Zobrazeno 1 - 10
of 25
pro vyhledávání: '"YUJI NAKATSUKASA"'
Publikováno v:
Mathematical Programming. 193:447-483
We present an algorithm for the minimization of a nonconvex quadratic function subject to linear inequality constraints and a two-sided bound on the 2-norm of its solution. The algorithm minimizes the objective using an active-set method by solving a
Autor:
Yuji Nakatsukasa, Alex Townsend
Publikováno v:
SIAM Journal on Numerical Analysis. 59:314-333
An important observation in compressed sensing is that the $\ell_0$ minimizer of an underdetermined linear system is equal to the $\ell_1$ minimizer when there exists a sparse solution vector and a certain restricted isometry property holds. Here, we
Autor:
Yuji Nakatsukasa, Evan S. Gawlik
A landmark result from rational approximation theory states that x 1 ∕ p on [ 0 , 1 ] can be approximated by a type- ( n , n ) rational function with root-exponential accuracy. Motivated by the recursive optimality property of Zolotarev functions (
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::642c87ac7c39e9807a1888739ffe108d
https://doi.org/10.1016/j.jat.2021.105577
https://doi.org/10.1016/j.jat.2021.105577
Publikováno v:
KAUST Repository
We present a high-performance implementation of the Polar Decomposition (PD) on distributed-memory systems. Building upon on the QR-based Dynamically Weighted Halley (QDWH) algorithm, the key idea lies in finding the best rational approximation for t
Publikováno v:
Numerische Mathematik
Rational approximations of functions with singularities can converge at a root-exponential rate if the poles are exponentially clustered. We begin by reviewing this effect in minimax, least-squares, and AAA approximations on intervals and complex dom
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::8c66e0aaf14e7ed256631b6ac981171a
http://arxiv.org/abs/2007.11828
http://arxiv.org/abs/2007.11828
Autor:
Yuji Nakatsukasa, Roland W. Freund
Publikováno v:
Nakatsukasa, Y; & Freund, RW. (2016). Computing fundamental matrix decompositions accurately via the matrix sign function in two iterations: The power of Zolotarev's functions. SIAM Review, 58(3), 461-493. doi: 10.1137/140990334. UC Davis: Department of Mathematics. Retrieved from: http://www.escholarship.org/uc/item/5qs3v0rs
SIAM Review, vol 58, iss 3
SIAM Review, vol 58, iss 3
© 2016 Society for Industrial and Applied Mathematics. The symmetric eigenvalue decomposition and the singular value decomposition (SVD) are fundamental matrix decompositions with many applications. Conventional algorithms for computing these decomp
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::336f943ed5d046b4259079b03d4509a5
https://ora.ox.ac.uk/objects/uuid:a67ef52e-2417-4cdf-8370-d4a04e1da61f
https://ora.ox.ac.uk/objects/uuid:a67ef52e-2417-4cdf-8370-d4a04e1da61f
Publikováno v:
SIAM Journal on Scientific Computing. 40:A1494-A1522
We introduce a new algorithm for approximation by rational functions on a real or complex set of points, implementable in 40 lines of Matlab and requiring no user input parameters. Even on a disk or interval the algorithm may outperform existing meth
Publikováno v:
Li, Z, Nakatsukasa, Y, Soma, T & Uschmajew, A 2018, ' On orthogonal tensors and best rank-one approximation ratio ', SIAM Journal on Matrix Analysis and Applications, vol. 39, no. 1, pp. 400-425 . https://doi.org/10.1137/17M1144349
As is well known, the smallest possible ratio between the spectral norm and the Frobenius norm of an m × n matrix with m ≤ n is 1/√m and is (up to scalar scaling) attained only by matrices having pairwise orthonormal rows. In the present paper,
Publikováno v:
SIAM Journal on Scientific Computing
SIAM Journal on Scientific Computing, Society for Industrial and Applied Mathematics, In press, 40 (4), pp.A2427-A2455
SIAM Journal on Scientific Computing, In press, 40 (4), pp.A2427-A2455
SIAM Journal on Scientific Computing, Society for Industrial and Applied Mathematics, In press, 40 (4), pp.A2427-A2455
SIAM Journal on Scientific Computing, In press, 40 (4), pp.A2427-A2455
Computing rational minimax approximations can be very challenging when there are singularities on or near the interval of approximation - precisely the case where rational functions outperform polynomials by a landslide. We show that far more robust
We revisit the landmark paper [D. S. Mackey, N. Mackey, C. Mehl, and V. Mehrmann, SIAM J. Matrix Anal. Appl., 28 (2006), pp.~971--1004] and, by viewing matrices as coefficients for bivariate polynomials, we provide concise proofs for key properties o
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::a90e80c6909f46ffa7d8ba9aaeed4c09
https://doi.org/10.1137/15m1013286
https://doi.org/10.1137/15m1013286