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pro vyhledávání: '"YUJI NAKATSUKASA"'
Publikováno v:
Linear Algebra and its Applications. 594:177-192
When a projection of a symmetric or Hermitian matrix to the positive semidefinite cone is computed approximately (or to working precision on a computer), a natural question is to quantify its accuracy. A straightforward bound invoking standard eigenv
Autor:
Vanni Noferini, Yuji Nakatsukasa
Sylvester's law of inertia states that the number of positive, negative and zero eigenvalues of Hermitian matrices is preserved under congruence transformations. The same is true of generalized Hermitian definite eigenvalue problems, in which the two
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::74277c576a0d8c6982cf44f1e37e0fe2
Autor:
Yuji Nakatsukasa
Publikováno v:
Applied Numerical Mathematics. 62:67-78
We derive new perturbation bounds for eigenvalues of Hermitian matrices with block tridiagonal structure. The main message of this paper is that an eigenvalue is insensitive to blockwise perturbation, if it is well-separated from the spectrum of the
Autor:
Yuji Nakatsukasa
Publikováno v:
Numerische Mathematik. 121:531-544
For standard eigenvalue problems, closed-form expressions for the condition numbers of a multiple eigenvalue are known. In particular, they are uniformly 1 in the Hermitian case and generally take different values in the non-Hermitian case. We consid
The unitary polar factor $Q=U_p$ in the polar decomposition of $Z=U_p \, H$ is the minimizer over unitary matrices $Q$ for both $\|{\rm Log}(Q^* Z)\|^2$ and its Hermitian part $\|{{\rm sym}{_{_*}}\!}({\rm Log}(Q^* Z))\|^2$ over both $\mathbb{R}$ and
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::ce0d8a0be6c0272850514d3367e11271
Autor:
Yuji Nakatsukasa
Publikováno v:
Nakatsukasa, Yuji. (2010). Perturbation behavior of a multiple eigenvalue in generalized Hermitian eigenvalue problems. BIT Numerical Mathematics, 50(1), pp 109-121. doi: 10.1007/s10543-010-0254-8. Retrieved from: http://www.escholarship.org/uc/item/8bg251c9
We show that a multiple eigenvalue has different sensitivities under perturbations in a generalized Hermitian eigenvalue problem. Our result provides a solution to a question raised by Stewart and Sun. We also show how this difference of sensitivitie
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::df9c3f21d5877de4b9f81177573ab4cb
http://www.escholarship.org/uc/item/8bg251c9
http://www.escholarship.org/uc/item/8bg251c9
Publikováno v:
SIAM Journal on Matrix Analysis and Applications. 34:280-281
The main purpose of this erratum is to correct mistakes in the proof of Theorem 2.4 of [R.-C. Li et al., SIAM J. Matrix Anal. Appl., 32 (2011), pp. 642--663] and in the inequalities (2.23), (2.24), and (2.25) on p. 653 of the same paper.
Autor:
Yuji Nakatsukasa
Publikováno v:
Linear Algebra and its Applications. (5):1528-1534
The Davis–Kahan tan θ theorem bounds the tangent of the angles between an approximate and an exact invariant subspace of a Hermitian matrix. When applicable, it gives a sharper bound than the sin θ theorem. However, the tan θ theorem requires mo
Autor:
Yuji Nakatsukasa
Publikováno v:
Linear Algebra and its Applications. (1):242-248
Weyl-type eigenvalue perturbation theories are derived for Hermitian definite pencils A - λ B , in which B is positive definite. The results provide a one-to-one correspondence between the original and perturbed eigenvalues, and give a uniform pertu