Research interestsI am generally interested in matrix eigenvalues and rational approximation theory, and their applications.
- Algorithms for matrix decompositions (SVD, eigenvalue decomposition)
- Rational and polynomial approximation theory
- Eigenvalue perturbation theory, matrix analysis
- Numerical integration (quadrature/cubature, Monte Carlo)
- Numerical optimization
- Spectral methods
- Yuji Nakatsukasa and Lloyd N. Trefethen, Rational approximation of x^n, to appear in Proceedings of the American Mathematical Society, pdf.
- Behnam Hashemi and Yuji Nakatsukasa, On the spectral problem for trivariate functions, to appear in BIT Numerical Mathematics, Preprint.
- Silviu-Ioan Filip, Yuji Nakatsukasa, Lloyd N. Trefethen, and Bernhard Beckermann, Rational minimax approximation via adaptive barycentric representations, to appear in SIAM Journal on Scientific Computing, Preprint.
- Shinji Ito and Yuji Nakatsukasa, Stable polefinding and rational least-squares via eigenvalues, to appear in Numerische Mathematik, pdf.
- Zhening Li, Yuji Nakatsukasa, Tasuku Soma, and André 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, to appear in SIAM Journal on Scientific Computing, pdf.
- Yuji Nakatsukasa, Leo Taslaman, Francoise Tisseur and Ion Zaballa, Reduction of matrix polynomials to simpler forms, pdf, SIAM Journal on Matrix Analysis and Applications, Vol. 39-1, pp. 148-177, 2018.
- Satoru Adachi and Yuji Nakatsukasa, Eigenvalue-based algorithm and analysis for nonconvex QCQP with one constraint, to appear in Mathematical Programming, 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, pdf, BIT Numerical Mathematics, Vol. 57 (4), pp. 1137-1152, 2017.
- 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.
- Yuji Nakatsukasa, Vanni Noferini and Alex Townsend, Vector spaces of linearizations for matrix polynomials: A bivariate polynomial approach, MIMS EPrint, SIAM Journal on Matrix Analysis and Applications. Vol 38-1, pp. 1-29, 2017.
- Yuji Nakatsukasa, Tasuku Soma and André Uschmajew, Finding a low-rank basis in a matrix subspace, Preprint, Mathematical Programming, Vol. 162(1), pp. 325-361, 2017.
- 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.
- 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,
pdf, SIAM Review, Vol 58(3),
pp. 461-493, 2016.
- Yuji Nakatsukasa and Vanni Noferini, On the stability of computing polynomial roots via confederate linearizations, pdf, Mathematics of Computation, Vol 85, pp.2391-2425, 2016.
- Stefan Guettel and Yuji Nakatsukasa, Scaled and squared subdiagonal Pade approximation for the matrix exponential, pdf, SIAM Journal on Matrix Analysis and Applications, Vol. 37(1), pp. 145-170, 2016. 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, pdf, Electronic Transactions on Numerical Analysis, Vol. 44, pp. 306-326, 2015.
- 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.
- 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
- Yuji Nakatsukasa, Off-diagonal perturbation, first-order approximation and quadratic residual bounds for matrix eigenvalue problems, to appear in Lecture Notes in Computer Science, EPASA proceedings, Preprint.
- 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
- Yuji Nakatsukasa, Approximate and integrate: Variance reduction in Monte Carlo integration via function approximation. Preprint.
- Evan S. Gawlik, Yuji Nakatsukasa and Brian D. Sutton, A backward stable algorithm for computing the CS decomposition via the polar decomposition. Preprint.
- Hatem Ltaief, Dalal E. Sukkari, Aniello Esposito, Yuji Nakatsukasa and David E. Keyes, Massively Parallel Polar Decomposition on Distributed-Memory Systems, Preprint.
- Yuji Nakatsukasa and Vanni Noferini, Inertia laws and localization of real eigenvalues for generalized indefinite eigenvalue problems, Preprint.
thesisAlgorithms and Perturbation Theory for Matrix Eigenvalue Problems and the Singular Value Decomposition, PhD dissertation, University of California at Davis, 2011. pdf
- Householder award, 2014.
- 15th Leslie Fox prize, 2011.
- 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.