• Randomized algorithms in linear algebra
• Eigenvalues and their applications (in optimization, nonlinear problems)
• Rational and polynomial approximation theory
• Linear algebra and approximation theory in statistics (Monte Carlo integration, PCA)
• Eigenvalue perturbation theory, matrix analysis

Publications

• Yuji Nakatsukasa and Joel A. Tropp, Fast & Accurate Randomized Algorithms for Linear Systems and Eigenvalue Problems, SIAM Journal on Matrix Analysis and Applications, to appear. Preprint.
• Maike Meier, Yuji Nakatsukasa, Alex Townsend, and Marcus Webb, Are sketch-and-precondition least squares solvers numerically stable? SIAM Journal on Matrix Analysis and Applications, to appear. Preprint.
• Maike Meier and Yuji Nakatsukasa, Fast randomized numerical rank estimation, Linear Algebra and its Applications, to appear. Preprint.
• Stephan Mohr, Yuji Nakatsukasa, Carolina Urzua-Torres, Full operator preconditioning and the accuracy of solving linear systems, IMA Journal on Numerical Analysis, to appear. Preprint.
• Alice Cortinovis, Daniel Kressner, and Yuji Nakatsukasa Speeding up Krylov subspace methods for computing f(A)b via randomization, SIAM Journal on Matrix Analysis and Applications, to appear. Preprint.
• Toby Driscoll, Yuji Nakatsukasa, Lloyd N. Trefethen AAA rational approximation on a continuum, SIAM Journal on Scientific Computing, to appear. Preprint.
• David Keyes, Hatem Ltaief, Yuji Nakatsukasa, Dalal Sukkari, High-performance SVD partial spectrum computation, Supercomputing SC23 . Preprint.
• Taejun Park and Yuji Nakatsukasa, Randomized low-rank approximation for symmetric indefinite matrices, SIAM Journal on Matrix Analysis and Applications, Vol. 44, No. 3, pp. 1370-1392, 2023. Preprint.
• Taejun Park and Yuji Nakatsukasa, A fast randomized algorithm for computing the null space, BIT Numerical Mathematics, (2023) 63:36. Preprint.
• Peter Benner, Yuji Nakatsukasa, and Carolin Penke, A structure-preserving divide-and-conquer method for pseudosymmetric matrices, SIAM Journal on Matrix Analysis and Applications, Vol. 44, No. 3, 2023, pp. 1245-1270. Preprint.
• Behnam Hashemi, Yuji Nakatsukasa and Lloyd N. Trefethen, Rectangular eigenvalue problems, Advances in Computational Mathematics, (2022) 48:80. pdf.
• Behnam Hashemi and Yuji Nakatsukasa, Least-squares spectral methods for ODE eigenvalue problems, SIAM Journal on Scientific Computing, Vol. 44, No. 50, pp A3244-A3264, 2022. pdf.
• Ethan N. Epperly, Lin Lin, and Yuji Nakatsukasa, A theory of quantum subspace diagonalization, SIAM Journal on Matrix Analysis and Applications, 43(3), pp.1263-1290 (2022). pdf.
• Peter Benner, Yuji Nakatsukasa, Carolin Penke Stable and Efficient Computation of Generalized Polar Decompositions, SIAM Journal on Matrix Analysis and Applications, Vol. 43, No. 3, pp. 1058-1083, (2022). pdf.
• Henrik Eisenmann and Yuji Nakatsukasa, Solving two-parameter eigenvalue problems using an alternating method, Linear Algebra and its Applications, Vol. 643, pp. 137-160 (2022). pdf.
• Andrew Horning and Yuji Nakatsukasa, Twice is enough for dangerous eigenvalues, SIAM Journal on Matrix Analysis and Applications, 43 (1), 68-93 (2022). pdf.
• Nikitas Rontsis, Paul J. Goulart, and Yuji Nakatsukasa, Efficient Semidefinite Programming with approximate ADMM, Journal of Optimization Theory and Applications, 192 (1), 292-320 (2022). Preprint.
• Yuji Nakatsukasa and Lloyd N. Trefethen, Reciprocal-log approximation and planar PDE solvers, SIAM Journal on Numerical Analysis, 59(6), 2801-2822 (2021). pdf.
• Evan S. Gawlik and Yuji Nakatsukasa, Approximating the pth root by composite rational functions, Journal of Approximation Theory, (266), 105577, 2021. pdf.
• Nikitas Rontsis, Paul J. Goulart, and Yuji Nakatsukasa, An active-set algorithm for norm constrained quadratic problems, Mathematical Programming, 193, pp. 447-483 (2022). pdf.
• Yuji Nakatsukasa and Alex Townsend, Error localization of best L1 polynomial approximants. SIAM Journal on Numerical Analysis, 59(1), 314-333 (2021). pdf.
• Lloyd N. Trefethen, Yuji Nakatsukasa, J. A. C. Weideman, Exponential node clustering at singularities for rational approximation, quadrature, and PDEs, Numerische Mathematik, 147, 227-254 (2021). pdf.
• Pablo D. Brubeck, Yuji Nakatsukasa and Lloyd N. Trefethen, Vandermonde with Arnoldi, SIAM Review, 63(2), 405-415 (2021). pdf.

• Yuji Nakatsukasa and Lloyd N. Trefethen, An algorithm for real and complex rational minimax approximation, SIAM Journal on Scientific Computing, 42(5), A3157--A3179 (2020). pdf.
• Yuji Nakatsukasa, Sharp error bounds for Ritz vectors and approximate singular vectors. Mathematics of Computation, Vol. 89, pp. 1843-1866, 2020. pdf.
• Yuanchao Bai, Fen Wang, Gene Cheung, Yuji Nakatsukasa and Wen Gao, Fast Graph Sampling Set Selection Using Gershgorin Disc Alignment, IEEE Transactions on Signal Processing, Vol. 68, pp. 2419--2434, 2020. pdf.
• Paul Goulart, Yuji Nakatsukasa and Nikitas Rontsis, Accuracy of approximate projection to the semidefinite cone, Linear Algebra and its Applications, Vol. 594, pp. 177-192, 2020. pdf.
• Takeshi Fukaya, Ramaseshan Kannan, Yuji Nakatsukasa, Yusaku Yamamoto, and Yuka Yanagisawa, Shifted CholeskyQR for computing the QR factorization of ill-conditioned matrices. SIAM Journal on Scientific Computing, 42(1), A477-A503, 2020. pdf.
• Nicolas Boulle, Vassilios Dallas, Yuji Nakatsukasa, and D. Samaddar Classification of chaotic time series with deep learning Physica D: Nonlinear Phenomena, Volume 403, 132261, 2020. pdf.
• Yuji Nakatsukasa and Vanni Noferini, Inertia laws and localization of real eigenvalues for generalized indefinite eigenvalue problems, Linear Algebra and its Applications, Vol. 578, pp. 272-296, 2019. pdf.
• Hatem Ltaief, Dalal E. Sukkari, Aniello Esposito, Yuji Nakatsukasa and David E. Keyes, Massively Parallel Polar Decomposition on Distributed-Memory Systems, ACM Transactions on Parallel Computing, Vol. 6 (1),No. 4, 2019. pdf.
• Evan S. Gawlik, Yuji Nakatsukasa and Brian D. Sutton, A backward stable algorithm for computing the CS decomposition via the polar decomposition. SIAM Journal on Matrix Analysis and Applications, 39(3), 1448-1469, 2018.pdf
• Yuji Nakatsukasa and Lloyd N. Trefethen, Rational approximation of x^n, Proceedings of the American Mathematical Society, Vol. 146, Num. 12, pp. 5219--5224, 2018. pdf.
• Behnam Hashemi and Yuji Nakatsukasa, On the spectral problem for trivariate functions, BIT Numerical Mathematics, Vol. 58 (4), pp 981-1008, 2018. pdf
• Silviu-Ioan Filip, Yuji Nakatsukasa, Lloyd N. Trefethen, and Bernhard Beckermann, Rational minimax approximation via adaptive barycentric representations, SIAM Journal on Scientific Computing, , 40(4), A2427-A2455, 2018. pdf
• Shinji Ito and Yuji Nakatsukasa, Stable polefinding and rational least-squares via eigenvalues, pdf, Numerische Mathematik, Vol. 139 (3), pp 633-682, 2018.
• Zhening Li, Yuji Nakatsukasa, Tasuku Soma, and Andre Uschmajew, On orthogonal tensors and best rank-one approximation ratio, SIAM Journal on Matrix Analysis and Applications, 39(1), pp. 400-425, 2018. pdf
• Yuji Nakatsukasa, Olivier Sete and Lloyd N. Trefethen, The AAA algorithm for rational approximation, SIAM Journal on Scientific Computing, 40(3), A1494-A1522, 2018. pdf
• Yuji Nakatsukasa, Leo Taslaman, Francoise Tisseur and Ion Zaballa, Reduction of matrix polynomials to simpler forms, SIAM Journal on Matrix Analysis and Applications, Vol. 39-1, pp. 148-177, 2018. pdf
• Satoru Adachi and Yuji Nakatsukasa, Eigenvalue-based algorithm and analysis for nonconvex QCQP with one constraint, Mathematical Programming, , Vol. 173, pp. 79--116 (2019). pdf.
• Hadrien Montanelli and Yuji Nakatsukasa, Fourth-order time-stepping for stiff PDEs on the sphere, SIAM Journal on Scientific Computing, Vol. 40 (1), pp. A421--A451, 2018. pdf
• Yuji Nakatsukasa, Accuracy of singular vectors obtained by projection-based SVD methods, BIT Numerical Mathematics, Vol. 57 (4), pp. 1137-1152, 2017. pdf
• Satoru Adachi, Satoru Iwata, Yuji Nakatsukasa and Akiko Takeda, Solving the trust-region subproblem by a generalized eigenvalue problem, SIAM Journal on Optimization, Vol. 27 (1), pp. 269-291, 2017. pdf, MATLAB code
  
• Yuji Nakatsukasa, Vanni Noferini and Alex Townsend, Vector spaces of linearizations for matrix polynomials: A bivariate polynomial approach, SIAM Journal on Matrix Analysis and Applications. Vol 38-1, pp. 1-29, 2017.pdf
• Yuji Nakatsukasa, Tasuku Soma and Andre Uschmajew, Finding a low-rank basis in a matrix subspace, Mathematical Programming, Vol. 162(1), pp. 325-361, 2017. pdf
• Shinsaku Sakaue, Yuji Nakatsukasa, Akiko Takeda and Satoru Iwata, Solving generalized CDT problems via two-parameter eigenvalues, SIAM Journal on Optimization, Vol 26-3, pp. 1669-1694, 2016. pdf
  
• Yuji Nakatsukasa and Roland W. Freund, Computing Fundamental Matrix Decompositions Accurately via the Matrix Sign Function in Two Iterations: The Power of Zolotarev's Functions, SIAM Review, Vol 58(3), pp. 461-493, 2016. pdf MATLAB codes
  
• Yuji Nakatsukasa and Vanni Noferini, On the stability of computing polynomial roots via confederate linearizations, , Mathematics of Computation, Vol 85, pp.2391-2425, 2016. pdf
• Stefan Guettel and Yuji Nakatsukasa, Scaled and squared subdiagonal Pade approximation for the matrix exponential, SIAM Journal on Matrix Analysis and Applications, Vol. 37(1), pp. 145-170, 2016. pdf MATLAB codes
• Satoru Iwata, Yuji Nakatsukasa and Akiko Takeda, Computing the signed distance between overlapping ellipsoids, SIAM Journal on Optimization, Vol. 25(4), pp. 2359-2384, 2015. pdf (with corrections)
• Yusaku Yamamoto, Yuji Nakatsukasa, Yuka Yanagisawa and Takeshi Fukaya, Roundoff Error Analysis of the CholeskyQR2 Algorithm, Electronic Transactions on Numerical Analysis, Vol. 44, pp. 306-326, 2015. pdf
• Yuji Nakatsukasa, Vanni Noferini and Alex Townsend, Computing the common zeros of two bivariate functions via Bezout resultants, Numerische Mathematik, Vol. 129, pp. 181-209, 2015. pdf MATLAB code
• Patrizio Neff, Yuji Nakatsukasa and Andreas Fischle, A logarithmic minimization property of the unitary polar factor in the spectral and Frobenius norms, SIAM Journal on Matrix Analysis and Applications, Vol. 35(3), pp. 1132-1154, 2014. pdf
• Johannes Lankeit, Patrizio Neff and Yuji Nakatsukasa, The minimization of matrix logarithms - on a fundamental property of the unitary polar factor, Linear Algebra and its Applications, Vol. 449, pp. 28-42, 2014. pdf
• Fernando de Teran, Ross Lippert, Yuji Nakatsukasa and Vanni Noferini, Flanders' theorem for many matrices under commutativity assumptions, Linear Algebra and its Applications, Vol. 443, pp. 120-138, 2014. pdf
• Yuji Nakatsukasa and Nicholas J. Higham, Stable and efficient spectral divide and conquer algorithms for the symmetric eigenvalue decomposition and the SVD, SIAM Journal on Scientific Computing, Vol. 35(3), pp. A1325-A1349, 2013. pdf. Codes available at MATLAB Central File Exchange
• Yuji Nakatsukasa, Naoki Saito and Ernest Woei, Mysteries around the graph Laplacian eigenvalue 4, Linear Algebra and its Applications, Vol. 438 (8), pp. 3231-3246, 2013. pdf
• Yuji Nakatsukasa and Nicholas J. Higham, Backward stability of iterations for computing the polar decomposition, SIAM Journal on Matrix Analysis and Applications, Vol. 33, No. 2, pp. 460-479, 2012. pdf
• Ren-Cang Li, Yuji Nakatsukasa, Ninoslav Truhar and Wei-guo Wang, Perturbation of multiple eigenvalues of Hermitian matrices, Linear Algebra and its Applications, Vol. 437, pp. 202-213, 2012. pdf
• Yuji Nakatsukasa, On the condition numbers of a multiple eigenvalue of a generalized eigenvalue problem, Numerische Mathematik, Vol. 121, No. 3, pp. 531-544, 2012. pdf
• Yuji Nakatsukasa, Kensuke Aishima and Ichitaro Yamazaki, dqds with aggressive early deflation, SIAM Journal on Matrix Analysis and Applications, Vol. 33, No. 1, pp. 22-51, 2012. Fortran Code pdf
• Yuji Nakatsukasa, Eigenvalue perturbation bounds for Hermitian block tridiagonal matrices, Applied Numerical Mathematics, Vol.62, No. 1, pp. 67-78, 2012. pdf
• Yuji Nakatsukasa, The tan theta theorem with relaxed conditions, Linear Algebra and its Applications, Vol. 436, pp. 1528-1534, 2012. pdf
• Ren-Cang Li, Yuji Nakatsukasa, Ninoslav Truhar and Shufang Xu, Perturbation of partitioned Hermitian definite generalized eigenvalue problems, SIAM Journal on Matrix Analysis and Applications, Vol.32, No.2, pp. 642-663, 2011. pdf Erratum
• Yuji Nakatsukasa, Gerschgorin's theorem for generalized eigenvalue problems in the Euclidean metric, Mathematics of Computation, Vol.80, pp. 2127-2142, 2011. pdf
• Yuji Nakatsukasa, Zhaojun Bai and Francois Gygi, Optimizing Halley's iteration for computing the matrix polar decomposition, SIAM Journal on Matrix Analysis and Applications, Vol.31, No.5, pp. 2700-2720, 2010. pdf
• Yuji Nakatsukasa, Perturbation behavior of a multiple eigenvalue in generalized Hermitian eigenvalue problems, BIT Numerical Mathematics, Vol. 50, No. 1, pp. 109-121, 2010. pdf

• Yuji Nakatsukasa, Absolute and relative Weyl theorems for generalized eigenvalue problems, Linear Algebra and its Applications, Vol. 432, No. 1, pp. 242-248, 2010. pdf

conference proceedings

• Nicolas Boulle, Yuji Nakatsukasa and Alex Townsend Rational neural networks, NeurIPS 2020: Neural Information Processing Systems, pdf.
• Takeshi Fukaya, Ramaseshan Kannan, Yuji Nakatsukasa, Yusaku Yamamoto, Yuka Yanagisawa, Performance evaluation of the shifted Cholesky QR algorithm for ill-conditioned matrices, Supercomputing SC18 poster.
• Yuji Nakatsukasa, Off-diagonal perturbation, first-order approximation and quadratic residual bounds for matrix eigenvalue problems, Lecture Notes in Computer Science, EPASA 2015, pp 233-249. pdf.
• Yusaku Yamamoto, Yuji Nakatsukasa, Yuka Yanagisawa and Takeshi Fukaya, Roundoff error analysis of the CholeskyQR2 algorithm in an oblique inner product, JSIAM Letters, Vol. 8, pp.5-8, 2016.
• Satoru Iwata, Yuji Nakatsukasa and Akiko Takeda, Global optimization methods for extended Fisher discriminant analysis, AISTATS 2014, pp. 411-419. link Related codes at MATLAB Central File Exchange
• Takeshi Fukaya, Yuji Nakatsukasa, Yuka Yanagisawa and Yusaku Yamamoto, CholeskyQR2: A Simple and communication-avoiding algorithm for computing a tall-skinny QR factorization on a large-scale parallel system, ScalA 2014, pp. 31-38. link

preprints

• Behnam Hashemi and Yuji Nakatsukasa, RTSMS: Randomized Tucker with single-mode sketching Preprint.
• Taejun Park and Yuji Nakatsukasa, Approximating Sparse Matrices and their Functions using Matrix-vector products, Preprint.
• Yijun Dong, Per-Gunnar Martinsson, and Yuji Nakatsukasa, Efficient Bounds and Estimates for Canonical Angles in Randomized Subspace Approximations, Preprint.
• Wenqi Zhu and Yuji Nakatsukasa, Convergence and Near-optimal Sampling for Multivariate Function Approximations in Irregular Domains via Vandermonde with Arnoldi, Preprint.
• Yuji Nakatsukasa and Vanni Noferini, Eigenvalue avoidance of structured matrices depending smoothly on a real parameter, Preprint.
• Robert A. Baston and Yuji Nakatsukasa, Stochastic diagonal estimation: probabilistic bounds and an improved algorithm , Preprint.
• Evan S. Gawlik and Yuji Nakatsukasa, Zolotarev's fifth and sixth problems, Preprint.
• Yuji Nakatsukasa, Fast and stable randomized low-rank matrix approximation, Preprint.
• Yuji Nakatsukasa, Approximate and integrate: Variance reduction in Monte Carlo integration via function approximation. Preprint.

thesis

awards

• Inaugural Frontiers of Science Award, International Congress of Basic Science, 2023. For AAA paper with Oliver Sete and Nick Trefethen.
• Householder award, 2014.
• 15th Leslie Fox prize, 2011.
• JSIAM spring meeting outstanding talk, March 2019.
• SIAM UKIE annual meeting best poster prize (second prize), January 2018.
• JSIAM annual meeting outstanding talks, September 2014.
• SIAM UKIE Best Student Talks, Biennial NA Meeting, July 2011.
• Yueh-Jing Lin Fund, UC Davis Department of Mathematics, June 2011.