for Ritz vectors and approximate singular vectors. - Yuji Nakatsukasa (Math. Comput., 2020)

Shifted Cholesky QR for Computing the QR Factorization of Ill-Conditioned Matrices. - Takeshi Fukaya; Ramaseshan Kannan; Yuji Nakatsukasa; Yusaku Yamamoto; Yuka Yanagisawa (SIAM J. Sci. Comput., 2020)

An Algorithm for Real and Complex Rational Minimax Approximation. - Yuji Nakatsukasa; Lloyd N. Trefethen (SIAM J. Sci. Comput., 2020)

Fast Graph Sampling Set Selection Using Gershgorin Disc Alignment. - Yuanchao Bai; Fen Wang; Gene Cheung; Yuji Nakatsukasa; Wen Gao 001 (IEEE Trans. Signal Process., 2020)

High-Performance Partial Spectrum Computation for Symmetric eigenvalue problems and the SVD. - David E. Keyes; Hatem Ltaief; Yuji Nakatsukasa; Dalal Sukkari (CoRR, 2021)

Fast randomized numerical rank estimation. - Maike Meier; Yuji Nakatsukasa (CoRR, 2021)

Full operator preconditioning and the accuracy of solving linear systems. - Stephan Mohr; Yuji Nakatsukasa; Carolina Urzúa-Torres (CoRR, 2021)

Fast & Accurate Randomized Algorithms for Linear Systems and Eigenvalue Problems. - Yuji Nakatsukasa; Joel A. Tropp (CoRR, 2021)

Approximating the pth root by composite rational functions. - Evan S. Gawlik; Yuji Nakatsukasa (J. Approx. Theory, 2021)

Exponential node clustering at singularities for rational approximation, quadrature, and PDEs. - Lloyd N. Trefethen; Yuji Nakatsukasa; J. A. C. Weideman (Numerische Mathematik, 2021)

Error Localization of Best L1 Polynomial Approximants. - Yuji Nakatsukasa; Alex Townsend (SIAM J. Numer. Anal., 2021)

Reciprocal-Log Approximation and Planar PDE Solvers. - Yuji Nakatsukasa; Lloyd N. Trefethen (SIAM J. Numer. Anal., 2021)

Vandermonde with Arnoldi. - Pablo D. Brubeck; Yuji Nakatsukasa; Lloyd N. Trefethen (SIAM Rev., 2021)

Rectangular eigenvalue problems. - Behnam Hashemi; Yuji Nakatsukasa; Lloyd N. Trefethen (Adv. Comput. Math., 2022)

Stochastic diagonal estimation: probabilistic bounds and an improved algorithm. - Robert A. Baston; Yuji Nakatsukasa (CoRR, 2022)

Randomized algorithms for Tikhonov regularization in linear least squares. - Maike Meier; Yuji Nakatsukasa (CoRR, 2022)

A Fast Randomized Algorithm for computing the Null Space. - Yuji Nakatsukasa; Taejun Park (CoRR, 2022)

Speeding up Krylov subspace methods for computing f(A)b via randomization. - Alice Cortinovis; Daniel Kressner; Yuji Nakatsukasa (CoRR, 2022)

Efficient Semidefinite Programming with Approximate ADMM. - Nikitas Rontsis; Paul Goulart; Yuji Nakatsukasa (J. Optim. Theory Appl., 2022)

An active-set algorithm for norm constrained quadratic problems. - Nikitas Rontsis; Paul J. Goulart; Yuji Nakatsukasa (Math. Program., 2022)

Stable and Efficient Computation of Generalized Polar Decompositions. - Peter Benner; Yuji Nakatsukasa; Carolin Penke (SIAM J. Matrix Anal. Appl., 2022)

Twice Is Enough for Dangerous Eigenvalues. - Andrew Horning; Yuji Nakatsukasa (SIAM J. Matrix Anal. Appl., 2022)

A Theory of Quantum Subspace Diagonalization. - Ethan N. Epperly; Lin Lin 001; Yuji Nakatsukasa (SIAM J. Matrix Anal. Appl., 2022)

Least-Squares Spectral Methods for ODE Eigenvalue Problems. - Behnam Hashemi; Yuji Nakatsukasa (SIAM J. Sci. Comput., 2022)

High-Performance SVD Partial Spectrum Computation. - David E. Keyes; Hatem Ltaief; Yuji Nakatsukasa; Dalal Sukkari (SC, 2023)

Convergence and Near-optimal Sampling for Multivariate Function Approximations in Irregular Domains via Vandermonde with Arnoldi. - Wenqi Zhu; Yuji Nakatsukasa (CoRR, 2023)

AAA rational approximation on a continuum. - Toby Driscoll; Yuji Nakatsukasa; Lloyd N. Trefethen (CoRR, 2023)

Approximating Sparse Matrices and their Functions using Matrix-vector products. - Taejun Park; Yuji Nakatsukasa (CoRR, 2023)

RTSMS: Randomized Tucker with single-mode sketching. - Behnam Hashemi; Yuji Nakatsukasa (CoRR, 2023)

The first five years of the AAA algorithm. - Yuji Nakatsukasa; Olivier Sète; Lloyd N. Trefethen (CoRR, 2023)

A Structure-Preserving Divide-and-Conquer Method for Pseudosymmetric Matrices. - Peter Benner; Yuji Nakatsukasa; Carolin Penke (SIAM J. Matrix Anal. Appl., 2023)

Randomized Low-Rank Approximation for Symmetric Indefinite Matrices. - Yuji Nakatsukasa; Taejun Park (SIAM J. Matrix Anal. Appl., 2023)

A Cholesky QR type algorithm for computing tall-skinny QR factorization with column pivoting. - Takeshi Fukaya; Yuji Nakatsukasa; Yusaku Yamamoto (IPDPS, 2024)

Fast randomized least-squares solvers can be just as accurate and stable as classical direct solvers. - Ethan N. Epperly; Maike Meier; Yuji Nakatsukasa (CoRR, 2024)

A Sherman-Morrison-Woodbury approach to solving least squares problems with low-rank updates. - Stefan Güttel; Yuji Nakatsukasa; Marcus Webb; Alban Bloor Riley (CoRR, 2024)

Matrix perturbation analysis of methods for extracting singular values from approximate singular subspaces. - Lorenzo Lazzarino; Hussam Al Daas; Yuji Nakatsukasa (CoRR, 2024)

Polynomial approximation of noisy functions. - Takeru Matsuda; Yuji Nakatsukasa (CoRR, 2024)

Eigen-componentwise convergence of SGD for quadratic programming. - Lehan Chen; Yuji Nakatsukasa (CoRR, 2024)

Efficient Bounds and Estimates for Canonical Angles in Randomized Subspace Approximations. - Yijun Dong; Per-Gunnar Martinsson; Yuji Nakatsukasa (SIAM J. Matrix Anal. Appl., 2024)

Are Sketch-and-Precondition Least Squares Solvers Numerically Stable? - Maike Meier; Yuji Nakatsukasa; Alex Townsend; Marcus Webb (SIAM J. Matrix Anal. Appl., 2024)

Fast and Accurate Randomized Algorithms for Linear Systems and Eigenvalue Problems. - Yuji Nakatsukasa; Joel A. Tropp (SIAM J. Matrix Anal. Appl., 2024)

AAA Rational Approximation on a Continuum. - Tobin A. Driscoll; Yuji Nakatsukasa; Lloyd N. Trefethen (SIAM J. Sci. Comput., 2024)

Speeding Up Krylov Subspace Methods for Computing ( boldsymbol{{f}(A){b}} ) via Randomization. - Alice Cortinovis; Daniel Kressner; Yuji Nakatsukasa (SIAM J. Matrix Anal. Appl., 2024)

Accuracy and Stability of CUR Decompositions with Oversampling. - Taejun Park; Yuji Nakatsukasa (SIAM J. Matrix Anal. Appl., 2025)

Low-Rank Approximation of Parameter-Dependent Matrices via CUR Decomposition. - Taejun Park; Yuji Nakatsukasa (SIAM J. Sci. Comput., 2025)

Preconditioned normal equations for solving discretised partial differential equations. - Lorenzo Lazzarino; Yuji Nakatsukasa; Umberto Zerbinati (CoRR, 2025)

Stable algorithms for general linear systems by preconditioning the normal equations. - Ethan N. Epperly; Anne Greenbaum; Yuji Nakatsukasa (CoRR, 2025)

A minimax method for the spectral fractional Laplacian and related evolution problems. - José A. Carrillo 001; Stefano Fronzoni; Yuji Nakatsukasa; Endre Süli (CoRR, 2025)

Sharp error bounds for approximate eigenvalues and singular values from subspace methods. - Irina-Beatrice Haas; Yuji Nakatsukasa (CoRR, 2025)

Efficient Function Approximation Under Heteroskedastic Noise. - Yuji Nakatsukasa; Yifu Zhang (CoRR, 2025)