- Polynomial eigenvalue problems
- Matrix decompositions (SVD, eigendecomposition)
- Eigenvalue perturbation theory, Gerschgorin's theorem
- Patrizio Neff, Yuji Nakatsukasa and Andreas Fischle, The unitary polar factor Q = Up minimizes ||Log(QZ)|| and ||sym Log(QZ)|| in the spectral norm in any dimension and the Frobenius matrix norm in three dimensions, preprint
- Alex Townsend, Vanni Noferini and Yuji Nakatsukasa, Vector spaces of linearizations for matrix polynomials: A bivariate polynomial approach, MIMS EPrint, Oxford Eprints
- Yuji Nakatsukasa and Nicholas J. Higham, Stable and efficient spectral divide and conquer algorithms for the symmetric eigenvalue decomposition and the SVD, MIMS EPrint 2012.52; Codes available at MATLAB Central File Exchange, SIAM Journal on Scientific Computing, to appear.
- 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.
- 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.
- 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.
- 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.
- 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
- Yuji Nakatsukasa, Eigenvalue perturbation bounds for Hermitian block tridiagonal matrices, Applied Numerical Mathematics, Vol.62, No. 1, pp. 67-78, 2012.
- Yuji Nakatsukasa, The tan theta theorem with relaxed conditions, Linear Algebra and its Applications, Vol. 436, pp. 1528-1534, 2012.
- 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.
- Yuji Nakatsukasa, Gerschgorin's theorem for generalized eigenvalue problems in the Euclidean metric, Mathematics of Computation, Vol.80, pp. 2127-2142, 2011.
- 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.
- 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.
- 15th Leslie Fox prize, 2011.
- SIAM UKIE Best Student Talks, Biennial NA Meeting, July 2011.
- Yueh-Jing Lin Fund, UC Davis Department of Mathematics, June 2011.